The (R, Q) Control of A Mixture Inventory Model with Backorders and Lost Sales with Controllable Set Up Cost And Variable Lead Time with Service Level Constraint
This document summarizes an inventory model that considers a mixture of backorders and lost sales when stockouts occur. The model has the following key features:
1) The set-up cost and lead time are controllable variables that can be optimized.
2) Instead of minimizing stockout costs, the model employs a service level constraint to bound the stockout level per cycle.
3) The model is solved using a genetic algorithm approach to find optimal values for ordering quantity, set-up cost, and lead time that minimize total costs while satisfying the service level constraint.
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.
A Modified PSO Based Solution Approach for Economic Ordered Quantity Problem ...irjes
This paper presents formulation of Economic Ordered Quantity (EOQ) problem considering Order
Size Limits, Stock Limits and Prohibited Ordering Segments, after that a modified PSO algorithm that utilizes
the PSO with double chaotic maps is presented to solve this problem. In proposed approach, the logistic map
and lozi map are applied alternatively to the velocity updating function of the particles. Using PSO with
irregular velocity updates which is performed by these maps forces the particles to search greater space for best
global solution. However the random function itself derived from a well-defined mathematical expression which
limits its redundancy hence in the paper we are utilizing the two different chaotic maps which are used
alternatively this mathematically increased the randomness of the function. The simulation of the algorithm for
the formulated EOQ problem verifies the effectiveness and superiority of the algorithm over standard
algorithms for such a complex problem which are difficult to solve by analytical approaches.
Solving Multi-level, Multi-product and Multi-period Lot Sizing and Scheduling...Editor IJCATR
In this paper, a new model of capacitated lot sizing and scheduling in a permutation flow shop is developed. In this model
demand can be totally backlogged. Setups can be carryover and are sequence-dependent. It is well-known from literatures that
capacitated lot sizing problem in permutation flow shop systems are NP-hard. This means the model is solved in polynomial time and
metaheuristics algorithms are capable of solving these problems within reasonable computing load. Metaheuristic algorithms find more
applications in recent researches. On this concern this paper proposes two evolutionary algorithms, one of the most popular namely,
Genetic Algorithm (GA) and one of the most powerful population base algorithms namely, Imperialist Competitive Algorithm (ICA).
The proposed algorithms are calibrate by Taguchi method and be compared against a presented lower bound. Some numerical
examples are solved by both the algorithms and the lower bound. The quality of solution obtained by the proposed algorithm showed
superiority of ICA to GA.
Procurement Strategy for Manufacturing and JITIJERD Editor
Procurement involves the purchase of goods and services from the suppliers for the manufacturing units. Procuring the items in the most optimized way is very much desired to implement JIT effectively. Manufacturer-supplier relationship is very crucial for effective procurement policy. The present paper deals with various procurement strategies of manufacturing that include the optimization of manufacturing quantity along with the procurement of multiple input items. The procurement cycles for input items are considered in small lot sizes, which are essential for the effective implementation of JIT. The method of integer programming has been used to find the optimum integer values of number of orders for procuring the input items, which is usually found to be in fraction for a real manufacturing environment.
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a. Observe the critical path diagram. Why are there two arrows pointing to task F? b. Why is the critical path shown as A-B-E-G-I? How is the critical path defined? c. What
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.
A Modified PSO Based Solution Approach for Economic Ordered Quantity Problem ...irjes
This paper presents formulation of Economic Ordered Quantity (EOQ) problem considering Order
Size Limits, Stock Limits and Prohibited Ordering Segments, after that a modified PSO algorithm that utilizes
the PSO with double chaotic maps is presented to solve this problem. In proposed approach, the logistic map
and lozi map are applied alternatively to the velocity updating function of the particles. Using PSO with
irregular velocity updates which is performed by these maps forces the particles to search greater space for best
global solution. However the random function itself derived from a well-defined mathematical expression which
limits its redundancy hence in the paper we are utilizing the two different chaotic maps which are used
alternatively this mathematically increased the randomness of the function. The simulation of the algorithm for
the formulated EOQ problem verifies the effectiveness and superiority of the algorithm over standard
algorithms for such a complex problem which are difficult to solve by analytical approaches.
Solving Multi-level, Multi-product and Multi-period Lot Sizing and Scheduling...Editor IJCATR
In this paper, a new model of capacitated lot sizing and scheduling in a permutation flow shop is developed. In this model
demand can be totally backlogged. Setups can be carryover and are sequence-dependent. It is well-known from literatures that
capacitated lot sizing problem in permutation flow shop systems are NP-hard. This means the model is solved in polynomial time and
metaheuristics algorithms are capable of solving these problems within reasonable computing load. Metaheuristic algorithms find more
applications in recent researches. On this concern this paper proposes two evolutionary algorithms, one of the most popular namely,
Genetic Algorithm (GA) and one of the most powerful population base algorithms namely, Imperialist Competitive Algorithm (ICA).
The proposed algorithms are calibrate by Taguchi method and be compared against a presented lower bound. Some numerical
examples are solved by both the algorithms and the lower bound. The quality of solution obtained by the proposed algorithm showed
superiority of ICA to GA.
Procurement Strategy for Manufacturing and JITIJERD Editor
Procurement involves the purchase of goods and services from the suppliers for the manufacturing units. Procuring the items in the most optimized way is very much desired to implement JIT effectively. Manufacturer-supplier relationship is very crucial for effective procurement policy. The present paper deals with various procurement strategies of manufacturing that include the optimization of manufacturing quantity along with the procurement of multiple input items. The procurement cycles for input items are considered in small lot sizes, which are essential for the effective implementation of JIT. The method of integer programming has been used to find the optimum integer values of number of orders for procuring the input items, which is usually found to be in fraction for a real manufacturing environment.
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a. Observe the critical path diagram. Why are there two arrows pointing to task F? b. Why is the critical path shown as A-B-E-G-I? How is the critical path defined? c. What
ON Fuzzy Linear Programming Technique Applicationijsrd.com
A solution approach based on fuzzy linear programming is proposed and applied to optimal machine scheduling problem. In this solution approach errors in the demand of various products during the next production period are considered to be fuzzy in nature. In conventional linear programming approach it is assumed that there is no error in the expected demand of various products. A fuzzy linear programming approach is proposed to obtain an optimal solution under fuzzy conditions. In the proposed method expected demand of products & profit are expressed by fuzzy set notations. The proposed fuzzy linear programming formulation is then transformed to an equivalent conventional linear programming problem and solutions obtained by solving this transformed linear programming problem. For illustration purpose the proposed method is applied to a profit maximization related machine scheduling problem.
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.
Risk Management Requirements Implementation in ISO 9001:2015 Clauses including Objects and Subjects of Control as well as recommended regulatory document (if provided in the Standard)
ON Fuzzy Linear Programming Technique Applicationijsrd.com
A solution approach based on fuzzy linear programming is proposed and applied to optimal machine scheduling problem. In this solution approach errors in the demand of various products during the next production period are considered to be fuzzy in nature. In conventional linear programming approach it is assumed that there is no error in the expected demand of various products. A fuzzy linear programming approach is proposed to obtain an optimal solution under fuzzy conditions. In the proposed method expected demand of products & profit are expressed by fuzzy set notations. The proposed fuzzy linear programming formulation is then transformed to an equivalent conventional linear programming problem and solutions obtained by solving this transformed linear programming problem. For illustration purpose the proposed method is applied to a profit maximization related machine scheduling problem.
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.
Risk Management Requirements Implementation in ISO 9001:2015 Clauses including Objects and Subjects of Control as well as recommended regulatory document (if provided in the Standard)
AS 9100:2016 and ISO 9001:2015 - Clause 9.3 Management Review : What's New?Meghana Ransing
This presentation gives a holistic overview of key changes in AS9100:2016 and ISO9001:2015. The authors prepared these slides for an invited presentation at the 14th World Conference on Investment Casting held in Paris at the Le Palais des Congrès between 17th and 20th April 2016.
ISO 9001-2015 Revision Training PresentationDQS Inc.
ISO 9001 is a great tool that is used for managing an organization and implementing continuous improvement. More than one million organizations worldwide are certified to ISO 9001 in order to help ensure that good quality products and services are provided to customers.
Get an in-depth overview of the upcoming changes to ISO 9001:2015, including:
- Revision timing and roll out
- Details on structure change
- In-depth review of changes including risk assessment
- Transitioning from ISO 9001:2008 to ISO 9001:2015 timing and requirements
- and more.
The new ISO 9001:2015 committee draft is published and distributed. There are changes which affect organizations who applied this standard. As it is among most famous ISO standards, follow up the changes would be critical and it is time to consider changes which might affect organizations' management systems.
Similar to The (R, Q) Control of A Mixture Inventory Model with Backorders and Lost Sales with Controllable Set Up Cost And Variable Lead Time with Service Level Constraint
Periodic Review Model for Determining Inventory Policy for Aircraft Consumabl...Waqas Tariq
This research is conducted to develop inventory policy of aircraft consumable spare parts which are needed on aircraft maintenance activity . In this research, we used periodic review model to determine the optimal policy of aircraft spare parts inventory. By using the periodic review model, we find optimal period of inventory review and maximum level of inventory. The optimal decision is determined based on the minimum total cost. We have classified consumable spare parts using ABC method to categorize them based on their dollar contribution and demand frequency. Therefore in this research, we focus on managing the inventory level for spare parts on class C. The result from this study shows that the proposed periodic review policy result in lower total inventory cost compared the the company policy. The proposed policy gives an average saving 35.38 %.
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.
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.
Determination Inventory Level for Aircraft Spare Parts Using Continuous Revie...Waqas Tariq
In this paper, we determine ordering quantity and reorder point for aircraft consumable spare parts. We use continuous review model to propose a spare part inventory policy that can be used in a aircraft maintenance company in Indonesia. We employ ABC classification system to categorize the spare parts based on their dollar contribution. We focus our research on managing the inventory level for spare parts on class A and B which commonly known as important classes. The result from the research indicates that the continuous review policy gives a significant amount of saving compared to an existing policy used by the company.
References:
Inventory Control Models, 2013 Pearson Education, Inc. publishing as Prentice Hall
Special Inventory Models, 2010 Pearson Education, Inc. publishing as Prentice Hall
6.3 Further Business Applications: Economic Lot Size
Dr. Grethe Hystad, Mathematics Department, The University of Arizona (www.math.arizona.edu)
Business Dictionary (www.businessdictionary.com)
Bayesian approach for spare parts replenishment policies under uncertaintiesIJERD Editor
The legislative constraints, the need to optimize the dismantling process, the introduction of recycled
parts on the spare parts market are reinforced since the systems in end-of-life phase have become increasingly
profitable. There are few works that treat recycled spare parts integration problem in economic models of
inventory control. These works do not consider uncertainty. In order to manage more realistically the inventory
control of spare parts, we propose a probabilistic model formalized by a Bayesian network. The model is used to
identify the best purchase policy. More precisely, it allows choosing the best proportions between new spare
parts (NSP) and recycled spare parts (RSP) by taking into account the traditional criteria of inventory control
and the availability of the spare parts on the market. The proposed method provides a decision-making tool for
manufacturers who are interested both in reducing the costs of stocks and guaranteeing a minimal availability in
an uncertain environment.
A Fuzzy Arithmetic Approach for Perishable Items in Discounted Entropic Order...Waqas Tariq
This paper uses fuzzy arithmetic approach to the system cost for perishable items with instant deterioration for the discounted entropic order quantity model. Traditional crisp system cost observes that some costs may belong to the uncertain factors. It is necessary to extend the system cost to treat also the vague costs. We introduce a new concept which we call entropy and show that the total payoff satisfies the optimization property. We show how special case of this problem reduce to perfect results, and how post deteriorated discounted entropic order quantity model is a generalization of optimization. It has been imperative to demonstrate this model by analysis, which reveals important characteristics of discounted structure. Further numerical experiments are conducted to evaluate the relative performance between the fuzzy and crisp cases in EnOQ and EOQ separately.
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.
Ops 571 final exam guide (new, 2018) which of the following is a principle of...ramuq12345
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1.
Which of the following is a measure of operations and supply management efficiency used by Wall Street?
Dividend payout ratio
Receivable turnover
Current ratio
Financial leverage
Earnings per share growth
Getting an autograph from a famous person might involve standing in which typ...ramuaa127
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1.
Which of the following is a measure of operations and supply management efficiency used by Wall Street?
Dividend payout ratio
Receivable turnover
Current ratio
Financial leverage
Earnings per share growth
For which of the following should we use a p chart to monitor process qualityyearstart2
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1.
Which of the following is a measure of operations and supply management efficiency used by Wall Street?
Dividend payout ratio
Receivable turnover
Current ratio
Financial leverage
Earnings per share growth
For which of the following should we use a p chart to monitor process qualityramuaa126
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1.
Which of the following is a measure of operations and supply management efficiency used by Wall Street?
Dividend payout ratio
Receivable turnover
Current ratio
Financial leverage
Earnings per share growth
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1. Which of the following is a measure of operations and supply management efficiency used by Wall Street? Dividend payout ratio Receivable turnover Current ratio Financial leverage Earnings per share growth
2. An activity-system map is which of the following? A diagram that shows how a company's strategy is delivered to customers A timeline displaying major planned events A network guide to route airlines A facility layout schematic noting what is done where A listing of activities that make up a project
In hau lee's uncertainty framework to classify supply chainsjohann11371
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1. Which of the following is a measure of operations and supply management efficiency used by Wall Street? Dividend payout ratio Receivable turnover Current ratio Financial leverage Earnings per share growth
2. An activity-system map is which of the following? A diagram that shows how a company's strategy is delivered to customers A timeline displaying major planned events A network guide to route airlines A facility layout schematic noting what is done where A listing of activities that make up a project
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.
Which of the following is a total measure of productivityjohann11373
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1. Which of the following is a measure of operations and supply management efficiency used by Wall Street? Dividend payout ratio Receivable turnover Current ratio Financial leverage Earnings per share growth
2. An activity-system map is which of the following? A diagram that shows how a company's strategy is delivered to customers A timeline displaying major planned events A network guide to route airlines A facility layout schematic noting what is done where A listing of activities that make up a project
An Enhance PSO Based Approach for Solving Economical Ordered Quantity (EOQ) P...IJMER
The Meta-heuristic approaches can provide a sufficiently good solution to an
optimization problem, especially with incomplete or imperfect information and with lower
computational complexity especially for numerical solutions. This paper presents an enhanced PSO
(Particle Swarm Optimization) technique for solving the same problem. Through the PSO performs well
but it may require some more iteration to converge or sometimes many repetitions for the complex
problems. To overcome these problems an enhanced PSO is presented which utilizes the PSO with
double chaotic maps to perform irregular velocity updates which forces the particles to search greater
space for best global solution. Finally the comparison between both algorithms is performed for the
EOQ problem considering deteriorating items, shortages and partially backlogging. The simulation
results shows that the proposed enhanced PSO converges quickly and found much closer solution then
PSO.
Similar to The (R, Q) Control of A Mixture Inventory Model with Backorders and Lost Sales with Controllable Set Up Cost And Variable Lead Time with Service Level Constraint (20)
Cars are a very important part of this modern world because they give luxury and comfort. Even
though they are comfortable, some problems always keep arising on the safety side. After a lot of research they
rectified certain problems using air bags, auto parking, turbo charger, pedal shift…, etc.
And now we are going to discuss about one such problem that arises on the safety side. An unsuspected
accident occurs when people smash their fingers in between the car doors. Due to this kind of accident around
120,000 people are injured every year. But this was not taken as a very major safety concern for the customer.
To avoid this kind accident due to car doors, we are introducing “SAFETY DOOR LOCK SYSTEM”
with the help of “HYDRAULIC PISTON AND IR SENSORS”.
The major working process of the “SAFETY DOOR LOCK SYSTEM”is, when a person places his/her
hand or fingers in the gap between the door and the outer panel, at the time when the closing action of the door
takes place, the Sensors start to transmit the Infra Red Rays to the Receivers at the
other end, and so even if someone closes the door without anybody‟s knowledge the hydraulic piston will
automatically come out and stop the door from closing and prevent the person from the unsuspected accident
and minor injuries by the car door and ensure maximum safety to the customer.
Extrusion can be defined as the process of subjecting a material to compression so that it is forced to
flow through an opening of a die and takes the shape of the hole. Multi-hole extrusion is the process of
extruding the products through a die having more than one hole. Multi-hole extrusion increases the production
rate and reduces the cost of production. In this study the ram force has calculated experimentally for single hole
and multi-hole extrusion. The comparison of ram forces between the single hole and multi-hole extrusion
provides the inverse relation between the numbers of holes in a die and ram force. The experimental lengths of
the extruded products through the various holes of multi-hole die are different. It indicates that the flow pattern
is dependent on the material behavior. The micro-hardness test has done for the extruded products of lead
through multi-hole die. It is observed that the hardness of the extruded lead products from the central hole is
found to be more than that of the products extruded from other holes. The study suggests that multi-hole
extrusion can be used for obtaining the extruded products of lead with varying hardness. The micro-structure
study has done for the lead material before and after extrusion. It is observed that the size of grains of lead
material after extrusion is smaller than the original lead.
Analysis of Agile and Multi-Agent Based Process Scheduling Modelirjes
As an answer of long growing frustration of waterfall Software development life cycle concepts,
agile software development concept was evolved in 90’s. The most popular agile methodologies is the Extreme
Programming (XP). Most software companies nowadays aim to produce efficient, flexible and valuable
Software in short time period with minimal costs, and within unstable, changing environments. This complex
problem can be modeled as a multi-agent based system, where agents negotiate resources. Agents can be used to
represent projects and resources. Crucial for the multi-agent based system in project scheduling model, is the
availability of an effective algorithm for prioritizing and scheduling of task. To evaluate the models, simulations
were carried out with real life and several generated data sets. The developed model (Multi-agent based System)
provides an optimized and flexible agile process scheduling and reduces overheads in the software process as it
responds quickly to changing requirements without excessive work in project scheduling.
Effects of Cutting Tool Parameters on Surface Roughnessirjes
This paper presents of the influence on surface roughness of Co28Cr6Mo medical alloy machined
on a CNC lathe based on cutting parameters (rotational speed, feed rate, depth of cut and nose radius).The
influences of cutting parameters have been presented in graphical form for understanding. To achieve the
minimum surface roughness, the optimum values obtained for rpm, feed rate, depth of cut and nose radius were
respectively, 318 rpm, 0,1 mm/rev, 0,7 mm and 0,8 mm. Maximum surface roughness has been revealed the
values obtained for rpm, feed rate, depth of cut and nose radius were respectively, 318 rpm, 0,25 mm/rev, 0,9
mm and 0,4 mm.
Possible limits of accuracy in measurement of fundamental physical constantsirjes
The measurement uncertainties of Fundamental Physical Constants should take into account all
possible and most influencing factors. One from them is the finiteness of the model that causes the existence of
a-priori error. The proposed formula for calculation of this error provides a comparison of its value with the
actual experimental measurement error that cannot be done an arbitrarily small. According to the suggested
approach, the error of the researched Fundamental Physical Constant, measured in conventional field studies,
will always be higher than the error caused by the finite number of dimensional recorded variables of physicalmathematical
models. Examples of practical application of the considered concept for measurement of fine
structure constant, speed of light and Newtonian constant of gravitation are discussed.
Performance Comparison of Energy Detection Based Spectrum Sensing for Cogniti...irjes
With the rapid deployment of new wireless devices and applications, the last decade has witnessed a growing
demand for wireless radio spectrum. However, the policy of fixed spectrum assignment produces a bottleneck for more
efficient spectrum utilization, such that a great portion of the licensed spectrum is severely under-utilized. So the concept of
cognitive radio was introduced to address this issue.The inefficient usage of the limited spectrum necessitates the
development of dynamic spectrum access techniques, where users who have no spectrum licenses, also known as secondary
users, are allowed to use the temporarily unused licensed spectrum. For this purpose we have to know the presence or
absence of primary users for spectrum usage. So spectrums sensing is one of the major requirements of cognitive radio.Many
spectrum sensing techniques have been developed to sense the presence or absence of a licensed user. This paper evaluates
the performance of the energy detection based spectrum sensing technique in noisy and fading environments.The
performance of the energy detection technique will be evaluated by use of Receiver Operating Characteristics (ROC) curves
over additive white Gaussian noise (AWGN) and fading channels.
Comparative Study of Pre-Engineered and Conventional Steel Frames for Differe...irjes
In this paper, the conventional steel frames having triangular Pratt truss as a roofing system of 60 m
length, span 30m and varying bay spacing 4m, 5m and 6m respectively having eaves level for all the portals is at
10m and the EOT crane is supported at the height of 8m from ground level and pre-engineered steel frames of
same dimensions are analyzed and designed for wind zones (wind zone 2, wind zone 3, wind zone 4 and wind
zone 5) by using STAAD Pro V8i. The study deals with the comparative study of both conventional and preengineered
with respect to the amount of structural steel required, reduction in dead load of the structure.
Flip bifurcation and chaos control in discrete-time Prey-predator model irjes
The dynamics of discrete-time prey-predator model are investigated. The result indicates that the
model undergo a flip bifurcation which found by using center manifold theorem and bifurcation theory.
Numerical simulation not only illustrate our results, but also exhibit the complex dynamic behavior, such as the
periodic doubling in period-2, -4 -8, quasi- periodic orbits and chaotic set. Finally, the feedback control method
is used to stabilize chaotic orbits at an unstable interior point.
Energy Awareness and the Role of “Critical Mass” In Smart Citiesirjes
A Smart City could be depicted as a place, logical and physical, in which a crowd of heterogeneous
entities is related in time and space through different types of interactions. Any type of entity, whether it is a
device or a person, clustered in communities, becomes a source of context-based data.
Energy awareness is able to drive the process of bringing our society to limit energy waste and to optimize
usage of available resources, causing a strong environmental and social impact. Then, following social network
analysis methodologies related to the dynamics of complex systems, it is possible to find out, emergent and
sometimes hidden new habits of electricity usage. Through an initial Critical Mass, involving a multitude of
consumers, each related to more contexts, we evaluate the triggering and spreading of a collective attitude. To
this aim, in this paper, we propose a novel analytical model defining a new concept of critical mass, which
includes centrality measures both in a single layer and in a multilayer social network.
A Firefly Algorithm for Optimizing Spur Gear Parameters Under Non-Lubricated ...irjes
Firefly algorithm is one of the emerging evolutionary approaches for complex and non-linear
optimization problems. It is inspired by natural firefly‟s behavior such as movement of fireflies based on
brightness and by overcoming the constraints such as light absorption, obstacles, distance, etc. In this research,
firefly‟s movement had been simulated computationally to identify the best parameters for spur gear pair by
considering the design and manufacturing constraints. The proposed algorithm was tested with the traditional
design parameters and found the results are at par in less computational time by satisfying the constraints.
The Effect of Orientation of Vortex Generators on Aerodynamic Drag Reduction ...irjes
One of the main reasons for the aerodynamic drag in automotive vehicles is the flow separation
near the vehicle’s rear end. To delay this flow separation, vortex generators are used in recent vehicles. The
vortex generators are commonly used in aircrafts to prevent flow separation. Even though vortex generators
themselves create drag, but they also reduce drag by delaying flow separation at downstream. The overall effect
of vortex generators is more beneficial and proved by experimentation. The effect depends on the shape,size and
orientation of vortex generators. Hence optimized shape with proper orientation is essential for getting better
results.This paper presents the effect of vortex generators at different orientation to the flow field and the
mechanism by which these effects takes place.
An Assessment of The Relationship Between The Availability of Financial Resou...irjes
The availability of financial resources is an important element in impacting the success of a planning
process for an effective physical planning. The extent to which however, they are articulated in the process
remained elusive both in scholarly and public discourse. The objective of this study wastherefore, to examine
the extent to which financial resources affect physical planning. In doing so, the study examinedwhether
financial resources were adequate or not to facilitate planning processes in Paidha. According to the study
findings,budget prioritization and ceilings are still a challenge in Paidha Town Council. This is partly due
limited level of knowledge of physical planning among the officials of Paidha Town Council. As a result, there
were no dedicated budget line for routine inspection of physical development plan compliance and enforcement
tools in Paidha. In conclusion, in addressing uncoordinated patterns of physical development that characterize
Uganda‟s urban centres, a critical starting point ought to be the analysis of physical planning process. The
research of this kind is not only significant to other emerging urban centres facing poor a road network,
mushrooming informal settlements and poor social services including poor pattern of residential and commercial
developments but also to all institutions that are involved in planning these towns. Knowing the extent of need
for financial influences in planning may assist local authorities to take the processes of planning seriously which
will help enhance the sustainable development of emerging urban centres including Paidha.
The Choice of Antenatal Care and Delivery Place in Surabaya (Based on Prefere...irjes
- Person's desire to do a pregnancy examination is determined by the service place that suits the tastes
and facilities owned by it. Until now, the utilization of antenatal care by pregnant women is still low (Mardiana,
2014). The purpose of the study is to analyze factors affecting the utilization of antenatal care and delivery place
in Surabaya city based on the preferences and choice theory.
Type of survey research is cross sectional approach, the population is mothers who have children aged 1-
12 months in Surabaya. The large sample of 250 mothers who have children aged 1-12 months in 2013 is taken
by simple random sampling technique. Variables of the research are the preference elements and steps, choice
elements and steps, utilization of antenatal care and delivery place. Data were collected through questionnaires
and secondary data were then analyzed with descriptive statistics in the form of a frequency distribution, shown
by the schematic diagram.
The result showed that the preference elements and steps showed almost half (42.9%) desire to give birth
in a health care because of information got from someone else, while the choice element and step shows the
bulk (57.1%) of the criteria of delivery place chosen is a safe, comfortable and cheap delivery place, the labor
place which is the main choice most (57.1%) is cheap, comfortable, close.
Conclusion of the research based on the preferences and choice theory can be found three (3) new
theories, they are preferences become choice, preferences do not become choice, choice is preceded by
preferences
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
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More examples of our work https://www.r-r-consult.dk/en/cases-en/
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
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Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
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This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
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Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
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Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
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• Compatible with MAFI CCR system
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Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
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.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...
The (R, Q) Control of A Mixture Inventory Model with Backorders and Lost Sales with Controllable Set Up Cost And Variable Lead Time with Service Level Constraint
1. International Refereed Journal of Engineering and Science (IRJES)
ISSN (Online) 2319-183X, (Print) 2319-1821
Volume 4, Issue 6 (June 2015), PP.50-56
www.irjes.com 50 | Page
The (R, Q) Control of A Mixture Inventory Model with
Backorders and Lost Sales with Controllable Set Up Cost
And Variable Lead Time with Service Level Constraint
Dr Sudipta Sinha
Department of Mathematics Burdwan Raj College Burdwa, West Bengal, Pin- 713104
Abstract:- This paper modifies Chuang et al‟s[6] inventory model by adding service level constraint. In this
study, I investigate the periodic review inventory model with a mixture of back orders and lost sales. The lead
time varies with the ordered quantity. The set-up cost is not constant, it is controllable. Also, instead of having a
stock out cost in the objective function, a service level constraint is employed. Furthermore, with the help of a
numerical example the problem is described.
Keywords:- Mixture inventory, Periodic review, Service level, Lead time,JIT
I. INTRODUCTION
In traditional EOQ and EPQ models, set up cost is treated as constant. However, in practice, set-up cost
can be controlled and reduced through various efforts such as worker training, procedural changes and
specialized equipment acquisition. Through the Japanese experience of using Just-in-Time (JIT) production, the
advantages and benefits associated with efforts to reduce set up cost can clearly be perceived. The ultimate goal
of JIT from an Inventory stand point is to produce small lot-size with good quality, lower investment in
inventory, less scrap and reduced storage space requirement. In order to achieve this goal, investing capital in
reducing set-up cost is regard as one of the effective ways.
According to Silver et al [29] the implementation of electronic data interchange (EDI) may reduce the
fixed set-up cost and result in new replenishment policy and the corresponding lower cost. Nasri et
al[19]studied JIT manufacturing system and pointed out that the impact of investing in reduced set-up cost has
been observed in many manufacturing setting including job shops, batch shops and flow shops. This type of
investment differs from the traditional approach of investment aimed at increasing capacity because, in most
production systems, production scheduling is affected directly by set-up cost. In addition, set-up control has
been a topic of interest for many researchers in the field of inventory/production management. Porteus [23]
studied the impact of capital investment in reducing set-up cost in the standard undiscounted EOQ model.
Porteus [24] later extended this research to consider the discounted model. The effects of set-up cost reduction
on the EOQ model with stochastic lead time is investigated by Nasri et al [19], Kim et al [13] focused on several
classes of set-up cost reduction functions and described a general solution procedure on the EPQ model.
Paknejad et al[22] presented a quality adjusted lot-sizing model with stochastic demand and constant lead time,
and studied the benefits of lower set up cost in the model. Sarkar and Coates[27]extended EPQ model with set
up cost reduction under stochastic lead time and finite number of investment possibilities to reduce set up cost.
Ouyang et al [21] developed a mixture inventory model involving set up cost reduction with a service level
constraint. Chuang et al [6] present a note on periodic review inventory model with controllable set up cost and
lead time.Hariga[10] modified Kim and Benton‟s [12] model by rectifying the annual backorder cost and
proposing another relation for the revised lot-size.Hariga‟s [10] model is more consistent with JIT‟s objectives
in the sense that it results in smaller lot-sizes.
In most of the literature dealing with inventory problems, either deterministic models, lead time is
treated as constant which therefore is not subject to control (Montgomery et al [15], Silver and Peterson[29]).
However it can be controlled and reduced through various efforts. Bendaya et al [2] considered lead time as
decision variable in his inventory model. in his an inventory model In many practical situations lead time can be
reduced at an added crashing cost; in other words, it is controllable. By shortening lead time we can lower the
safety stock, reduce the stock out loss, save product costs and improve the customer service level so as to gain
competitive edges in business. The Japanese experiences of using Just-in-time (JIT) production have evidenced
the advantages and benefits associated with the efforts to reduce lead time. The spirits of JIT emphasizes small
lot production and provide high quality products.The goal of JIT inventory philosophies is the focus that keeps
the inventory level and lead time to a practical minimum. Morton [17] analyzed Toyota production system and
clearly addressed that lead time reduction is a crux of elevating productivity. In real world, in order to avoid the
shortage,we have to maintain a buffer stock and determine the ordering time.Eppen et al [7] and Fotopouls et al
2. The (R, Q) Control Of A Mixture Inventory Model With Backorders And Lost Sales With Controllable Set Up…
www.irjes.com 51 | Page
[8] determined the safety stock.Again reorder level is determined by Ray et al[25] and Urban et al [31] when
demands are correlated.
Recently,several continuous review inventory models have been developed [Liao and
Shyu[14],Baganha et al[1] Beyer et al[3], Cakanyildirim [4], Charnes et al[5] , Moon and Choi [16] Salameh et
al[26]]. But in the periodic review inventory model, literature discussing mixture inventory with service level is
few. The cases of lost sales is considered in most of the inventory models i.e.Nahimas[18] where a demand
occurs when the system is out of stock, is lost for ever.Jonasen et al [11] developed an inventory model of (r,Q)
control with lost sales. In this paper we propose a mixture inventory model i.e.mixture of back order and lost
sales. When stock out occurs, only a fraction γ (0<γ<1) of the unsatisfied demand is backordered and the
remaining fraction is lost. Ouyang[20 ]modified Parknejad et al‟s[22 ]model by considering a mixture of
backorders and lost sales when stock out occurs. Besides instead of having a stock out cost in the objective
function,a service level constraint is included. I solve this inventory model by using the minimax distribution
free approach, which was originally proposed by Scarf [28]and has been disseminated by Gallego and Moon[
9].Silver et al [30 ]studied distribution free approach on some production or inventory models. A numerical
example is solved in support of the model and sensitivity analysis is performed.
II. NOTATIONS
D = Average demand per year
Q = Replenishment order quantity.
L = Length of the lead time
h = Stock holding cost /unit/review interval.
A0= Original set-up cost.
A = Fixed cost of placing a replenishment order.
A*
= Optimal Set-up cost.
EAC= Expected annual cost.
ELS(r) = Expected lost sales incurred during an order cycle when the reorder level is r.
γ= The fraction of the demand during the stock out period that will be backordered, 0≤γ≤1.
μ = Expected demand per unit time.
μL = Expected demand per unit time during lead time where μL = μ L
σ= Standard deviation of the demand per unit time.
σL= Standard deviation of the demand per unit time during lead time where σL = σ L
III. ASSUMPTIONS
The following assumptions are made:
(i) We consider lead time L depends on the ordered quantity i.e. L=√(pQ+b) where p,b are constants.
(ii) The reorder point r =expected demand during lead time +safety stock (SS) and SS =k (standard deviation of
lead time demand) i.e. r =μL+k ở√L where k is the safety factor.
(iii) Inventory is continuously reviewed. Replenishments are made whenever the inventory level falls to the
reorder point r.
IV. MODEL FORMULATION
Ouyang and Chuang [ ] considered an inventory system for a periodic review model with controllable
lead time and asserted the following function of total expected annual cost which is the sum of set-up cost,
holding cost, stock-out cost and lead time crashing cost.
In contrast to the Ouyang and Chung‟s [ ] model,we consider the set-up cost A as a decision variable and seek
to minimize the sum of the capital investment cost of reducing set-up cost A and the inventory related costs[as
expected in (1)] by optimizing over T,a and constrained on 0<A≤ A0, where A0 is the original set-up cost.
Therefore, the objective of our problem is to minimize the following total expected annual cost
EAC(A,Q) = η M(A)+EAC(Q) (1)
over AЄ(0, A0] where η is the fractional opportunity cost of capital per year, M(A) follows a logarithmic
investment function given by
]A(0,Afor)
A
A
ln(
δ
1
M(A) 0
0
(2)
where δ is the percentage decrease in A per dollar increase in investment. This logarithmic investment function
has been utilized by Nasri et al [19],Porteus et al [23].
Therefore from the function (2) we note that the set-up cost level AЄ(0,A0]; It implies that if the optimal set-up
cost obtained does not satisfy the restriction on A,then no set-up cost reduction investment is made.for this
special case,the optimal set-up cost is the original set-up cost.
3. The (R, Q) Control Of A Mixture Inventory Model With Backorders And Lost Sales With Controllable Set Up…
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We have assumed that when stock out occurs, only a fraction γ (0 γ 1) of the unsatisfied demand is
backordered and the lead time demand x has a normal probability density function(p.d.f) f(x) with mean μL and
standard deviation σ√L and the reorder point r= LkL ,where k be defined as safety factor. The expected
number of back orders per cycle is γELS(r) and the expected lost sales per cycle is (1-γ) ELS(r).
The expected net inventory level just before the order arrives is r-μL+(1-γ)ELS(r)
and the expected net inventory level at the beginning of the cycle is
Q+r-μL+(1-γ)ELS(r). Therefore, the expected annual holding cost is h[ )]()1(
2
rELSLr
Q
.An
order of size Q is placed as soon as the inventory position reaches the reorder point r.
In this paper we modify some of the assumptions of Chuang et al‟s [6] as follows
(i) The lead time L =√(pQ+b) depends on the ordered quantity and it is a variable
(ii) Instead of having a stock-out cost term in the objective function, a service level constraint which
implies that the stock-out level per cycle is bounded, is added to the model
Therefore our problem can be expressed as
)ELS(r)]-(1-r
2
Q
h[
Q
AD
A
A
ln
δ
η
A)EAC(Q,Min L
0
(3) subject to the
service level constraint is )1αα(0whereα
Q
ELS(r)
is the proportion of demands which are
not met from the stock and hence 1-α is the service level.
Since the form of the probability distribution of lead time demand is unknown, the exact value of the
expected demand at the end of the cycle ELS(r) can not be obtained, hence Minimax distribution free approach
is applied for the problem.
Let F denote the class of p.d.f.s with finite mean μL and standard deviation σL, then the minimax principle for
this problem is to find the most favourable p.d.f. fx in F for each (Q, L) and then minimize over (Q,L) more
exactly our problem is
Min Max EAC
(Q,L) fxЄF
This task can be achieved by utilizing the following proposition, which was asserted by Gallego and Moon[9 ].
Proposition
(4)}LkσLσkLσ{
2
1
)μ(r)μ(rσ{
2
1
ELS(r)
222
L
2
L
2
L
Moreover, the upper bound of (3) is tight.
Proof: The proof is similar to that of lemma 1 given by Gallego and Moon[9] and hence we omit it.
Since the reorder point r = expected demand during lead time + safety stock
i.e. LkσμLr ; k=safety factor
V. THE BASIC ALGORITHM (GENETIC ALGORITHM)
Genetic Algorithm:
Genetic Algorithm is a class of adaptive search technique based on the principle of population
genetics.The algorithm is an example of a search procedure that uses random choice as a tool to guide a highly
exploitative search through a coding of parameter space.Genetic Algorithm work according to the principles of
natural genetics on a population of string structures representing the problem variables.All these features make
genetic algorithm search robust,allowing them to be applied to a wide variety of problems.
Implementing GA:
The following are adopted in the proposed GA to solve the problem :
(1) Parameters
(2) Chromosome represention
(3) Initial population production
(4) Evaluation
(5) Selection
4. The (R, Q) Control Of A Mixture Inventory Model With Backorders And Lost Sales With Controllable Set Up…
www.irjes.com 53 | Page
(6) Crossover
(7) Mutation
(8) Termination
Parameters
Firstly,we set the different parameters on which this GA depends.all these are the number of generation
(MAXGEN), population size (POPSIZE), probability of crossover(PCROS), probability of mutation (PMUTE).
Chromosome representation
An important issue in applying a GA is to design an appropriate chromosome representation of
solutions of the problem together with genetic operators.Traditional binary vectors used to represent the
chrosones are not effective in many non-linear problems.Since the proposed problem is highly non-linear,hence
to overcome the difficulty,a real-number represention is used.In this representation,each chromosome Vi is a
string of n numbers of genes Gij, (j =1,2,…n) where these n numbers of genes respectively denote n number of
decision variables(Xi, i=1,2,…n).
Initial population production
The population generation technique proposed in the present GA is illustrated by the following
procedure: For each chromosome Vi,every gene Gij is randomly generated between its boundary (LBj,UBj0
where LBj and UBj are the lower and upper bounds of the variables Xj,i= 1,2,….,n and i=1,2,…n, POPSIZE.
Evaluation
Evaluation function plays the some role in GA as that which the environment plays in natural
evalution.Now, evaluation function (EVAL) for the chromosome Vi is equivalent to the objective function
PF(X).These are following steps of evaluation.
Step 1: find EVAL (Vi) by EVAL (Vi) = f(X1,X2,…Xn)
where the genes Gij represent the decision variable Xj, j =1,2,…n, POPSIZE and f is the objective function.
Step 2 : find total fitness of the population : F=
POPSIZE
1i
i )EVAL(V
Step 3 : calculate the probability pi of selection for each chromosome Vi as
i
1j
ji pY
Selection
The selection scheme in GA determines which solutions in the current population are to be selected for
recombination. Many selection schemes, such as Stochastic random sampling, Roulette wheel selection have
been proposed for various problems.In this paper we adopt roulette wheel selection process.
This roulette selection process is based on spinning the roulette wheel POPSIZE times, each time we select a
single chromosome for the new population in the following way:
(a) Generate a random (float) number r between 0 to 1.
(b) If r < Yi then the first chromosome is Vi otherwise select the ith
chromosome
Vi (2 ≤ i ≤ POPSIZE) such that Ti-1 ≤ r ≤ Yi
Crossover
Crossover operator is mainly responsible for the search of new string. The exploration and exploitation
of the solution space is made possible by exchanging genetic information of the current chromosomes.
Crossover operates on two parent solutions at a time and generates offspring solutions by recombining both
parent solution features. After selection chromosomes for new population, the crossover operator is applied.
Here, the whole arithmetic crossover operation is used. It is defined as a linear combination of two consecutive
selected chromosomes Vm and Vn and the resulting offspring‟s
/
mV and are
/
nV calculated as:
/
mV = c.Vm + (1-c).Vn
/
nV = c.Vn + (1-c). Vm
where c is a random number between 0 and 1.
5. The (R, Q) Control Of A Mixture Inventory Model With Backorders And Lost Sales With Controllable Set Up…
www.irjes.com 54 | Page
Mutation
Mutation operator is used to prevent the search process from converging to local optima rapidly.It is
applied to a single chromosome Vi. the selection of a chromosome for mutation is performed in the following
way :
Step 1. Set i ← 1
Step 2. Generate a random number u from the range [0,1]
Step 3. If u < PMUTE,then go to step 2.
Step 4. Set i ← i + 1
Step 5. If i ≤ POPSIZE,then go to Step 2.
Then the particular gene Gij of the chromosome Vi selected by the above mentioned steps is randomly
selected.in this problem,the mutation is defined as
mut
ijG = random number from the range (0,1)
Termination
If the number of iteration is less than or equal to MAXGEN then the process is going on,otherwise it
terminates.
The GA‟s procedure is given below:
begin
do {
t ← 0
while(all constraints are not satisfied)
{
initialize Population (t)
}
evaluate Population(t)
while (not terminate)
{
t ← t +1
select Population(t) from Population(t-1)
crossover and mutate Population(t)
evaluate Population(t)
}
Print Optimum Result
}
end.
VI. NUMERICAL ILLUSTRATION
In order to illustrate the above model, we consider an inventory system with the following datas used
by Chuang et al [6 ],Ouyang et al [20 ] and Ouyang et al[ 21]. The problem is solved by Genetic algorithm.
h = $15.0, A =50.0/per review ,D=600.0units per cycle,,σ =7.0, μ=5.0
TABLE: 1
α =0.02 SL=98%
Changing
parameter
Change in
parameter Set-up cost reduction Fixed set-up cost
Optimal
Order(Q)
A*
EAC Optimal
Order(Q)
EAC Savings
(%)
γ
0.0
0.5
0.8
1.0
229.2161
233.5628
243.8241
248.4321
42.93
48.49
49.26
54.17
1238.33
1173.53
1152.34
1120.30
332.7788
337.3219
361.3425
368.3217
1309.77
1246.78
1224.93
1202.76
5.77
6.24
6.30
7.36
6. The (R, Q) Control Of A Mixture Inventory Model With Backorders And Lost Sales With Controllable Set Up…
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TABLE: 2
α =0.015 SL=98.5%
Changing
parameter
Change in
parameter Set-up cost reduction Fixed set-up cost
Optimal
Order(Q) A*
EAC Optimal
Order(Q)
EAC Savings
(%)
γ
0.0
0.2
0.3
0.4
235.3206
255.8502
259.9286
266.8764
43.73
46.51
50.16
55.87
1245.68
1212.13
1172.61
1144.58
339.5959
378..7718
386.o445
397.0433
1315.61
1282.19
1246.17
1227.30
5.61
5.77
6.27
7.23
TABLE: 3
α =0.01 SL=99%
Changing
parameter
Change in
parameter
Set-up cost reduction Fixed set-up cost
Optimal
Order(Q) A*
EAC Optimal
Order(Q)
EAC Savings
(% )
γ
0.0
0.5
0.8
1.0
239.4417
256.4844
260.3799
267.6839
43.89
46.98
50.94
56.03
1251.86
1201.67
1171.18
1145.30
342.2090
381.0924
386.8227
396.8971
1317.90
1284.31
1246..89
1227.17
5.28
5.99
6.46
7.14
VII. RESULT DISCUSSION
From Table-1 to 3 we can infer that as γ increases optimal order quantity also increases.Total cost are
decreased for both cases i.e. for set-up cost reduction and fixed set-up cost. Percentage of savings is increased
due to set-up cost reduction for various service levels.
VIII. CONCLUSION
The purpose of this paper is to present a mixture of backorders and lost sales periodic review inventory
control for minimizing the sum of the ordering cost, holding cost and backorder. A service level constraint is
added instead of stockout cost. The optimal reorder level and lot-size for various service levels are determined.
From the above table we infer that as γ increases the reorder point also increases but the lot-size and the
total cost decreases.
REFERENCES
[1]. Baganha. M. P, Pyke. D. F, Ferrer, (1996), “The undershoot of the reorder point, Tests of an
approximation”,International Journal Of Production Economics, 45, 311-320.
[2]. Ben-daya. M and raof. A (1994), „Inventory models involvig lead time as decision variable”,Journal of
Operational Research Society,45,579-582.
[3]. Beyer. D, (1994), “An inventory model with Weiner demand process and positive lead time”,
Optimization, 29, 181-193
[4]. Cakanyildirim,M; Bookbinder,JH and Gerchak,Y.(2000), “Contious review inventory models where
random lead time depends on lot size and reserved capacity”,Int.J. Production Economics, 68,217-228.
[5]. Charnes J.M.,Marmorstein H and Zinn W(1995) Safely stock determination with serially correlated
demand in a periodic review inventory system.J.Opl.Res Soc 46:1006-1013.
[6]. Chuang,B.R.,Ouyang,L.Y. and Chuang,K.W.(2004) “A note on periodic review inventory model with
controllable set up cost and lead time”. Computers and Operations Research, vol.31, pp.549-561.
[7]. Eppen,GD and Martin RK (1988) , “Determining safety stock in the presence of stochastic lead time
and demand” ,Mgmt Science,34,1380-1390.
[8]. Foto pouls S. Wang MC and Rao SS, (1988), “Safety stock determination with correlated demands and
arbitrary lead times”. Eur J. Opl Res, 35, 172-181.
[9]. Gallego. G. and Moon. I, (1993) “The distributions free news boy problem review and extensions.”
Journal of Operational Research Society, 44, 825-834.
7. The (R, Q) Control Of A Mixture Inventory Model With Backorders And Lost Sales With Controllable Set Up…
www.irjes.com 56 | Page
[10]. Hariga. G (1999), “A stoachstic inventory model with lead time and lot-size interaction”,Production
Planning & Control,10,434 – 438.
[11]. Jonansen. S. G. and Hill. R. M, (2000), “The (r,Q) Control of a periodic- review inventory system with
continuous demand and lost sales”, Int. J. Production Economics 68, 279-286.
[12]. Kim,J.S. and Benton,W.C.(1995), “Lot-size dependent lead times in a (Q,r) inventory system”,
International Journal of Production Research,33,41-58.
[13]. Kim;K.L; Hayya J.C and Hong,J.D, (1992), “Set-up reduction in economic production quantity
model”,Deciison Sciences,1992, 23,500-508.
[14]. Liao, CJ and Shyu,CH (1991), “An analytical determination of lead time with normal demand”,
International Journal Of Production Economics,11,72-78.
[15]. Montgomery DC, Bazaraa MS and Keswani AK, (1973), “Inventory models with a mixture of back
orders and lost sales”, Naval Research Logistics Quarterly, 20, 255-263.
[16]. Moon and Choi. S, (1994), “The distribution free continuous review inventory system with a service
level constraint”, Comp Ind Eng, 27, 213-216.
[17]. Morton, TE, (1971), “The near-myopic nature of the hagged-proportional cost inventory problem with
lost sales”. Operations Research 19, 1708-1716.
[18]. Nahmias. S, (1978), “Simple approximations for a variety of dynamic lead time lost-sales inventory
models”. Operations Rescarch 27, 904-924.
[19]. Nasri.F,Affisco.J.F. and Paknejad,M.J.(1990), “Set-up cost reduction in a inventory model with finite
range stochastic lead times”, International Journal of Production Research, Vol.28,pp.199-212.
[20]. Ouyang, LY; Yeh NC and Wu,KS, (1996), “Mixture inventory model with backorders and lost sales
for variable lead time”, Opsearch, Vol. 37, No. 4 ,327-339.
[21]. Ouyang, LY and Chang HC, (2000), “Mixture inventory model involving setup cost reduction with a
service level constraint”, Journal of Opl Res Soc, Vol. 47, 829-832.
[22]. Paknejad MJ, Nasri F and Affisco JF, (1995), “Defective units is a continuous review (s,Q) system, Int.
J. prod. Res, 33, 2767-2777.
[23]. Porteus,E.L.(1985), “Investing in reduced set-ups in the EOQ model”, Management Sciences,
Vol.31,pp.998-1010.
[24]. Porteus,E.L.(1986), “Investing in new parameter values in the discounted EOQ model”, Naval
Research Logistics,Vol.33,pp. 39-48.
[25]. Ray, WD (1981), “Computation of reorder levels when the demands are correlated and the lead time
random”.Journal of Opl Res Soc 32: 27-34.
[26]. Salameh,M.K;Abboud,N.E. El-Kassar,A.N. and Ghattas,RE,(2003),Continuous review inventory
model with delay in payments,International Journal Of Production Economics,85, 91-95.
[27]. Sarkar,B.R and Coates, I.R (1990), “Manufacturing set-up cost reduction under variable lead times and
finite opportunities for investment”, International Journal of Priduction Economics,49,237-247.
[28]. Scarf,H (1958), “Studies in the mathematical theory of inventory and production”,Stanford University
Press,Stanford,California.
[29]. Silver, EA and Peterson,R.(1985), “Decision systems for inventory management and production
planning”, New York:Wiley.
[30]. Silver,EA, Pyke DF and Peterson R, (1998) “Inventory Management and production planning and
scheduling”, John Wiley, New York
[31]. Urban,T.L.(2000) “Reorder level determination with serially correlated demand”, Journal of
Operational Research Society, 51,762-768.