An EOQ model is constructed for deteriorating items with time dependent quadratic demand rate. It is assumed that the deterioration rate is constant and the supplier offers his retailer the credit period to settle the account of the procurement units. To solve the model it is further assumed that shortages are not allowed and the replenishment rate is instantaneous. We have presented the models under two different scenarios, viz., (i)the offered credit period is less than or equal to the cycle time and (ii) the offered credit period by the supplier to the retailer for settling the account is greater than cycle time. The objective is to minimize the retailers total inventory cost. Salvage value is also taken to see its effect on the total cost. A numerical example is given to study the effect of allowable credit period and the total cost of the retailer.
A Deterministic Inventory Model for Perishable Items with Price Sensitive Qua...IJMERJOURNAL
ABSTRACT: An inventory system is considered with trended demand which is assumed to be a function of price and time dependent quadratic demand. For minimizing the total cost of the inventory system, it is assumed that the deterioration rate is constant and the supplier offers the retailer a credit period to settle the account of the procurement units. To solve the model it is further assumed that shortages are not allowed. Salvage value is also considered and observed its effect on the total cost. A numerical example is given to test the strength of the model. Critical parameters are identified by studying the sensitivity of the system.
Order Size Dependent Trade Credit Study in a Three Echelon Supply Chain ModelEditor IJCATR
In present study, we generalize order linked trade credit policy in three echelon supply chain system where manufacturer,
distributor and retailer are involved and manufacturer provide a delay period to distributor and distributor also provide a order linked
trade credit policy to his retailers. Whole study is discussed in time dependent production and demand rate. We model a three echelon
supply chain system as cost minimization to determine the system’s optimal cycle time. In this paper, we determine the optimal cycle
time, optimal order quantity and optimal payment time. Finally numerical examples are given to illustrate the result and the managerial
insights are also obtained
EOQ Inventory Models for Deteriorating Item with Weibull Deterioration and Ti...ijceronline
This paper develops an EOQ inventory model for deterioratingitemswith two parameters Weibull deterioration. Shortages are permissible andpartially backlogged. In this model we consider time varying quadratic holding cost and ramp-type demand. The model is developed under two different replenishment policies: (i) Starting with no shortages (ii) Starting with shortages.The aim of this study is to find the optimal solutiontominimizing the total inventory costs for both the above mentioned strategies. To elevate the model a numerical example has been carried out and a sensitivity analysis occurred to study the result of parameters on essential variables and the entire cost of this model.
In paper (2004) Chang studied an inventory model under a situation in which the supplier provides the purchaser with a permissible delay of payments if the purchaser orders a large quantity. Tripathi (2011) also studied an inventory model with time dependent demand rate under which the supplier provides the purchaser with a permissible delay in payments. This paper is motivated by Chang (2004) and Tripathi (2011) paper extending their model for exponential time dependent demand rate. This study develops an inventory model under which the vendor provides the purchaser with a credit period; if the purchaser orders large quantity. In this chapter, demand rate is taken as exponential time dependent. Shortages are not allowed and effect of the inflation rate has been discussed. We establish an inventory model for deteriorating items if the order quantity is greater than or equal to a predetermined quantity. We then obtain optimal solution for finding optimal order quantity, optimal cycle time and optimal total relevant cost. Numerical examples are given for all different cases. Sensitivity of the variation of different parameters on the optimal solution is also discussed. Mathematica 7 software is used for finding numerical examples.
International Journal of Research in Engineering and Science is an open access peer-reviewed international forum for scientists involved in research to publish quality and refereed papers. Papers reporting original research or experimentally proved review work are welcome. Papers for publication are selected through peer review to ensure originality, relevance, and readability.
A Retail Category Inventory Management Model Integrating Entropic Order Quant...Waqas Tariq
A retail category inventory management model that considers the interplay of entropic product assortment and trade credit financing is presented. Specifically, the proposed model takes into consideration of key factors like discounted cash flow. Therefore, to incorporate the concept of supplier-retailer integration and order size dependent trade credit, we established a stylized model to determine the optimal strategy for an integrated supplier-retailer inventory system under the condition of trade credit financing and is entropy type demand. This paper demonstrates that the optimal solution is flexible enough to accommodate the supplier retail relationship under a perfect trade credit understanding without significantly deviating from the main goal at increasing sales revenue of supplier and retailer. Finally numerical examples are used to illustrate the theoretical results followed by the insights into a lot of managerial inputs.
A Deterministic Inventory Model for Perishable Items with Price Sensitive Qua...IJMERJOURNAL
ABSTRACT: An inventory system is considered with trended demand which is assumed to be a function of price and time dependent quadratic demand. For minimizing the total cost of the inventory system, it is assumed that the deterioration rate is constant and the supplier offers the retailer a credit period to settle the account of the procurement units. To solve the model it is further assumed that shortages are not allowed. Salvage value is also considered and observed its effect on the total cost. A numerical example is given to test the strength of the model. Critical parameters are identified by studying the sensitivity of the system.
Order Size Dependent Trade Credit Study in a Three Echelon Supply Chain ModelEditor IJCATR
In present study, we generalize order linked trade credit policy in three echelon supply chain system where manufacturer,
distributor and retailer are involved and manufacturer provide a delay period to distributor and distributor also provide a order linked
trade credit policy to his retailers. Whole study is discussed in time dependent production and demand rate. We model a three echelon
supply chain system as cost minimization to determine the system’s optimal cycle time. In this paper, we determine the optimal cycle
time, optimal order quantity and optimal payment time. Finally numerical examples are given to illustrate the result and the managerial
insights are also obtained
EOQ Inventory Models for Deteriorating Item with Weibull Deterioration and Ti...ijceronline
This paper develops an EOQ inventory model for deterioratingitemswith two parameters Weibull deterioration. Shortages are permissible andpartially backlogged. In this model we consider time varying quadratic holding cost and ramp-type demand. The model is developed under two different replenishment policies: (i) Starting with no shortages (ii) Starting with shortages.The aim of this study is to find the optimal solutiontominimizing the total inventory costs for both the above mentioned strategies. To elevate the model a numerical example has been carried out and a sensitivity analysis occurred to study the result of parameters on essential variables and the entire cost of this model.
In paper (2004) Chang studied an inventory model under a situation in which the supplier provides the purchaser with a permissible delay of payments if the purchaser orders a large quantity. Tripathi (2011) also studied an inventory model with time dependent demand rate under which the supplier provides the purchaser with a permissible delay in payments. This paper is motivated by Chang (2004) and Tripathi (2011) paper extending their model for exponential time dependent demand rate. This study develops an inventory model under which the vendor provides the purchaser with a credit period; if the purchaser orders large quantity. In this chapter, demand rate is taken as exponential time dependent. Shortages are not allowed and effect of the inflation rate has been discussed. We establish an inventory model for deteriorating items if the order quantity is greater than or equal to a predetermined quantity. We then obtain optimal solution for finding optimal order quantity, optimal cycle time and optimal total relevant cost. Numerical examples are given for all different cases. Sensitivity of the variation of different parameters on the optimal solution is also discussed. Mathematica 7 software is used for finding numerical examples.
International Journal of Research in Engineering and Science is an open access peer-reviewed international forum for scientists involved in research to publish quality and refereed papers. Papers reporting original research or experimentally proved review work are welcome. Papers for publication are selected through peer review to ensure originality, relevance, and readability.
A Retail Category Inventory Management Model Integrating Entropic Order Quant...Waqas Tariq
A retail category inventory management model that considers the interplay of entropic product assortment and trade credit financing is presented. Specifically, the proposed model takes into consideration of key factors like discounted cash flow. Therefore, to incorporate the concept of supplier-retailer integration and order size dependent trade credit, we established a stylized model to determine the optimal strategy for an integrated supplier-retailer inventory system under the condition of trade credit financing and is entropy type demand. This paper demonstrates that the optimal solution is flexible enough to accommodate the supplier retail relationship under a perfect trade credit understanding without significantly deviating from the main goal at increasing sales revenue of supplier and retailer. Finally numerical examples are used to illustrate the theoretical results followed by the insights into a lot of managerial inputs.
Predicting e-Customer behavior in B2C Relationships for CLV modelWaqas Tariq
E-Commerce sales have demonstrated an amazing growth in the last few years. And it is thus clear that the web is becoming an increasingly important channel and companies should strive for a successful web site. In this completion knowing e-customer and predicting his behavior is very important. In this paper we describe e-customer behavior in B2C relationships and then according to this behavior a new model for evaluating e-customer in B2C e-commerce relationships will be described. The most important thing in our e-CLV (Electronic Customer Lifetime Value) model is considering market\'s risks that are affecting customer cash flow in future. A lot of CLV models are based on simple NPV (simple net present value). However simple NPV can assess a good value for CLV, but simple NPV ignores two important aspects of B2C e-relationship which are market risks and big amount of customer data in e-commerce context. Therefore, simple NPV isn\'t enough for assessing e-CLV in high risk B2C markets. Instead of NPV, real option analyses could lead us to a better estimation for future cash flow of customers. With real option analyses, we predict all the future states with probability of each of them. And then calculate the more accurate of future customer cash flow. In this paper after a brief history of CLV, we explain customer behavior in B2C markets especially for e-retailers. Then with using real option analyses, we introduce our CLV model. Two extended examples explain our model and introduce the steps in finding CLV of customer in a B2C relationship.
Coordination in Three-Level Supply Chain under Output and Demand Uncertaintyinventionjournals
Purpose: The purpose of this research is to designing a contract that can coordinate three -level supply chain with output and demand uncertainty. Design/methodology/approach: This paper focuses on three-level supply chain with a supplier, a manufacturer and a retailer. If the supplier and the manufacturer’s production is subject to random yield and the retailer faces uncertain demand, the existence of supply chain demonstrates doubled marginalizing lead to analyses of supply chain coordination and buyback contract. Findings: Although buyback contract cannot coordinate the three – level supply chain, it can improve the performance of supply chain. Therefore, we design the buyback-cost sharing contract from the perspective of risk sharing to coordination supply chain, and the profits of all members of the supply chain have been improved by Pareto. The numerical examples further to research the effects of demand and output uncertainty on supply chain performance. Originality/value: Comprehensively comparing risk-sharing contract and buyback contract is only presented in the supply chain.
Counterfeit Resistant Framework for Single Machine Booking and Grouping in a ...IJERA Editor
This paper addresses a generation and outbound dissemination planning issue in which a few occupations must be prepared on a solitary machine for conveyance to clients or to different machines for further handling. We accept that there is an adequate number of vehicles. Likewise, it is expected that the conveyance cost is free of bunch size, yet it is reliant on every excursion. In this paper, we introduce an Artificial Immune System (AIS) for this issue. The goal is to limit the total of the aggregate weighted number of late employments and the cluster conveyance costs. A cluster setup time must be included before preparing the principal work in every group. Utilizing computational test, we contrast our technique and a current strategy for the specified iss ue in writing, specifically Simulated Annealing (SA). Computational tests demonstrate the huge change of the AIS over the SA.
Implementation of Wide Band Frequency Synthesizer Base on DFS (Digital Frequ...IJMER
Wide Band Frequency Synthesizer has become essential components in wireless communication
systems. They are used as frequency synthesizers with precise and convenient digital control in both traditional
electronics, such as televisions and AM/FM radios, and modern consumer products among which cellular
mobile phone is a striking example.
IC fabrication technology advances have made monolithic integration possible. More and more
electronic devices can be put on the same chip to reduce the number of external components and then the costs.
Therefore, on a single chip we can accomplish many functions for which we might need to make several chips
work together a few years ago. A monolithic wide-band PLL is of great interests to wireless communication
applications due to both its low cost and convenience to switch between different communication standards.
The focus of this work is to implement a wide-band Frequency Synthesizer using as few as possible building
blocks and also as simple as possible structure.
Numerical Investigation of Multilayer Fractal FSSIJMER
Numerical investigations are presented for a multilayer frequency selective surface with Koch
fractal (levels 1 and 2) conducting patch elements. The structure investigated is obtained using two FSS
screens separated by an air gap layer. For the proposed investigation were used three different values an
air gap height. The results obtained using the numerical method were compared with other technique and
using the commercial software Ansoft DesignerTM. A good agreement was observed in terms of the
bandwidth.
Fuzzy soft set is one of the recent topics developed for dealing with the uncertainties present
in most of our real life situations. The parameterization tool of soft set theory enhances the flexibility of
its application. In this paper, we have studied membership grade, power set,
-cut set , strong fuzzy
-
cut set ,some standard operation fuzzy soft set, degree of subset hood and proposed some results with
examples.
Design, Simulation and Implementation of Flyback based, True Single Stage, Is...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Reduction of Topology Control Using Cooperative Communications in ManetsIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Nanoscience and nanotechnology primarily deal with the synthesis, characterization,
exploration, and exploitation of nanostructures materials. These materials are characterized by at least
one dimension in the nanometer (1nm = 10−9 m) range. In this research project nano materials are
synthesized or deposited by sputtering process. Prior to this sputtering process, the desired specimen and
its pattern is prepared with one of the mask less lithographic techniques such as electron beam
lithography (EBL). In this process, EBL machine is used with 220 KV of power and it is used to write the
pattern with raster scan method. After co-deposition of Al2O3 and SiO2 with the help of sputtering then
finally characterization has taken place. In this characterization, Scanning electron microscope (SEM)
images are taken and then finally atomic force microscope (AFM) images are taken in order to know the
deflection error, adhesiveness, and DMT modulus
Experimental Investigations of Exhaust Emissions of four Stroke SI Engine by ...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
: The main objective of this paper is the systematic description of the current research and
development of small or miniature unmanned aerial vehicles and micro aerial vehicles, with a focus on
rotary wing vehicles. In recent times, unmanned/Micro aerial vehicles have been operated across the
world; they have also been the subject of considerable research. In particular, UAVs/MAVs with rotary
wings have been expected to perform various tasks such as monitoring at fixed points and surveillance
from the sky since they can perform not only perform static flights by hovering but also achieve vertical
takeoffs and landing. Helicopters have been used for personnel transport, carrying goods, spreading
information, and performing monitoring duties for long periods. A manned helicopter has to be used for
all these duties. On the other hand, unmanned helicopters that can be operated by radio control have
been developed as a hobby. Since unmanned helicopters are often superior to manned helicopters in
terms of cost and safety, in recent years, accomplishing tasks using unmanned helicopters has become
popular. Considerable expertise is required to operate unmanned helicopters by radio control, and
hence, vast labor resources are employed to train operators. Moreover, it is impossible to operate
unmanned helicopters outside visual areas because of lack of radio control, and the working area is
hence limited remarkably. For solving the above problems, it is necessary to realize autonomous
control of unmanned helicopters. However, no general method for designing the small unmanned
helicopters has been developed yet – today, various design techniques by different study groups using
different helicopters exist. In this paper the conceptual design process is explained.
Effect of Chemical Reaction and Radiation Absorption on Unsteady Convective H...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Predicting e-Customer behavior in B2C Relationships for CLV modelWaqas Tariq
E-Commerce sales have demonstrated an amazing growth in the last few years. And it is thus clear that the web is becoming an increasingly important channel and companies should strive for a successful web site. In this completion knowing e-customer and predicting his behavior is very important. In this paper we describe e-customer behavior in B2C relationships and then according to this behavior a new model for evaluating e-customer in B2C e-commerce relationships will be described. The most important thing in our e-CLV (Electronic Customer Lifetime Value) model is considering market\'s risks that are affecting customer cash flow in future. A lot of CLV models are based on simple NPV (simple net present value). However simple NPV can assess a good value for CLV, but simple NPV ignores two important aspects of B2C e-relationship which are market risks and big amount of customer data in e-commerce context. Therefore, simple NPV isn\'t enough for assessing e-CLV in high risk B2C markets. Instead of NPV, real option analyses could lead us to a better estimation for future cash flow of customers. With real option analyses, we predict all the future states with probability of each of them. And then calculate the more accurate of future customer cash flow. In this paper after a brief history of CLV, we explain customer behavior in B2C markets especially for e-retailers. Then with using real option analyses, we introduce our CLV model. Two extended examples explain our model and introduce the steps in finding CLV of customer in a B2C relationship.
Coordination in Three-Level Supply Chain under Output and Demand Uncertaintyinventionjournals
Purpose: The purpose of this research is to designing a contract that can coordinate three -level supply chain with output and demand uncertainty. Design/methodology/approach: This paper focuses on three-level supply chain with a supplier, a manufacturer and a retailer. If the supplier and the manufacturer’s production is subject to random yield and the retailer faces uncertain demand, the existence of supply chain demonstrates doubled marginalizing lead to analyses of supply chain coordination and buyback contract. Findings: Although buyback contract cannot coordinate the three – level supply chain, it can improve the performance of supply chain. Therefore, we design the buyback-cost sharing contract from the perspective of risk sharing to coordination supply chain, and the profits of all members of the supply chain have been improved by Pareto. The numerical examples further to research the effects of demand and output uncertainty on supply chain performance. Originality/value: Comprehensively comparing risk-sharing contract and buyback contract is only presented in the supply chain.
Counterfeit Resistant Framework for Single Machine Booking and Grouping in a ...IJERA Editor
This paper addresses a generation and outbound dissemination planning issue in which a few occupations must be prepared on a solitary machine for conveyance to clients or to different machines for further handling. We accept that there is an adequate number of vehicles. Likewise, it is expected that the conveyance cost is free of bunch size, yet it is reliant on every excursion. In this paper, we introduce an Artificial Immune System (AIS) for this issue. The goal is to limit the total of the aggregate weighted number of late employments and the cluster conveyance costs. A cluster setup time must be included before preparing the principal work in every group. Utilizing computational test, we contrast our technique and a current strategy for the specified iss ue in writing, specifically Simulated Annealing (SA). Computational tests demonstrate the huge change of the AIS over the SA.
Implementation of Wide Band Frequency Synthesizer Base on DFS (Digital Frequ...IJMER
Wide Band Frequency Synthesizer has become essential components in wireless communication
systems. They are used as frequency synthesizers with precise and convenient digital control in both traditional
electronics, such as televisions and AM/FM radios, and modern consumer products among which cellular
mobile phone is a striking example.
IC fabrication technology advances have made monolithic integration possible. More and more
electronic devices can be put on the same chip to reduce the number of external components and then the costs.
Therefore, on a single chip we can accomplish many functions for which we might need to make several chips
work together a few years ago. A monolithic wide-band PLL is of great interests to wireless communication
applications due to both its low cost and convenience to switch between different communication standards.
The focus of this work is to implement a wide-band Frequency Synthesizer using as few as possible building
blocks and also as simple as possible structure.
Numerical Investigation of Multilayer Fractal FSSIJMER
Numerical investigations are presented for a multilayer frequency selective surface with Koch
fractal (levels 1 and 2) conducting patch elements. The structure investigated is obtained using two FSS
screens separated by an air gap layer. For the proposed investigation were used three different values an
air gap height. The results obtained using the numerical method were compared with other technique and
using the commercial software Ansoft DesignerTM. A good agreement was observed in terms of the
bandwidth.
Fuzzy soft set is one of the recent topics developed for dealing with the uncertainties present
in most of our real life situations. The parameterization tool of soft set theory enhances the flexibility of
its application. In this paper, we have studied membership grade, power set,
-cut set , strong fuzzy
-
cut set ,some standard operation fuzzy soft set, degree of subset hood and proposed some results with
examples.
Design, Simulation and Implementation of Flyback based, True Single Stage, Is...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Reduction of Topology Control Using Cooperative Communications in ManetsIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Nanoscience and nanotechnology primarily deal with the synthesis, characterization,
exploration, and exploitation of nanostructures materials. These materials are characterized by at least
one dimension in the nanometer (1nm = 10−9 m) range. In this research project nano materials are
synthesized or deposited by sputtering process. Prior to this sputtering process, the desired specimen and
its pattern is prepared with one of the mask less lithographic techniques such as electron beam
lithography (EBL). In this process, EBL machine is used with 220 KV of power and it is used to write the
pattern with raster scan method. After co-deposition of Al2O3 and SiO2 with the help of sputtering then
finally characterization has taken place. In this characterization, Scanning electron microscope (SEM)
images are taken and then finally atomic force microscope (AFM) images are taken in order to know the
deflection error, adhesiveness, and DMT modulus
Experimental Investigations of Exhaust Emissions of four Stroke SI Engine by ...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
: The main objective of this paper is the systematic description of the current research and
development of small or miniature unmanned aerial vehicles and micro aerial vehicles, with a focus on
rotary wing vehicles. In recent times, unmanned/Micro aerial vehicles have been operated across the
world; they have also been the subject of considerable research. In particular, UAVs/MAVs with rotary
wings have been expected to perform various tasks such as monitoring at fixed points and surveillance
from the sky since they can perform not only perform static flights by hovering but also achieve vertical
takeoffs and landing. Helicopters have been used for personnel transport, carrying goods, spreading
information, and performing monitoring duties for long periods. A manned helicopter has to be used for
all these duties. On the other hand, unmanned helicopters that can be operated by radio control have
been developed as a hobby. Since unmanned helicopters are often superior to manned helicopters in
terms of cost and safety, in recent years, accomplishing tasks using unmanned helicopters has become
popular. Considerable expertise is required to operate unmanned helicopters by radio control, and
hence, vast labor resources are employed to train operators. Moreover, it is impossible to operate
unmanned helicopters outside visual areas because of lack of radio control, and the working area is
hence limited remarkably. For solving the above problems, it is necessary to realize autonomous
control of unmanned helicopters. However, no general method for designing the small unmanned
helicopters has been developed yet – today, various design techniques by different study groups using
different helicopters exist. In this paper the conceptual design process is explained.
Effect of Chemical Reaction and Radiation Absorption on Unsteady Convective H...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Study of Performance of Different Blends of Biodiesel Prepared From Waste Co...IJMER
The use of biodiesel is rapidly expanding around the world, making it imperative to fully
understand the impacts of biodiesel on the diesel engine combustion process and pollutant formation.
Biodiesel was made by the well-known transesterification process. Waste cottonseed oil was selected for
biodiesel production. Three different blends of biodiesel were prepared i.e. B10, B20 and B30. These three
blends were fuelled in a compression ignition (C.I.) engine. A maximum of 77% biodiesel was produced
with 20% methanol in presence of 0.5% sodium hydroxide. Different parameters for the optimization of
biodiesel production were investigated in the first phase of this study, while in the next phase of the study
performance test of a diesel engine with neat diesel fuel and biodiesel mixtures are to be carried out. The
performance characteristics like brake power (B.P.), brake specific fuel consumption (BSFC) and brake
thermal efficiency. This performance was then compared with that of petro diesel.
On ranges and null spaces of a special type of operator named 𝝀 − 𝒋𝒆𝒄𝒕𝒊𝒐𝒏. – ...IJMER
In this article, 𝜆 − 𝑗𝑒𝑐𝑡𝑖𝑜𝑛 has been introduced which is a generalization of trijection
operator as introduced in P.Chandra’s Ph. D. thesis titled “Investigation into the theory of operators
and linear spaces” (Patna University,1977). We obtain relation between ranges and null spaces of two
given 𝜆 − 𝑗𝑒𝑐𝑡𝑖𝑜𝑛𝑠 under suitable conditions
Mitigation of Fault in the Distribution System by using Flexible Distributed ...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Cross Spectral Density Analysis for Various Codes Suitable for Spread Spectru...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Analysis and Performance evaluation of Traditional and Hierarchal Sensor NetworkIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
INVENTORY MODEL FOR DETERIORATING ITEMS WITH QUADRATIC DEMAND, PARTIAL BACKLO...orajjournal
This article develops inventory model for deteriorating items with quadratic demand. Shortages are allowed. We study the partial delay in payments. The objective is to find the optimal cycle times that minimize the total cost. In this study first, we developed arithmetical model and procedure of finding the
most favorable solution is developed. Also the solution process is developed in order to minimize the total cost. The total costs are calculated by various principles. A solution process is developed to find the optimal solution and statistical examples are presented to demonstrate the result of the proposal model.
Compassion study of the most favorable solution with respect to the parameters of the system is carried out
and recommendations for further research are provided.
An Inventory Model with Variable Demand Rate for Deteriorating Items under Pe...Editor IJCATR
A continuous production control inventory model for deteriorating items with variable demand rate is developed. Demand
rate is the linear function of time. In this paper we have done all work in the environment of permissible delay of payments. A number
of structural properties of the inventory system are studied analytically. We have discussed the minimum total system cost under the
condition of permissible delay is relaxed to that at the end of the credit period, the retailer will make a partial payment on total
purchasing cost to the supplier and pay off the remaining balance by loan from the bank. Numerical examples are taken to illustrate the
procedure of finding the optimal total inventory cost and production cycle time. Sensitivity analysis is carried out to demonstrate the
effects of changing parameter values on the optimal solution of the system.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
An EOQ Model for Weibull Deteriorating Items With Price Dependent DemandIOSR Journals
In the present paper we developed an economic order quantity model for Weibull deteriorating items with price dependent demand rate together with a replenishment policy for profit maximization. The demand rate is a continuous and differentiable function of price. The variable items deteriorate with time shortages are allowed and completely back-ordered. Further it is illustrated with the help of numerical examples.
STRATEGIES OF DELAY DELIVERY AND CONTROLLABLE LEAD TIME IN SUPPLY CHAIN CONSI...IAEME Publication
This paper describes about two strategies in consignment inventory based supply
chain with controllable lead time and delaying last delivery comprising a two level
supply chain involving single vendor and multi buyers. This model would give
minimum joint total expected cost of the strategies involving vendor and buyer,
simultaneously to optimize quantitative decision variables. Numerical examples are
presented to demonstrate the benefit of the proposed strategies and the effect of
changes on the cost and parameters are studied.
Impact of Variable Ordering Cost and Promotional Effort Cost in Deteriorated ...IJAEMSJORNAL
The instantaneous economic order quantity (EOQ) profit optimization model for deteriorating items is introduced for analyzing the impact of variable ordering cost and promotional effort cost for leveraging profit margins in finite planning horizons. The objective of this model is to maximize the net profit so as to determine the order quantity and promotional effort factor. For any given number of replenishment cycles the existence of a unique optimal replenishment schedule are proved and further the concavity of the net profit function of the inventory system in the number of replenishments is established. The numerical analysis shows that an appropriate policy can benefit the retailer, especially for deteriorating items. Finally, sensitivity analyses with respect to the major parameters are also studied to draw managerial decisions in production systems.
In this paper, we have developed the multi-item inventory model in the fuzzy environment. Here we considered the demand rate is constant and production cost is dependent on the demand rate. Set-up- cost is dependent on average inventory level as well as demand. Lead time crashing cost is considered the continuous function of leading time. Limitation is considered on storage of space. Due to uncertainty all cost parameters of the proposed model are taken as generalized trapezoidal fuzzy numbers. Therefore this model is very real. The formulated multi objective inventory problem has been solved by various techniques like as Geometric Programming (GP) approach, Fuzzy Programming Technique with Hyperbolic Membership Function (FPTHMF), Fuzzy Nonlinear Programming (FNLP) technique and Fuzzy Additive Goal Programming (FAGP) technique. An example is given to illustrate the model. Sensitivity analysis and graphical representation have been shown to test the parameters of the model.
Optimal Pricing Policy for a Manufacturing Inventory Model with Two Productio...IJERDJOURNAL
ABSTRACT: When a new product is launched, a manufacturer applies the strategy of offering a quantity incentive initially for some time to boost up the demand of the product. The present paper describes a manufacturing inventory model with price sensitive demand enhanced by a quantity incentive. Later on demand becomes time increasing also. Inventory cycle starts with low production rate which is followed by higher production rate when demand is boosted up. Shortages are not allowed in this model. Presentation of numerical examples, tables, graphs and sensitivity analysis describes the model very well. Lastly case without incentive illustrates that usually the quantity incentive offered initially is beneficial.
CONSIGNMENT INVENTORY SIMULATION MODEL FOR SINGLE VENDOR- MULTI BUYERSIAEME Publication
The focus on the studies of supply chain management has been increasing in
recent years among academics as well as practitioners. In this paper, we present an
extendable multi agent supply chain simulation model for consignment stock inventory
model for a single vendor - multiple buyers. The simulation study dealt the
quantitative measures of performance of consignment stock model with respect to
number of shipments, delay deliveries, number of shipments shifted due to partial
information sharing, average inventory levels of buyer and vendor and joint total
economic cost (JTEC) as key performance parameters. Flexsim V3.0 a discrete event
simulation software is used for simulating the model
CONSIGNMENT INVENTORY SIMULATION MODEL FOR SINGLE VENDOR-MULTI BUYERS IN A SU...IAEME Publication
The focus on the studies of supply chain management has been increasing in
recent years among academics as well as practitioners. In this paper, we present an
extendable multi agent supply chain simulation model for consignment stock inventory
model for a single vendor - multiple buyers. The simulation study dealt the
quantitative measures of performance of consignment stock model with respect to
number of shipments, delay deliveries, number of shipments shifted due to partial
information sharing, average inventory levels of buyer and vendor and joint total
economic cost (JTEC) as key performance parameters. Flexsim V3.0 a discrete event
simulation software is used for simulating the model.
CONSIGNMENT INVENTORY SIMULATION MODEL FOR SINGLE VENDOR-MULTI BUYERS IN A SU...IAEME Publication
The focus on the studies of supply chain management has been increasing in
recent years among academics as well as practitioners. In this paper, we present an
extendable multi agent supply chain simulation model for consignment stock inventory
model for a single vendor - multiple buyers. The simulation study dealt the
quantitative measures of performance of consignment stock model with respect to
number of shipments, delay deliveries, number of shipments shifted due to partial
information sharing, average inventory levels of buyer and vendor and joint total
economic cost (JTEC) as key performance parameters. Flexsim V3.0 a discrete event
simulation software is used for simulating the model.
Inventory Models Involving Lead Time Crashing Cost as an Exponential Functionijmvsc
Inventory management and control is concerned with the acquisition and storage of materials required for
supporting various business operations. Lead time reduction is another important production activity in an
integrated inventory control. Lead time plays a vital role and has been a topic of interest for many authors
in inventory organization.
Lead time is a necessary aspect in any supply chain management and inventory management system. The
time gap between placing of an order and its actual arrival in the inventory is known as lead time. In most
of the literature dealing with inventory problems, either in deterministic or probabilistic model, lead time is
viewed as a prescribed constant or a stochastic variable, which therefore, is not subject to control. But, in
numerous sensible circumstances, lead time can he reduced by an additional crashing cost; in other words,
it is controllable, so in this article, we have considered the lead time crashing cost is an exponential
function of lead time. A solution procedure is developed to find the optimal solution.
In this article, both lead time and the order quantity are considered as the decision variables. The
behaviour of the model is presented graphically. The result is illustrated with the help of a numerical
example. Finally, Graphical representation is presented to illustrate the model. The solution procedure
with the help of the software Matlab 2008 is furnished to determine the optimal solution.
Fuzzy Inventory Model for Constantly Deteriorating Items with Power Demand an...iosrjce
IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A two-storage model for deteriorating items with holding cost under infla...INFOGAIN PUBLICATION
A deterministic inventory model has been developed for deteriorating items and Genetic Algorithms (GA) having a ramp type demands with the effects of inflation with two-storage facilities. The owned warehouse (OW) has a fixed capacity of W units; the rented warehouse (RW) has unlimited capacity. Here, we assumed that the inventory holding cost in RW is higher than those in OW. Shortages in inventory are allowed and partially backlogged and Genetic Algorithms (GA) it is assumed that the inventory deteriorates over time at a variable deterioration rate. The effect of inflation has also been considered for various costs associated with the inventory system and Genetic Algorithms (GA). Numerical example is also used to study the behaviour of the model. Cost minimization technique is used to get the expressions for total cost and other parameters.
A production - Inventory model with JIT setup cost incorporating inflation an...IJMER
A production inventory model with Just-In-Time (JIT) set-up cost has been developed in which inflation and time value of money are considered under an imperfect production process. The demand rate is considered to be a function of advertisement cost and selling price. Unit production cost is considered incorporating several features like energy and labour cost, raw material cost and development cost of the manufacturing system. Development cost is assumed to be a function of reliability parameter.
Considering these phenomena, an analytic expression is obtained for the total profit of the model. The model provides an analytical solution to maximize the total profit function.A numerical example is presented to illustrate the model along with graphical analysis. Sensitivity analysis has been carried out to identify the most sensitive parameters of the model.
A Study on Translucent Concrete Product and Its Properties by Using Optical F...IJMER
- Translucent concrete is a concrete based material with light-transferring properties,
obtained due to embedded light optical elements like Optical fibers used in concrete. Light is conducted
through the concrete from one end to the other. This results into a certain light pattern on the other
surface, depending on the fiber structure. Optical fibers transmit light so effectively that there is
virtually no loss of light conducted through the fibers. This paper deals with the modeling of such
translucent or transparent concrete blocks and panel and their usage and also the advantages it brings
in the field. The main purpose is to use sunlight as a light source to reduce the power consumption of
illumination and to use the optical fiber to sense the stress of structures and also use this concrete as an
architectural purpose of the building
Developing Cost Effective Automation for Cotton Seed DelintingIJMER
A low cost automation system for removal of lint from cottonseed is to be designed and
developed. The setup consists of stainless steel drum with stirrer in which cottonseeds having lint is mixed
with concentrated sulphuric acid. So lint will get burn. This lint free cottonseed treated with lime water to
neutralize acidic nature. After water washing this cottonseeds are used for agriculter purpose
Study & Testing Of Bio-Composite Material Based On Munja FibreIJMER
The incorporation of natural fibres such as munja fiber composites has gained
increasing applications both in many areas of Engineering and Technology. The aim of this study is to
evaluate mechanical properties such as flexural and tensile properties of reinforced epoxy composites.
This is mainly due to their applicable benefits as they are light weight and offer low cost compared to
synthetic fibre composites. Munja fibres recently have been a substitute material in many weight-critical
applications in areas such as aerospace, automotive and other high demanding industrial sectors. In
this study, natural munja fibre composites and munja/fibreglass hybrid composites were fabricated by a
combination of hand lay-up and cold-press methods. A new variety in munja fibre is the present work
the main aim of the work is to extract the neat fibre and is characterized for its flexural characteristics.
The composites are fabricated by reinforcing untreated and treated fibre and are tested for their
mechanical, properties strictly as per ASTM procedures.
Hybrid Engine (Stirling Engine + IC Engine + Electric Motor)IJMER
Hybrid engine is a combination of Stirling engine, IC engine and Electric motor. All these 3 are
connected together to a single shaft. The power source of the Stirling engine will be a Solar Panel. The aim of
this is to run the automobile using a Hybrid engine
Fabrication & Characterization of Bio Composite Materials Based On Sunnhemp F...IJMER
The present day technology demands eco-friendly developments. In this era the
composite material are playing a vital roal in different field of Engineering .The composite materials
are using as a principle materials. Nowaday the composite materials are utilizing as a important
component of engineering field .Where as the importance of the applications of composites is well
known, but thrust on the use of natural fibres in it for reinforcement has been given priority for some
times. But changing from synthetic fibres to natural fibres provides only half green-composites. A
partial green composite will be achieved if the matrix component is also eco-friendly. Keeping this in
view, a detailed literature surveyed has been carried out through various issues of the Journals
related to this field. The material systems used are sunnhemp fibres. Some epoxy and hardener has
been also added for stability and drying of the bio-composites. Various graphs and bar-charts are
super-imposed on each other for comparison among themselves and Graphs is plotted on MAT LAB
and ORIGIN 6.0 software. To determining tensile strengths, Various properties for different biocomposites
have been compared among themselves. Comparison of the behaviour of bio-composites of
this work has been also compare with other works. The bio-composites developed in this work are
likely to get applications in fall ceilings, partitions, bio-degradable packagings, automotive interiors,
sports things (e.g. rackets, nets, etc.), toys etc.
Geochemistry and Genesis of Kammatturu Iron Ores of Devagiri Formation, Sandu...IJMER
The Greenstone belts of Karnataka are enriched in BIFs in Dharwar craton, where Iron
formations are confined to the basin shelf, clearly separated from the deeper-water iron formation that
accumulated at the basin margin and flanking the marine basin. Geochemical data procured in terms of
major, trace and REE are plotted in various diagrams to interpret the genesis of BIFs. Al2O3, Fe2O3 (T),
TiO2, CaO, and SiO2 abundances and ratios show a wide variation. Ni, Co, Zr, Sc, V, Rb, Sr, U, Th,
ΣREE, La, Ce and Eu anomalies and their binary relationships indicate that wherever the terrigenous
component has increased, the concentration of elements of felsic such as Zr and Hf has gone up. Elevated
concentrations of Ni, Co and Sc are contributed by chlorite and other components characteristic of basic
volcanic debris. The data suggest that these formations were generated by chemical and clastic
sedimentary processes on a shallow shelf. During transgression, chemical precipitation took place at the
sediment-water interface, whereas at the time of regression. Iron ore formed with sedimentary structures
and textures in Kammatturu area, in a setting where the water column was oxygenated.
Experimental Investigation on Characteristic Study of the Carbon Steel C45 in...IJMER
In this paper, the mechanical characteristics of C45 medium carbon steel are investigated
under various working conditions. The main characteristic to be studied on this paper is impact toughness
of the material with different configurations and the experiment were carried out on charpy impact testing
equipment. This study reveals the ability of the material to absorb energy up to failure for various
specimen configurations under different heat treated conditions and the corresponding results were
compared with the analysis outcome
Non linear analysis of Robot Gun Support Structure using Equivalent Dynamic A...IJMER
Robot guns are being increasingly employed in automotive manufacturing to replace
risky jobs and also to increase productivity. Using a single robot for a single operation proves to be
expensive. Hence for cost optimization, multiple guns are mounted on a single robot and multiple
operations are performed. Robot Gun structure is an efficient way in which multiple welds can be done
simultaneously. However mounting several weld guns on a single structure induces a variety of
dynamic loads, especially during movement of the robot arm as it maneuvers to reach the weld
locations. The primary idea employed in this paper, is to model those dynamic loads as equivalent G
force loads in FEA. This approach will be on the conservative side, and will be saving time and
subsequently cost efficient. The approach of the paper is towards creating a standard operating
procedure when it comes to analysis of such structures, with emphasis on deploying various technical
aspects of FEA such as Non Linear Geometry, Multipoint Constraint Contact Algorithm, Multizone
meshing .
Static Analysis of Go-Kart Chassis by Analytical and Solid Works SimulationIJMER
This paper aims to do modelling, simulation and performing the static analysis of a go
kart chassis consisting of Circular beams. Modelling, simulations and analysis are performed using 3-D
modelling software i.e. Solid Works and ANSYS according to the rulebook provided by Indian Society of
New Era Engineers (ISNEE) for National Go Kart Championship (NGKC-14).The maximum deflection is
determined by performing static analysis. Computed results are then compared to analytical calculation,
where it is found that the location of maximum deflection agrees well with theoretical approximation but
varies on magnitude aspect.
In récent year various vehicle introduced in market but due to limitation in
carbon émission and BS Séries limitd speed availability vehicle in the market and causing of
environnent pollution over few year There is need to decrease dependancy on fuel vehicle.
bicycle is to be modified for optional in the future To implement new technique using change in
pedal assembly and variable speed gearbox such as planetary gear optimise speed of vehicle
with variable speed ratio.To increase the efficiency of bicycle for confortable drive and to
reduce torque appli éd on bicycle. we introduced epicyclic gear box in which transmission done
throgh Chain Drive (i.e. Sprocket )to rear wheel with help of Epicyclical gear Box to give
number of différent Speed during driving.To reduce torque requirent in the cycle with change in
the pedal mechanism
Integration of Struts & Spring & Hibernate for Enterprise ApplicationsIJMER
The proposal of this paper is to present Spring Framework which is widely used in
developing enterprise applications. Considering the current state where applications are developed using
the EJB model, Spring Framework assert that ordinary java beans(POJO) can be utilize with minimal
modifications. This modular framework can be used to develop the application faster and can reduce
complexity. This paper will highlight the design overview of Spring Framework along with its features that
have made the framework useful. The integration of multiple frameworks for an E-commerce system has
also been addressed in this paper. This paper also proposes structure for a website based on integration of
Spring, Hibernate and Struts Framework.
Microcontroller Based Automatic Sprinkler Irrigation SystemIJMER
Microcontroller based Automatic Sprinkler System is a new concept of using
intelligence power of embedded technology in the sprinkler irrigation work. Designed system replaces
the conventional manual work involved in sprinkler irrigation to automatic process. Using this system a
farmer is protected against adverse inhuman weather conditions, tedious work of changing over of
sprinkler water pipe lines & risk of accident due to high pressure in the water pipe line. Overall
sprinkler irrigation work is transformed in to a comfortableautomatic work. This system provides
flexibility & accuracy in respect of time set for the operation of a sprinkler water pipe lines. In present
work the author has designed and developed an automatic sprinkler irrigation system which is
controlled and monitored by a microcontroller interfaced with solenoid valves.
On some locally closed sets and spaces in Ideal Topological SpacesIJMER
In this paper we introduce and characterize some new generalized locally closed sets
known as
δ
ˆ
s-locally closed sets and spaces are known as
δ
ˆ
s-normal space and
δ
ˆ
s-connected space and
discussed some of their properties
Intrusion Detection and Forensics based on decision tree and Association rule...IJMER
This paper present an approach based on the combination of, two techniques using
decision tree and Association rule mining for Probe attack detection. This approach proves to be
better than the traditional approach of generating rules for fuzzy expert system by clustering methods.
Association rule mining for selecting the best attributes together and decision tree for identifying the
best parameters together to create the rules for fuzzy expert system. After that rules for fuzzy expert
system are generated using association rule mining and decision trees. Decision trees is generated for
dataset and to find the basic parameters for creating the membership functions of fuzzy inference
system. Membership functions are generated for the probe attack. Based on these rules we have
created the fuzzy inference system that is used as an input to neuro-fuzzy system. Fuzzy inference
system is loaded to neuro-fuzzy toolbox as an input and the final ANFIS structure is generated for
outcome of neuro-fuzzy approach. The experiments and evaluations of the proposed method were
done with NSL-KDD intrusion detection dataset. As the experimental results, the proposed approach
based on the combination of, two techniques using decision tree and Association rule mining
efficiently detected probe attacks. Experimental results shows better results for detecting intrusions as
compared to others existing methods
Natural Language Ambiguity and its Effect on Machine LearningIJMER
"Natural language processing" here refers to the use and ability of systems to process
sentences in a natural language such as English, rather than in a specialized artificial computer
language such as C++. The systems of real interest here are digital computers of the type we think of as
personal computers and mainframes. Of course humans can process natural languages, but for us the
question is whether digital computers can or ever will process natural languages. We have tried to
explore in depth and break down the types of ambiguities persistent throughout the natural languages
and provide an answer to the question “How it affects the machine translation process and thereby
machine learning as whole?” .
Today in era of software industry there is no perfect software framework available for
analysis and software development. Currently there are enormous number of software development
process exists which can be implemented to stabilize the process of developing a software system. But no
perfect system is recognized till yet which can help software developers for opting of best software
development process. This paper present the framework of skillful system combined with Likert scale. With
the help of Likert scale we define a rule based model and delegate some mass score to every process and
develop one tool name as MuxSet which will help the software developers to select an appropriate
development process that may enhance the probability of system success.
Material Parameter and Effect of Thermal Load on Functionally Graded CylindersIJMER
The present study investigates the creep in a thick-walled composite cylinders made
up of aluminum/aluminum alloy matrix and reinforced with silicon carbide particles. The distribution
of SiCp is assumed to be either uniform or decreasing linearly from the inner to the outer radius of
the cylinder. The creep behavior of the cylinder has been described by threshold stress based creep
law with a stress exponent of 5. The composite cylinders are subjected to internal pressure which is
applied gradually and steady state condition of stress is assumed. The creep parameters required to
be used in creep law, are extracted by conducting regression analysis on the available experimental
results. The mathematical models have been developed to describe steady state creep in the composite
cylinder by using von-Mises criterion. Regression analysis is used to obtain the creep parameters
required in the study. The basic equilibrium equation of the cylinder and other constitutive equations
have been solved to obtain creep stresses in the cylinder. The effect of varying particle size, particle
content and temperature on the stresses in the composite cylinder has been analyzed. The study
revealed that the stress distributions in the cylinder do not vary significantly for various combinations
of particle size, particle content and operating temperature except for slight variation observed for
varying particle content. Functionally Graded Materials (FGMs) emerged and led to the development
of superior heat resistant materials.
Energy Audit is the systematic process for finding out the energy conservation
opportunities in industrial processes. The project carried out studies on various energy conservation
measures application in areas like lighting, motors, compressors, transformer, ventilation system etc.
In this investigation, studied the technical aspects of the various measures along with its cost benefit
analysis.
Investigation found that major areas of energy conservation are-
1. Energy efficient lighting schemes.
2. Use of electronic ballast instead of copper ballast.
3. Use of wind ventilators for ventilation.
4. Use of VFD for compressor.
5. Transparent roofing sheets to reduce energy consumption.
So Energy Audit is the only perfect & analyzed way of meeting the Industrial Energy Conservation.
An Implementation of I2C Slave Interface using Verilog HDLIJMER
The focus of this paper is on implementation of Inter Integrated Circuit (I2C) protocol
following slave module for no data loss. In this paper, the principle and the operation of I2C bus protocol
will be introduced. It follows the I2C specification to provide device addressing, read/write operation and
an acknowledgement. The programmable nature of device provide users with the flexibility of configuring
the I2C slave device to any legal slave address to avoid the slave address collision on an I2C bus with
multiple slave devices. This paper demonstrates how I2C Master controller transmits and receives data to
and from the Slave with proper synchronization.
The module is designed in Verilog and simulated in ModelSim. The design is also synthesized in Xilinx
XST 14.1. This module acts as a slave for the microprocessor which can be customized for no data loss.
Discrete Model of Two Predators competing for One PreyIJMER
This paper investigates the dynamical behavior of a discrete model of one prey two
predator systems. The equilibrium points and their stability are analyzed. Time series plots are obtained
for different sets of parameter values. Also bifurcation diagrams are plotted to show dynamical behavior
of the system in selected range of growth parameter
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software. It is a stable ,reliable and the powerful solution with the advanced features and advantages which are as follows: Data Security.MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
1. International
OPEN ACCESS Journal
Of Modern Engineering Research (IJMER)
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss. 3 | Mar. 2014 | 60 |
Time Dependent Quadratic Demand Inventory Models when
Delay in Payments is Acceptable
R. Venkateswarlu1
, M. S. Reddy2
1
GITAM School of International Business, GITAM University, Visakhapatnam – 530 045, India
2
BVSR Engineering College, Chimakurthy - 523 226, India
I. Introduction
It is well known that ‘trade credit policy’ is the most effective way of a supplier to encourage retailer to
buy more goods and to attract more retailers. Trade credit can also be used as a multi-faceted marketing
management (or relationship management) tool which gives some information to the market or to a buyer about
the firm or its products or its future plans. The EOQ model developed by Wilson was based on the assumption
that the retailer will pay for the items as soon as it is received by the system. In reality the supplier may offer
some credit period to the retailer to settle the accounts in a reasonable time period. Thus the delay in payment
can be treated as a kind of price discount to the retailer.
The relationship between inventory policy and credit policy in the context of the classical lot size
model was studied by Haley and Higgins (1973). Chapman et al. (1984) developed an economic order
quantity model which considers possible credit periods allowable by suppliers. This model is shown to
be very sensitive to the length of the permissible credit period and to the relationship between the
credit period and inventory level. Davis and Gaither (1985) developed optimal order quantities for firms
that are offered a one time opportunity to delay payment for an order of a commodity. A mathematical
model is developed by Goyal (1985) when supplier announces credit period in settling the account, so
that no interest charges are payable from the outstanding amount if the account is settled within the
allowable delay period. Shah et al. (1988) extended the above model by allowing shortages. Mandal and
Phaujdar (1989a, b) have studied Goyal (1985) model by including interest earned from the sales
revenue on the stock remaining beyond the settlement period. Carlson a n d Rousseau (1989) examined
EOQ under date terms supplier credit by partitioning carrying cost into financial cost and variable
holding costs. Chung and Huang (2003) extended Goyal (1985) model when replenishment rate is finite.
Dallenbach (1986, 1988), Ward and Chapman (1987), Chapman and Ward (1988) argued that the
usual assumptions as to the incidence and the value of the inventory investment opportunity cost made
by the traditional inventory theory are correct and also established that if trade credit surplus is
taken into account, the optimal ordering quantities decreases rather than increase. Chung (1998)
established the convexity of the total annual variable c o s t function for optimal economic order quantity
under conditions of permissible delay in payments. Jamal et al. (2000) discussed the problem in which
the retailer can pay the supplier either at the end of credit period or later incurring interest charges on
the unpaid balance for the overdue period. Sarker et al. (2001) obtained optimal payment time under
permissible delay in payments when units in an inventory are subject to deterioration. Abad and
Jaggi (2003) considered the seller-buyer channel in which the end demand is price sensitive and the
suppler offers trade credit to the buyer. Shinn and Hwang (2003) dealt with the problem of determining
the retailer’s optimal price and order size simultaneously under the condition of order size dependent
delay in payments. It is assumed that the length of the credit period is a function of the retailer’s order
size and also the demand rate is a function of the selling price. Chung et al. (2005) determined the
Abstract: An EOQ model is constructed for deteriorating items with time dependent quadratic demand
rate. It is assumed that the deterioration rate is constant and the supplier offers his retailer the credit
period to settle the account of the procurement units. To solve the model it is further assumed that
shortages are not allowed and the replenishment rate is instantaneous. We have presented the models
under two different scenarios, viz., (i)the offered credit period is less than or equal to the cycle time and
(ii) the offered credit period by the supplier to the retailer for settling the account is greater than cycle
time. The objective is to minimize the retailers total inventory cost. Salvage value is also taken to see its
effect on the total cost. A numerical example is given to study the effect of allowable credit period and
the total cost of the retailer.
Key words: Quadratic demand, perishable, constant deterioration, trade credit, holding cost.
2. Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss. 3 | Mar. 2014 | 61 |
economic order quantity under conditions of permissible delay in payments where the delay in payments
depends on the quantity ordered when the order quantity is less than the quantity at which the delay
in payments is permitted, the payment for the item must be made immediately. Otherwise, the fixed
credit period is allowed. Huang (2007) examined optimal retailer’s replenishment decisions in the
EOQ model under t w o levels of trade credit policy by assuming that the supplier would offer the
retailer partially permissible delay in payments when the order quantity is smaller than a
predetermined quantity. Teng et. al. (2007) derived retailer’s optimal ordering policies with trade credit
financing.
The literature is replete in the field of trade-credit. Previously several economic order quantity
inventory models were developed with trade-credit and a very few production inventory models were developed
under allowable delay in payment. All these works were based on the assumption that the demand rate is either
linear or exponential function of time. Several authors argued that, in realistic terms, the demand need not
follow either linear or exponential trend. So, it is reasonable to assume that the demand rate, in certain
commodities, is due to seasonal variations may follow quadratic function of time [i.e., D(t) = a + bt + ct2
;
0,0,0 cba ]. The functional form of time-dependent quadratic demand explains the accelerated
(retarded) growth/decline in the demand patterns which may arise due to seasonal demand rate (Khanra and
Chaudhuri (2003). We may explain different types of realistic demand patterns depending on the signs of b and
c. Bhandari and Sharma (2000) have studied a single period inventory problem with quadratic demand
distribution under the influence of marketing policies. Khanra and Chaudhuri (2003) have discussed an order-
level inventory problem with the demand rate represented by a continuous quadratic function of time. It is well
known that the demand for spare parts of new aero planes, computer chips of advanced computer machines, etc.
increase very rapidly while the demands for spares of the obsolete aero planes, computers etc. decrease very
rapidly with time. This type of phenomena can well be addressed by inventory models with quadratic demand
rate. Sana and Chaudhuri (2004) have developed a stock-review inventory model for perishable items with
uniform replenishment rate and stock-dependent demand. Recently, Ghosh and Chaudhuri (2004) have
developed an inventory model for a deteriorating item having an instantaneous supply, a quadratic time-varying
demand and shortages in inventory. They have used a two-parameter Weibull distribution to represent the time
to deterioration. Venkateswarlu and Mohan (2011) have developed inventory models for deteriorating items
with time dependent quadratic demand and salvage value. Recently Venkateswarlu and Mohan (2013) studied
inventory model for time varying deterioration and price dependent quadratic demand with salvage value.
In literature we seldom find on the inventory models with trade credit policy for perishable items with
time dependent quadratic demand rate. Thus, in this paper, we wish to develop a mathematical model when the
units in an inventory are subjected to a constant deterioration rate and the demand rate follows a time dependent
quadratic function. It is assumed that the supplier offers a credit period to the retailer to settle the account. We
have also considered the salvage value for deteriorating units of the inventory. Sensitivity analysis is presented
with a numerical example.
II. Assumptions and Notations
The following assumptions are used to develop the model:
The system deal with a single item
The demand rate R is time dependent quadratic demand
The replenishment rate is infinite.
The lead time is zero and shortages are not allowed.
The salvage value, p )10( is associated to deteriorated units during the cycle time. Here p is the
purchase cost of an item.
The following notations are used to develop the model:
The Demand rate )(tR at time t is assumed to be
2
)( ctbtatR 0,0,0 cba . Here a is the
initial rate of demand, b is the initial rate of change of the demand and c is the acceleration of demand rate.
θ )10( is the constant rate of deterioration.
A is the ordering cost per order.
S is the selling price per item )( pS .
Q(t) is the ordering quantity at time t=0
h is per unit holding cost excluding interest charges per unit per year.
Ie is the interest earned per year.
Ic is the interest charged per stocks per year.
3. Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss. 3 | Mar. 2014 | 62 |
M is the permissible delay in settling in the accounts, 0<M<1.
T is the interval between two successive orders
K(T) is the total cost per unit time.
III. Formulation and Solution of the Model
The objective of the model is to determine the total cost of the system and the demand rate of
items is time dependent quadratic function with constant rate of deterioration.
Let I(t) be the inventory level at time t ( Tt 0 ). The inventory depletes due to deterioration
and the demand, and then the differential equation which describes the inventory level at time t is given by
TttRtI
dt
tdI
0),()(
)(
(1)
)()( 2
ctbtatRwhere
and (i) 0)( TI when Tt , (ii) QI )0( . (2)
The solution of equation (1) using the boundary condition 0)( TI is given by
)
33
()
22
()(
)
44
()
33
)(()
22
)(()()(
3322
443322
tT
c
tT
btTat
tT
c
tT
cb
tT
batTatI
(3)
where we taken series expansion and ignored the second and higher powers of θ as θ is small.
Since QI )0( , we obtain
)
4
()
3
)(()
2
)(()(
432
T
c
T
cb
T
baaTtQ (4)
The number of deteriorated units D (T) during one cycle is given by
TTRQTD )()(
32432
32432
cTbTTcTbTa
(5)
The cost due to deterioration is given by
)(TpDCD
32432
32432
cTbTTcTbTa
p
(6)
The salvage value of deteriorated units is
CDSV (7)
The inventory holding cost during the cycle is
T
dttIhIHC
0
)(
120
121540304060 543432
TcTbTacTbTaT
h
(8)
The Ordering cost is given by
AOC (9)
Following Nita Shah and Pandey (2008), we have considered the following two cases for interest charged and
the interest earned:
Case-1: The offered credit period is less than or equal to the cycle time i.e., TM .
Figure-1
4. Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
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Case-2: The offered credit period for settling the account is greater than the cycle time i.e., TM .
Figure-2
3.1 Case-1
The retailer can sale units during [0, M] at a sale price: ‘S’ per unit which he can put an interest rate ‘ eI ’per
unit per annum in an interest bearing account. So the total interest earned during [0, M] is
M
e tdttRSIIE
0
1 )(
432
432
cMbMaM
SIe
(10)
Now, in the period [M, T], the supplier will charge the interest to the retailer on the remaining stock at
the rate ‘ cI ’ per unit per annum. Hence, total interest charges payble by the retailer during [M, T] is
T
M
c dttISIIC )(1
)461020
1215252040
20301060())((
120
1
22
3232
222
cTMcMTbMTaM
cTbTcMMaTTb
MbcTcMaTMSIc
(11)
Now, the total cost K1 (T) per time unit is
SVICIECDIHCOC
T
TK 111
1
)(
)461020
1215252040
20301060())(((
120
1
432
32432
)1(
120
121540304060
1
22
3232
222
432
32432
543432
cTMcMTbMTaM
cTbTcMbMaTTb
MbcTcMaTMSI
cMbMaM
SI
cTbTTcTbTa
p
TcTbTacTbTaT
hA
T
c
e
(12)
Since our objective is to minimize the total cost K1 (T) per unit time, the necessary condition for the total cost to
be minimum is 0)(1
TK
T
i.e.,
)(
1
)(
1)(
6543221
1
XXXX
T
XX
TT
TK
(13)
where
120
)6060120120120120( 43232
1
cMbMaMMacMbMh
X
))()(1( 322
2 aMcMcMMbbMpX
5. Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
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120
121540304060 543432
3
TcTbTacTbTaT
hAX
32432
)1(
32432
4
cTbTTcTbTa
pX
432
432
5
cMbMaM
SIX e
)4610
2012152520
4020301060()(()
120
1
(
22
3232
222
6
cTMcMTbMT
aMcTbTcMbMaT
TbMbcTcMaTMSIX c
From equation (13), we have
0
)()(1(
120
6060120120120120(
1
)461020
121525204020
301060())((
120
1
432
32432
)1(
120
121540304060
1
322
43232
22
3232
222
432
32432
543432
2
aMcMcMMbbMp
cMbMaMMacMbMh
T
cTMcMTbMTaM
cTbTcMbMaTTbMb
cTcMaTMSI
cMbMaM
SI
cTbTTcTbTa
p
TcTbTacTbTaT
hA
T
c
e
(14)
We solve the above equation for optimal T using MATHCAD. For this optimal T, the total cost is minimum
only if 0
)(
2
1
2
T
TK
.
3.1.1 Numerical Example
To demonstrate the effectiveness of the models developed, a numerical example is taken with the
following values for the parameters:
a =500 b=5 c=0.1 h=5 S=30 08.0
T=0.5 Ic=0.15 Ie=0.12 05.0 p=20 A=200
For the above example, it is found that the optimality conditions are satisfied in all the following four cases for
all T viz.,
(i) a > 0, b > 0 and c > 0 (i.e., accelerated growth model)
(ii) a > 0, b < 0 and c > 0 (i.e., retarded growth model)
(iii) a > 0, b < 0 and c < 0 (i.e., accelerated decline model)
(iv) a > 0, b > 0 and c < 0 (i.e., retarded decline model)
The MATHCAD output is given in Table-1 through table-4 which shows the variations of the deterioration rate,
and the delay period, M.
From the output shown in table-1 to table-4, it is observed that the buyer’s total cost decreases with the
increase in delay period for a fixed value of deterioration rate. For example, if the deterioration rate is 0.05, the
total cost K1(T) decreases when the delay in payment increases from 15 days to 60 days in all the models. We
may attribute this due to the interest earned by buyer who earns more revenue from the sold items. Further,
across all the models, it can be noticed that the buyer’s total cost increases when the rate of deterioration
increases from 0.05 to 0.10.
6. Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
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Table-1: a > 0, b > 0 and c > 0 (i.e., accelerated growth model)
S.No
.
M=15 days M=30 days M=45 days M=60 days
T K1(T) T K1(T) T K1(T) T K1(T)
1 0.05 0.28 1345.02 0.28 1256.13 0.28 1170.07 0.28 1086.76
2 0.06 0.28 1358.57 0.28 1269.65 0.28 1183.61 0.28 1100.37
3 0.07 0.27 1371.97 0.27 1283.02 0.28 1197.01 0.28 1113.84
4 0.08 0.27 1385.24 0.27 1296.27 0.27 1210.27 0.27 1127.17
5 0.09 0.27 1398.38 0.27 1310.36 0.27 1223.41 0.27 1140.38
6 0.10 0.27 1411.39 0.27 1322.36 0.27 1236.42 0.27 1153.46
Table-2: a > 0, b < 0 and c > 0 (i.e., retarded growth model)
S.No.
M=15 days M=30 days M=45 days M=60 days
T K1(T) T K1(T) T K1(T) T K1(T)
1 0.05 0.27 1367.99 0.28 1279.43 0.28 1193.75 0.28 1110.89
2 0.06 0.27 1381.29 0.27 1292.70 0.27 1207.05 0.28 1124.25
3 0.07 0.27 1394.46 0.27 1305.84 0.27 1220.20 0.27 1137.47
4 0.08 0.27 1407.50 0.27 1318.85 0.27 1233.24 0.27 1150.57
5 0.09 0.26 1420.41 0.27 1331.74 0.27 1246.15 0.27 1163.55
6 0.10 0.26 1433.21 0.26 1344.51 0.26 1258.94 0.27 1176.41
Table-3: a > 0, b < 0 and c < 0 (i.e., accelerated decline model)
S.No.
M=15 days M=30 days M=45 days M=60 days
T K1(T) T K1(T) T K1(T) T K1(T)
1 0.05 0.27 1368.07 0.28 1279.52 0.28 1193.84 0.28 1110.98
2 0.06 0.27 1381.37 0.27 1292.78 0.27 1207.13 0.28 1124.33
3 0.07 0.27 1394.54 0.27 1305.92 0.27 1220.29 0.27 1137.56
4 0.08 0.27 1407.58 0.27 1318.93 0.27 1233.32 0.27 1150.66
5 0.09 0.26 1420.49 0.27 1331.82 0.27 1246.23 0.27 1163.63
6 0.10 0.26 1433.28 0.26 1344.58 0.26 1259.02 0.27 1176.49
Table-4: a > 0, b > 0 and c < 0 (i.e., retarded decline model)
S.N
o.
M=15 days M=30 days M=45 days M=60 days
T K1(T) T K1(T) T K1(T) T K1(T)
1 0.05 0.28 1345.02 0.28 1256.22 0.28 1170.15 0.28 1086.85
2 0.06 0.28 1358.65 0.28 1269.73 0.28 1183.69 0.28 1100.46
3 0.07 0.27 1372.05 0.27 1283.11 0.28 1197.09 0.28 1113.93
4 0.08 0.27 1385.32 0.27 1296.35 0.27 1210.36 0.27 1127.26
5 0.09 0.27 1398.46 0.27 1309.46 0.27 1223.49 0.27 1140.47
6 0.10 0.27 1411.46 0.27 1322.44 0.27 1236.50 0.27 1153.54
7. Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
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3.2 Case-2
In this case, the interest earned is
TMTTRtdttRSIIE
T
e )()(
0
2
4
3
3
2
2
432
32 cTbTaT
cMTbMTaMTSIe
(15)
and the interest charges is zero 0.,. 2 ICei
The total cost K2 (T)per time unit is
SVICIECDIHCOC
T
TK 222
1
)(
4
3
3
2
2
32432
)1(
120
121540304060
1
432
32
32432
543432
cTbTaT
cMTbMTaMTSI
cTbTTcTbTa
p
TcTbTacTbTaT
hA
T
e
(16)
Since our object is to minimize the total cost K2 (T) per unit time, the necessary condition for the total
cost to be minimum is 0)(2
TK
T
i.e.,
65423212
1
)(
1
)( YYY
T
YYY
T
TK
T
(17)
where
322
1 )1( TcTbcTTbTapY
120
6060120120120120 43232
2
TcTbTaaTcTbT
hY
232
3 3232 cMTbMTaTcTbTaMSIY e
120
121540304060 543432
4
TcTbTacTbTaT
hAY
32432
)1(
32432
5
cTbTTcTbTa
pY
4
3
3
2
2
432
32
6
cTbTaT
cMTbMTaMTSIY e
Now from equation (17),
0)( 654321 YYYYYYT
0
4
3
3
2
2
32432
)1(
120
121540304060
3232
120
6060120120120120
)1(
.,.
432
32
32432
543432
232
43232
322
cTbTaT
cMTbMTaMTSI
cTbTTcTbTa
p
TcTbTacTbTaT
hA
cMTbMTaTcTbTaMSI
TcTbTaaTcTbT
h
TcTbcTTbTap
T
ei
e
e
(18)
which minimises the K2 (T) only if 0
)(
2
2
2
T
TK
for all values of T.
8. Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
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3.2.1 Numerical Example
Once again we consider the values of the parameters as given in 3.1.1. For these values, the output is
presented in Table-5 through Table-8. It can be observed that the behaviour of these models, in the case of M >
T, is quite similar to the results obtained as in the case of M < T. It is also observed that the total cost K2(T) is
less than K1(T ) when the delay period is increased from 15 days to 60 days. Thus it can be concluded that the
total cost in both the cases is almost same when the delay period increases from 15 days to 60 days.
For T = M, we have
)(
1
)()( 32121 ZZZ
M
MKMK
where
120
121540304060 543432
1
McMbMacMbMaM
hAZ
32432
)1(
32432
2
cMbMMcMbMa
pZ
432
432
3
cMbMaM
SIZ e
.
IV. Sensitivity Analysis
(a > 0, b > 0 and c > 0 i.e., accelerated growth model)
We now study the sensitivity of the models developed in 3.1.1 and 3.2.1 to examine the implications of
underestimating and overestimating the parameters a, b, c, Ic , Ie , h and p on optimal value of cycle time and
total cost of the system. Here we have taken the deterioration rate as θ=0.05 and the delay period is 30 days. The
sensitive analysis is performed by changing each of the parameter by -20%, -10%, +10% and +20% taking one
parameter at a time and keeping the remaining parameters are unchanged. The results are shown in Table-9 and
Table-10.
The following interesting observations are made from the above tables:
Case-1( TM )
(i) Increase (decrease) in parameters a, Ic , h and p decreases (increases) the cycle time where as the total cost
increases (decreases) with the increase (decrease) in these parameters. However the rate of
increase/decrease is more pronounced in case of the changes made in the parameters ‘a’ and ‘h’ which
indicate that the optimal values of cycle time and the total cost are less sensitive to ‘Ic’ and ‘p’ .
(ii) The effect of the parameters b, c and Ie on the optimum value of the cycle time and the total cost is similar
but the rate of change is insignificant.
(iii) The salvage value of deteriorated items is not shown much effect on the optimal total cost of the system.
Case-2( TM )
(iv) Increase (decrease) in parameters a, h and p decreases (increases) the cycle time where as the total cost
increases (decreases) with the increase (decrease) in these parameters. However the rate of
increase/decrease is more pronounced in case of the changes made in the parameters ‘a’ and ‘h’ and less
sensitive to the changes in ‘p’
(v) T and K2(T) are less sensitive to the changes made in the parameter ‘b’ and moderately sensitive to Ie.
(vi) The effect of salvage value is not so significant on optimal policies.
V. Conclusions
The main objective of this study is the formulation of a deterministic inventory model for items which
have constant deterioration rate and follows time dependent quadratic demand rate when supplier offers a
specific credit period. The total cost of the system is calculated when shortages are not allowed. Salvage value
is considered while calculating the total cost of the system. Sensitivity of the models is also discussed.
9. Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
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Table-5: a > 0, b > 0 and c > 0 (i.e., accelerated growth model)
S.N
o
M=15 days M=30 days M=45 days M=60 days
T K2(T) T K2(T) T K2(T) T K2(T)
1 0.05 0.29 1297.63 0.29 1223.44 0.29 1149.25 0.29 1075.06
2 0.06 0.29 1311.65 0.29 1237.46 0.29 1163.27 0.29 1089.09
3 0.07 0.28 1325.51 0.29 1251.32 0.29 1177.14 0.29 1102.95
4 0.08 0.28 1339.22 0.28 1265.04 0.28 1190.86 0.28 1116.67
5 0.09 0.28 1352.79 0.28 1278.61 0.28 1204.43 0.28 1130.25
6 0.10 0.28 1366.22 0.28 1292.05 0.28 1217.87 0.28 1143.69
Table-6: a > 0, b < 0 and c > 0 (i.e., retarded growth model)
S.No.
M=15 days M=30 days M=45 days M=60 days
T K2(T) T K2(T) T K2(T) T K2(T)
1 0.05 0.29 1320.95 0.29 1247.19 0.29 1173.43 0.29 1099.66
2 0.06 0.28 1334.71 0.28 1260.95 0.28 1187.18 0.28 1113.42
3 0.07 0.28 1348.32 0.28 1274.56 0.28 1200.79 0.28 1127.03
4 0.08 0.28 1361.80 0.28 1288.03 0.28 1214.26 0.28 1140.49
5 0.09 0.28 1375.14 0.28 1301.36 0.28 1227.59 0.28 1153.82
6 0.10 0.27 1388.34 0.27 1314.57 0.27 1240.80 0.27 1167.03
Table-7: a > 0, b < 0 and c < 0 (i.e., accelerated decline model)
S.No.
M=15 days M=30 days M=45 days M=60 days
T K2(T) T K2(T) T K2(T) T K2(T)
1 0.05 0.29 1321.03 0.29 1247.27 0.29 1173.51 0.29 1099.75
2 0.06 0.28 1334.79 0.28 1261.03 0.28 1187.27 0.28 1113.51
3 0.07 0.28 1348.40 0.28 1274.64 0.28 1200.88 0.28 1127.11
4 0.08 0.28 1361.87 0.28 1288.11 0.28 1214.34 0.28 1140.58
5 0.09 0.28 1375.21 0.28 1301.44 0.28 1227.68 0.28 1153.91
6 0.10 0.27 1388.42 0.27 1314.65 0.27 1240.88 0.27 1167.11
Table-8: a > 0, b > 0 and c < 0 (i.e., retarded decline model)
S.No.
M=15 days M=30 days M=45 days M=60 days
T K2(T) T K2(T) T K2(T) T K2(T)
1 0.05 0.29 1297.72 0.29 1223.53 0.29 1149.34 0.29 1075.16
2 0.06 0.29 1311.73 0.29 1237.55 0.29 1163.36 0.29 1089.18
3 0.07 0.28 1325.59 0.29 1251.41 0.29 1177.23 0.29 1103.04
4 0.08 0.28 1339.30 0.28 1265.12 0.28 1190.94 0.28 1116.76
5 0.09 0.28 1352.87 0.28 1278.69 0.28 1204.51 0.28 1130.34
6 0.10 0.28 1366.30 0.28 1292.13 0.28 1217.95 0.28 1143.77
11. Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
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Case-2( TM ): Table-10
REFERENCES
[1] Halley, C. G. & Higgins, R. C., (1973). Inventory Policy and Trade Credit Financing. Management Science. 20, 464
– 471.
[2] Chapman, C. B., Ward, S. C., Cooper, D. F. & Page, M. J., (1984). Credit Policy and Inventory Control. Journal of
the Operational Research Society. 35, 1055 – 1065.
[3] Davis, R. A. & Gaither, N. (1985). Optimal Ordering Policies Under Conditions of Extended Payment Privileges,
Management Sciences. 31, 499-509.
[4] Goyal, S. K. (1985). Economic Order Quantity Under Conditions of Permissible Delay in Payment. Journal of the
Operational Research Society. 36, 335–338.
[5] Shah, V. R., Patel, H. C. & Shah. Y. K., (1988). Economic Ordering Quantity when Delay in Payments of Orders and
Shortages are Permitted. Gujarat Statistical Review. 15, 51 – 56.126
[6] Mandal, B. N. & Phaujdar, S. (1989a). Some EOQ Models Under Permissible Delay in Payments. International
Journal of Managements Science, 5 (2), 99–108.
[7] Mandal, B.N. & Phaujdar, S. (1989b). An Inventory Model f or Deteriorating Items and Stock
Dependent Consumption Rate. Journal of Operational Research Society. 40, 483–488.
S.No Parameter
%
Change
%
Change
in T
%
Change
in K1(T)
1 a
-20% 11.4695 -9.4032
-10% 5.3763 -4.5309
10% -4.6595 4.2404
20% -8.9606 8.2299
2 b
-20% -0.3584 0.1865
-10% -0.3584 0.0933
10% 0.0000 -0.0935
20% 0.0000 -0.1869
3 c
-20% 0.0000 -0.2381
-10% 0.0000 0.0004
10% 0.0000 -0.0003
20% 0.0000 -0.0006
4 Ic
-20% 3.9427 -2.5888
-10% 1.7921 -1.2700
10% -2.1505 1.2244
20% -3.9427 2.4064
5 Ie
-20% 0.0000 0.3472
-10% 0.0000 0.1736
10% -0.3584 -0.1740
20% -0.3584 -0.3483
6 h
-20% 5.0179 -5.7520
-10% 2.5090 -2.8386
10% -2.5090 2.7693
20% -4.6595 5.4743
7 p
-20% 0.7168 -0.8201
-10% 0.3584 -0.4094
10% -0.3584 0.4079
20% -0.7168 0.8144
8 γ
-20% -0.3584 0.0711
-10% -0.3584 0.0356
10% 0.0000 -0.0356
20% 0.0000 -0.0712
12. Time Dependent Quadratic Demand Inventory Models when Delay in Payments is Acceptable
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss. 3 | Mar. 2014 | 71 |
[8] Carlson, M.L. & Rousseau, J.J. (1989). EOQ under Date-Terms Supplier Credit. Journal of the Operational Research
Society. 40 (5), 451–460.
[9] Chung, K.J. & Huang, Y.F. (2003). The Optimal Cycle Time for EPQ Inventory Model Under Permissible Delay in
Payments. International Journal of Production Economics. 84 (3), 307–318.
[10] Daellenbach, H. G., (1986). Inventory Control and Trade Credit. Journal of the Operational Research Society, 37,
525 – 528.
[11] Daellenbach, H. G., (1988): Inventory Control and Trade Credit – a rejoinder. Journal of the Operational Research
Society. 39, 218 – 219.
[12] Ward, S. C. & Chapman, C. B., (1987). Inventory Control and Trade Credit –a reply to Daellenbach. Journal of
Operational the Research Society. 32, 1081 – 1084.
[13] Chapman, C. B. & Ward, S. C., (1988): Inventory Control and Trade Credit –A Future Reply. Journal Of Operational
Research Society, 39, 219 – 220.
[14] Chung, K. J., (1998). A Theorem on the Deterioration of Economic Order Quantity Under Conditions of Permissible
Delay in Payments. Computers and Operations Research. 25,49 – 52.
[15] Jamal, A. M. M., Sarker, B. R & Wang, S. (2000). Optimal Payment Time for a Retailer Under Permitted Delay of
Payment by the Wholesaler. International Journal of Production Economics. 66, 59 - 66.
[16] Sarker, B. R., Jamal, A. M. M. & Wang, S., (2001). Optimal Payment Time Under Permissible Delay for Production
with Deterioration. Production Planning and Control. 11, 380 – 390.
[17] Abad, P.L. & Jaggi, C.K. (2003). A Joint Approach for Setting Unit Price and the Length of the Credit Period for a
Seller when End Demand is Price Sensitive. International Journal of Production Economics. 83 (2), 115–122.
[18] Shinn, S. W. & Hwang, H., (2003). Retailer’s Pricing and Lot – Sizing Policy for Exponentially Deteriorating
Products under the Conditions of Permissible Delay in Payments. Computers and Industrial Engineering. 24(6), 539
– 547.
[19] Chung, K.J., Goyal, S.K. & Huang, Yung-Fu (2005). The Optimal Inventory Policies Under Permissible Delay in
Payments Depending on the Ordering Quantity. International Journal of Production Economics. 95(2), 203–213.
[20] Huang, Y.F. (2007). Optimal Retailer’s Replenishment Decisions in the EPQ Model under Two Levels of Trade
Credit Policy. European Journal of Operational Research. 176 (2), 911–924.
[21] Teng, J.T., Chang, C.T., Chern, M.S. & Chan, Y.L. (2007). Retailer’s Optimal Ordering Policies with Trade Credit
Financing. International Journal of System Science. 38 (3), 269–278.
[22] Khanra, S. & Chaudhuri. K.S. (2003). A Note on Order-Level Inventory Model for a Deteriorating Item with Time-
Dependent Quadratic Demand. Computers and Operations Research. Vol.30, 1901-1916.
[23] Bhandari, R.M. & Sharma, P.K. (2000). A Single Period Inventory Problem with Quadratic Demand Distribution
under the Influence of Market Policies. Eng. Science 12(2) 117-127.
[24] Shibshankar Sana & Chaudhary, K.S. (2004). A Stock-Review EOQ Model with Stock-Dependent Demand,
Quadratic Deterioration Rate’. Advanced Modelling and Optimization. 6(2), 25-32.
[25] Ghosh, S.K. & Chaudhuri, K.S. (2004). An Order Level Inventory Model for a Deteriorating Item with Weibull
Deterioration, Time-Quadratic Demand and Shortages. Advanced Modelling and Optimization. 6(1), 21-35.
[26] Venkateswarlu, R & Mohan.R.(2011). Inventory Models for Deteriorating Items with Time Dependent Quadratic
Demand and Salvage Value. International Journal of Applied Mathematical Sciences. 5(1-2), 11-18.
[27] Venkateswarlu,R. & Mohan,R. (2013). An Inventory Model for Time Varying Deterioration and Price Dependent
Quadratic Demand with Salvage Value. Journal of Computational and Applied Mathematics. 1(1):21-27.