This document presents a mathematical model that links a flow shop scheduling problem to a parallel biserial queue network. The model considers jobs arriving to two parallel queues according to Poisson processes, then merging into a common third queue before entering a flow shop with two machines. The completion times from the queue network provide setup times for the first machine. The objective is to find a job sequence for the flow shop that minimizes total flow time, including job block criteria where some jobs have priority over others. An algorithm is proposed and assumptions are provided for analyzing the combined queueing and scheduling system.
This document describes the steps taken to clean and explore an automobile dataset. It discusses:
1) Importing libraries and data, removing whitespace, correcting typos and impossible values, and handling missing data.
2) Exploring the data by examining safety levels with histograms, body types with pie charts, and mileage distributions. Hypotheses about horsepower vs mileage, price differences by manufacturer, and mileage relationships with cylinders are explored with scatter plots.
3) A scatter matrix is created to examine relationships between all 15 numerical variables.
Application Of Local Search Methods For Solving A Quadratic Assignment Probl...ertekg
Download Link > https://ertekprojects.com/gurdal-ertek-publications/blog/application-of-local-search-methods-for-solving-a-quadratic-assignment-problem-a-case-study/
This paper discusses the design and application of local search methods to a real-life application at a steel cord manufacturing plant. The case study involves a layout problem that can be represented as a Quadratic Assignment Problem (QAP). Due to the nature of the manufacturing process, certain machinery need to be allocated in close proximity to each other. This issue is incorporated into the objective function through assigning high penalty costs to the unfavorable allocations. QAP belongs to one of the most difficult class of combinatorial optimization problems, and is not solvable to optimality as the number of facilities increases. We implement the well-known local search methods, 2-opt, 3-opt and tabu search. We compare the solution performances of the methods to the results obtained from the NEOS server, which provides free access to many optimization solvers on the internet.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
This 3 sentence summary provides the high level and essential information from the document:
The document discusses optimal assembly plans and control policies for networks of parallel queues with finite buffer sizes. It presents a cost model that considers both the quality of service cost and server holding cost. The problem is formulated as determining the number of processors for each queue and a routing policy to minimize the total cost, with the goal of maximizing the probability that all queues have a certain minimum number of occupied processors.
Discrete Time Batch Arrival Queue with Multiple VacationsIJERDJOURNAL
ABSTRACT:- In this paper we consider a discrete time batch arrival queueing system with multiple vacations. It is assume that the service of customers arrived in the system between a fixed intervals of time after which the service goes on vacations after completion of one service of cycle is taken up at the boundaries of the fixed duration of time. This is the case of late arrival. In case of early arrival i.e. arrival before the start of next cycles of service. If the customer finds the system empty, it is served immediately. We prove the Stochastic decomposition property for queue length and waiting time distribution for both the models.
IRJET- Two-Class Priority Queueing System with Restricted Number of Priority ...IRJET Journal
This document summarizes a research paper that analyzes a two-class priority queueing system with a restricted number of high priority customers and catastrophes. The system has Poisson arrivals for each class and exponential service times. Customers are served with preemptive priority, where high priority customers preempt low priority service. The paper derives the generating function and steady-state probabilities for the number of customers in each class. It then uses this to obtain expressions for performance measures like the mean queue length. The impact of catastrophes on the system is also studied.
This document discusses adaptive system-level scheduling under fluid traffic flow conditions in multiprocessor systems. It proposes a scheduling mechanism that accounts for traffic-centric system design. The mechanism evaluates scheduling methods based on effectiveness, robustness, and flexibility. It also introduces a processor-FPGA scheduling approach that reduces schedule length by taking advantage of FPGA reconfiguration. Simulation results show that processor-FPGA scheduling outperforms multiprocessor-only scheduling under certain traffic conditions. Future work will focus on formulating a traffic-centric scheduling method.
A Novel Cosine Approximation for High-Speed Evaluation of DCTCSCJournals
This article presents a novel cosine approximation for high-speed evaluation of DCT (Discrete Cosine Transform) using Ramanujan Ordered Numbers. The proposed method uses the Ramanujan ordered number to convert the angles of the cosine function to integers. Evaluation of these angles is by using a 4th degree Polynomial that approximates the cosine function with error of approximation in the order of 10^-3. The evaluation of the cosine function is explained through the computation of the DCT coefficients. High-speed evaluation at the algorithmic level is measured in terms of the computational complexity of the algorithm. The proposed algorithm of cosine approximation increases the overhead on the number of adders by 13.6%. This algorithm avoids floating-point multipliers and requires N/2log2N shifts and (3N/2 log2 N)- N + 1 addition operations to evaluate an N-point DCT coefficients thereby improving the speed of computation of the coefficients .
Investigative Compression Of Lossy Images By Enactment Of Lattice Vector Quan...IJERA Editor
In the digital era we live in, efficient representation of data generated by a discrete source and its reliable transmission are unquestionable need. In this work we have focused on source coding taking image as source. Lattice Vector Quantization (LVQ) can be used for source coding as well as for channel coding. (LVQ) with Generator Matrix (GM) and codebook is implemented. When implementation using codebook is done, two codebooks are constructed, one with 256 lattice points that are closest to (0,0,0,0) and another with 256 lattice points that are closest to (1,0,0,0). Energy for both the codes is calculated. When we compare the energy of both the codes we find that codes centered at a non lattice point is lower energy code.
This document describes the steps taken to clean and explore an automobile dataset. It discusses:
1) Importing libraries and data, removing whitespace, correcting typos and impossible values, and handling missing data.
2) Exploring the data by examining safety levels with histograms, body types with pie charts, and mileage distributions. Hypotheses about horsepower vs mileage, price differences by manufacturer, and mileage relationships with cylinders are explored with scatter plots.
3) A scatter matrix is created to examine relationships between all 15 numerical variables.
Application Of Local Search Methods For Solving A Quadratic Assignment Probl...ertekg
Download Link > https://ertekprojects.com/gurdal-ertek-publications/blog/application-of-local-search-methods-for-solving-a-quadratic-assignment-problem-a-case-study/
This paper discusses the design and application of local search methods to a real-life application at a steel cord manufacturing plant. The case study involves a layout problem that can be represented as a Quadratic Assignment Problem (QAP). Due to the nature of the manufacturing process, certain machinery need to be allocated in close proximity to each other. This issue is incorporated into the objective function through assigning high penalty costs to the unfavorable allocations. QAP belongs to one of the most difficult class of combinatorial optimization problems, and is not solvable to optimality as the number of facilities increases. We implement the well-known local search methods, 2-opt, 3-opt and tabu search. We compare the solution performances of the methods to the results obtained from the NEOS server, which provides free access to many optimization solvers on the internet.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
This 3 sentence summary provides the high level and essential information from the document:
The document discusses optimal assembly plans and control policies for networks of parallel queues with finite buffer sizes. It presents a cost model that considers both the quality of service cost and server holding cost. The problem is formulated as determining the number of processors for each queue and a routing policy to minimize the total cost, with the goal of maximizing the probability that all queues have a certain minimum number of occupied processors.
Discrete Time Batch Arrival Queue with Multiple VacationsIJERDJOURNAL
ABSTRACT:- In this paper we consider a discrete time batch arrival queueing system with multiple vacations. It is assume that the service of customers arrived in the system between a fixed intervals of time after which the service goes on vacations after completion of one service of cycle is taken up at the boundaries of the fixed duration of time. This is the case of late arrival. In case of early arrival i.e. arrival before the start of next cycles of service. If the customer finds the system empty, it is served immediately. We prove the Stochastic decomposition property for queue length and waiting time distribution for both the models.
IRJET- Two-Class Priority Queueing System with Restricted Number of Priority ...IRJET Journal
This document summarizes a research paper that analyzes a two-class priority queueing system with a restricted number of high priority customers and catastrophes. The system has Poisson arrivals for each class and exponential service times. Customers are served with preemptive priority, where high priority customers preempt low priority service. The paper derives the generating function and steady-state probabilities for the number of customers in each class. It then uses this to obtain expressions for performance measures like the mean queue length. The impact of catastrophes on the system is also studied.
This document discusses adaptive system-level scheduling under fluid traffic flow conditions in multiprocessor systems. It proposes a scheduling mechanism that accounts for traffic-centric system design. The mechanism evaluates scheduling methods based on effectiveness, robustness, and flexibility. It also introduces a processor-FPGA scheduling approach that reduces schedule length by taking advantage of FPGA reconfiguration. Simulation results show that processor-FPGA scheduling outperforms multiprocessor-only scheduling under certain traffic conditions. Future work will focus on formulating a traffic-centric scheduling method.
A Novel Cosine Approximation for High-Speed Evaluation of DCTCSCJournals
This article presents a novel cosine approximation for high-speed evaluation of DCT (Discrete Cosine Transform) using Ramanujan Ordered Numbers. The proposed method uses the Ramanujan ordered number to convert the angles of the cosine function to integers. Evaluation of these angles is by using a 4th degree Polynomial that approximates the cosine function with error of approximation in the order of 10^-3. The evaluation of the cosine function is explained through the computation of the DCT coefficients. High-speed evaluation at the algorithmic level is measured in terms of the computational complexity of the algorithm. The proposed algorithm of cosine approximation increases the overhead on the number of adders by 13.6%. This algorithm avoids floating-point multipliers and requires N/2log2N shifts and (3N/2 log2 N)- N + 1 addition operations to evaluate an N-point DCT coefficients thereby improving the speed of computation of the coefficients .
Investigative Compression Of Lossy Images By Enactment Of Lattice Vector Quan...IJERA Editor
In the digital era we live in, efficient representation of data generated by a discrete source and its reliable transmission are unquestionable need. In this work we have focused on source coding taking image as source. Lattice Vector Quantization (LVQ) can be used for source coding as well as for channel coding. (LVQ) with Generator Matrix (GM) and codebook is implemented. When implementation using codebook is done, two codebooks are constructed, one with 256 lattice points that are closest to (0,0,0,0) and another with 256 lattice points that are closest to (1,0,0,0). Energy for both the codes is calculated. When we compare the energy of both the codes we find that codes centered at a non lattice point is lower energy code.
Low complexity design of non binary ldpc decoder using extended min-sum algor...eSAT Journals
This document summarizes a research paper on reducing the computational complexity of non-binary LDPC decoders using an extended min-sum algorithm. It introduces low-density parity check codes and non-binary LDPC codes. It then describes an extended min-sum decoding algorithm and proposes two modifications to the parity check matrix - a lower diagonal matrix and a doubly diagonal matrix - to reduce complexity while maintaining performance. Simulation results on code lengths of 504 and 648 bits show the doubly diagonal matrix achieves the best bit error rate. Analysis finds the lower diagonal matrix has the lowest computational complexity of the approaches.
The document discusses solving two telecommunications network design problems:
1) The Caldata network is separated into two parts and each demand is separated, allowing the problem to be quickly solved. The total optimal cost is $37,731,000 and the optimal ADM locations are provided.
2) For the Barry network, the problem is separated into two groups and the connection points are combined, creating a lower bound model. Running the two groups separately and accounting for transfer costs provides the optimal solution. This approach allows getting a reasonable solution faster than solving the full model.
Comparative Analysis of Job Scheduling for Grid Environment ............................................................1
Neeraj Pandey, Ashish Arya and Nitin Kumar Agrawal
Hackers Portfolio and its Impact on Society ........................................................................................1
Dr. Adnan Omar and Terrance Sanchez, M.S.
Ontology Based Multi-Viewed Approach for Requirements Engineering ..............................................1
R. Subha and S. Palaniswami
Modified Colonial Competitive Algorithm: An Approach for Graph Coloring Problem ..........................1
Hojjat Emami and Parvaneh Hasanzadeh
Security and Privacy in E-Passport Scheme using Authentication Protocols and Multiple Biometrics
Technology ........................................................................................................................................1
V. K. Narendira Kumar and B. Srinivasan
Comparative Study of WLAN, WPAN, WiMAX Technologies ................................................................1
Prof. Mangesh M. Ghonge and Prof. Suraj G. Gupta
A New Method for Web Development using Search Engine Optimization ............................................1
Chutisant Kerdvibulvech and Kittidech Impaiboon
A New Design to Improve the Security Aspects of RSA Cryptosystem ..................................................1
Sushma Pradhan and Birendra Kumar Sharma
A Hybrid Model of Multimodal Approach for Multiple Biometrics Recognition ...................................1
P. Prabhusundhar, V.K. Narendira Kumar and B. Srinivasan
An Algorithm for Optimized Cost in a Distributed Computing SystemIRJET Journal
This document summarizes an algorithm for optimized cost allocation in a distributed computing system. The algorithm considers a set of tasks that need to be assigned to processors across multiple phases. It calculates execution costs, residing costs, communication costs, and reallocation costs to determine the optimal allocation that minimizes overall system costs. The algorithm is demonstrated on a sample problem involving 4 tasks to be allocated across 2 processors over 5 phases. Cost matrices are provided and the algorithm partitions the problem into subproblems to determine the lowest cost allocation for each phase and overall.
Design of a Novel Multiplier and Accumulator using Modified Booth Algorithm w...IRJET Journal
The document describes a novel design for a multiplier and accumulator (MAC) unit using the modified Booth algorithm and parallel self-timed adder (PASTA). The modified Booth algorithm reduces the number of partial products compared to a regular multiplication process, lowering delay. A carry save adder design is also proposed to further improve performance in terms of computation speed, power consumption, and area compared to a conventional design using the modified Booth algorithm. Simulation results show the proposed MAC design with PASTA has better performance and reduced area overhead and critical path delay compared to conventional methods.
REDUCING FREQUENCY OF GROUP REKEYING OPERATIONcsandit
In the past, Ad-hoc networks were used in limited areas which require secure group communication without Internet access, such as the army or emergencies. However, Ad-hoc networks currently are widely used in variety applications like group chat, smart applications, research testbed etc. Ad-hoc network is basically group based network in the absence of access point so it is prevalent to provide group key approach to prevent information leakage. When we use group key approach, we need to consider which group key management method is the most suitable for the architecture because the cost and frequency of the rekeying operation remain as an unresolved issue. In this paper, we present analysis about existing group key management solutions for Ad-hoc network and suggest a new approach to reduce frequency of the rekeying operation.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document proposes an optimized algorithm for parallel bitonic sort on modern coarse-grained parallel machines. The key ideas are:
1) Previous approaches remap data between blocked and cyclic layouts after each stage, but the optimal approach is to remap only after lg(N/P) steps to minimize communication.
2) By analyzing the bit patterns compared in each step, the algorithm derives a data layout that allows lg(N/P) consecutive local steps before the next remap.
3) Experimental results on a 64-node parallel machine show the approach reduces communication and outperforms previous bitonic sort implementations.
Research of 64-bits RISC Dual-core Microprocessor with High Performance and L...TELKOMNIKA JOURNAL
A 64-bits RISC Dual-Core microprocessor with high performance and low power consumption is
presented in this paper. The processor has a symmetric architecture with two cores. Each of them has
three stage pipeline, 64-bit data-path and 64-bit address port. A novel shared register module, redundant
Booth3 algorithm and leapfrog Wallace tree architecture are introduced to the microprocessor, and both
the performance and power consumption of it has been improved enormously. As the FPGA simulation
result indicates, the power consumption is decreased by 14% and the longest data-path is shortened by
25%.
High Speed Signed multiplier for Digital Signal Processing ApplicationsIOSR Journals
This document discusses high speed multiplier architectures for digital signal processing applications. It begins by introducing the importance of fast multiplication in DSP algorithms. It then describes the Vedic multiplication algorithm and how it can be implemented for 4-bit and 8-bit numbers using the Urdhva Tiryakbhyam technique. Next, it introduces the Booth encoding technique for radix-8 multiplication and discusses how it reduces the number of partial products. Simulation results are shown comparing the Vedic and radix-8 multiplier architectures. The radix-8 multiplier is concluded to have better performance in terms of power, delay, and power-delay product, making it well-suited for DSP applications.
11.flow shop scheduling problem, processing time associated with probabilitie...Alexander Decker
The document presents a heuristic algorithm for solving an n-job, 3-machine flow shop scheduling problem where processing times are associated with probabilities involving transportation time, breakdown intervals, job weights, and job block criteria. The algorithm aims to find an optimal or near-optimal sequence that minimizes total elapsed time when considering mean weighted production flow time. It uses Johnson's rule and introduces fictitious machines to handle transportation times, job weights, and job blocks before determining the optimal sequence. The algorithm is demonstrated through a numerical example involving 5 jobs.
Flow shop scheduling problem, processing time associated with probabilities i...Alexander Decker
This document summarizes a research paper that proposes a new heuristic algorithm for solving an n-job, 3-machine flow shop scheduling problem where processing times are associated with probabilities involving transportation time, breakdown intervals, job weights, and job block criteria. The algorithm aims to find an optimal or near-optimal sequence that minimizes the total elapsed time when considering the mean weighted production flow time. Notations used in the model and problem formulation are defined.
Parallel Line and Machine Job Scheduling Using Genetic AlgorithmIRJET Journal
This document summarizes research on using a genetic algorithm to solve a parallel line and machine job scheduling problem. The objective is to minimize the makespan (completion time) of all jobs. A genetic algorithm is applied that represents possible job schedules as chromosomes. The fitness function evaluates schedules based on makespan. Genetic operators like crossover and mutation create new schedules from existing ones. The algorithm was tested on sample job data using a MATLAB program. Results showed the genetic algorithm approach can find optimal job allocations and schedules that minimize makespan for parallel line scheduling problems.
Constrained flow shop scheduling with n jobs, 3-machines, processing time ass...Alexander Decker
This document presents a heuristic algorithm for solving a constrained flow shop scheduling problem involving n jobs, 3 machines, and processing times associated with probabilities involving transportation time, breakdown intervals, and job weights. The algorithm calculates expected processing times, checks for standard problem formulation, introduces fictitious machines G and H, applies Johnson's algorithm to obtain sequences, evaluates sequences based on weighted mean flow time, incorporates breakdown effects, and repeats to obtain an optimal sequence. A computer program in C++ is provided to implement the algorithm and clarify it through a numerical example.
Heuristic approach for bicriteria in constrained three stage flow shop schedu...Alexander Decker
This document presents a heuristic approach for solving a bicriteria scheduling problem to minimize total elapsed time and rental cost of machines in a three-stage flow shop. The problem considers processing times, setup times, transportation times between machines, machine breakdown intervals, and job block priorities. A numerical example is provided to illustrate the algorithm. The goal is to find a job sequence that minimizes both the total machine rental costs and overall completion time.
Bicriteria in n x 3 flow shop scheduling under specified rental policyAlexander Decker
This document summarizes a research paper that studies scheduling n jobs across 3 machines in a flowshop configuration, with the goal of minimizing both the total rental cost of the machines and the makespan (completion time of the last job). It considers factors like probabilistic processing times, transportation times between machines, and job blocking (prioritizing some jobs). The researchers propose a heuristic algorithm based on Johnson's rule to find near-optimal schedules. They define notation related to job sequences, machine times, costs and develop equations for completion times under the rental policy. The paper aims to extend previous work on bicriteria scheduling to include these additional real-world complexities.
An efficient simulated annealing algorithm for a No-Wait Two Stage Flexible F...ijait
In this paper, no wait two stage flexible flow shop scheduling problem (FFSSP) is solved using two metaheuristic algorithms. This problem with minimum makespan performance measure is NP-Hard. The proposed algorithms are Simulated Annealing and Genetic Algorithm. The results are analyzed in terms of Relative Percentage Deviation of Makespan. The performance of the proposed algorithms are studied and compared with that of MDA algorithm. For this propose a number of problems in different sizes are solved. The results of the studies proposes the effective algorithm. This is followed by describing the
outline of the study, concluding remarks and suggesting potential areas for further researches
11.bicriteria in n x 0003www.iiste.org call for paper flow shop scheduling un...Alexander Decker
This document discusses a mathematical model for optimizing a three machine flow shop scheduling problem with the objectives of minimizing total rental costs and makespan. Processing times have associated probabilities and transportation times between machines are considered. A heuristic algorithm is proposed based on Johnson's rule to find a near-optimal sequence that minimizes costs while rental under a specified policy. Theorems are presented to show that starting machine processing at certain times does not increase makespan. The model aims to find sequences that minimize total rental costs subject to minimizing makespan.
Bicriteria in n x 3 flow shop scheduling under specified rental policy (2)Alexander Decker
This document discusses a mathematical model for optimizing a three machine flow shop scheduling problem with the objectives of minimizing total rental costs and makespan. Processing times have associated probabilities and transportation times between machines are considered. A heuristic algorithm is proposed based on Johnson's rule to find a near optimal sequence that minimizes costs while rental under a specified policy. The key aspects addressed include equivalent job blocks, idle times, and theoretical results showing the algorithm does not increase makespan by starting machine processing at certain times.
A M ULTI -O BJECTIVE B ASED E VOLUTIONARY A LGORITHM AND S OCIAL N ETWOR...IJCI JOURNAL
In this paper, a multi-objective based NSGA-II algo
rithm is proposed for dynamic job-shop scheduling
problem (DJSP) with random job arrivals and machine
breakdowns. In DJSP schedules are usually
inevitable due to various unexpected disruptions. T
o handle this problem, it is necessary to select
appropriate key machines at the beginning of the si
mulation instead of random selection. Thus, this pa
per
seeks to address on approach called social network
analysis method to identify the key machines of the
addressed DJSP. With identified key machines, the e
ffectiveness and stability of scheduling i.e., make
span
and starting time deviations of the computational c
omplex NP-hard problem has been solved with propose
d
multi-objective based hybrid NSGA-ll algorithm. Sev
eral experiments studies have been conducted and
comparisons have been made to demonstrate the effic
iency of the proposed approach with classical multi
-
objective based NSGA-II algorithm. The experimental
results illustrate that the proposed method is ver
y
effective in various shop floor conditions
Planning and Scheduling of a Corrugated Cardboard Manufacturing Process in IoTijtsrd
The automation has revolutionized the traditional product development scheme by using advanced design and manufacturing technologies such as computer aided design, process planning, and scheduling. However, research in this field was still based mostly on experimentation, as most manufacturing companies did not use simulation techniques in the implementation of their manufacturing planning and scheduling process. In order to address this problem, software developers have put simulation software tools in the market such as Enterprise Resource Planning ERP , Advanced Planning and Scheduling APS , and Risk based Planning and Scheduling RPS systems. In this paper, a methodology to model high degree of accuracy for the production floor, the planning and scheduling of corrugated cardboard manufacturing process through RPS simulation in Internet of Things IoT environment is established. The RPS model is able to generate a deterministic schedule without randomness, create a risk analysis of the planning and scheduling, and handle the uncertainty. Bruno Kemen | Sarhan M. Musa "Planning and Scheduling of a Corrugated Cardboard Manufacturing Process in IoT" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, URL: https://www.ijtsrd.com/papers/ijtsrd37965.pdf Paper URL : https://www.ijtsrd.com/engineering/electrical-engineering/37965/planning-and-scheduling-of-a-corrugated-cardboard-manufacturing-process-in-iot/bruno-kemen
Low complexity design of non binary ldpc decoder using extended min-sum algor...eSAT Journals
This document summarizes a research paper on reducing the computational complexity of non-binary LDPC decoders using an extended min-sum algorithm. It introduces low-density parity check codes and non-binary LDPC codes. It then describes an extended min-sum decoding algorithm and proposes two modifications to the parity check matrix - a lower diagonal matrix and a doubly diagonal matrix - to reduce complexity while maintaining performance. Simulation results on code lengths of 504 and 648 bits show the doubly diagonal matrix achieves the best bit error rate. Analysis finds the lower diagonal matrix has the lowest computational complexity of the approaches.
The document discusses solving two telecommunications network design problems:
1) The Caldata network is separated into two parts and each demand is separated, allowing the problem to be quickly solved. The total optimal cost is $37,731,000 and the optimal ADM locations are provided.
2) For the Barry network, the problem is separated into two groups and the connection points are combined, creating a lower bound model. Running the two groups separately and accounting for transfer costs provides the optimal solution. This approach allows getting a reasonable solution faster than solving the full model.
Comparative Analysis of Job Scheduling for Grid Environment ............................................................1
Neeraj Pandey, Ashish Arya and Nitin Kumar Agrawal
Hackers Portfolio and its Impact on Society ........................................................................................1
Dr. Adnan Omar and Terrance Sanchez, M.S.
Ontology Based Multi-Viewed Approach for Requirements Engineering ..............................................1
R. Subha and S. Palaniswami
Modified Colonial Competitive Algorithm: An Approach for Graph Coloring Problem ..........................1
Hojjat Emami and Parvaneh Hasanzadeh
Security and Privacy in E-Passport Scheme using Authentication Protocols and Multiple Biometrics
Technology ........................................................................................................................................1
V. K. Narendira Kumar and B. Srinivasan
Comparative Study of WLAN, WPAN, WiMAX Technologies ................................................................1
Prof. Mangesh M. Ghonge and Prof. Suraj G. Gupta
A New Method for Web Development using Search Engine Optimization ............................................1
Chutisant Kerdvibulvech and Kittidech Impaiboon
A New Design to Improve the Security Aspects of RSA Cryptosystem ..................................................1
Sushma Pradhan and Birendra Kumar Sharma
A Hybrid Model of Multimodal Approach for Multiple Biometrics Recognition ...................................1
P. Prabhusundhar, V.K. Narendira Kumar and B. Srinivasan
An Algorithm for Optimized Cost in a Distributed Computing SystemIRJET Journal
This document summarizes an algorithm for optimized cost allocation in a distributed computing system. The algorithm considers a set of tasks that need to be assigned to processors across multiple phases. It calculates execution costs, residing costs, communication costs, and reallocation costs to determine the optimal allocation that minimizes overall system costs. The algorithm is demonstrated on a sample problem involving 4 tasks to be allocated across 2 processors over 5 phases. Cost matrices are provided and the algorithm partitions the problem into subproblems to determine the lowest cost allocation for each phase and overall.
Design of a Novel Multiplier and Accumulator using Modified Booth Algorithm w...IRJET Journal
The document describes a novel design for a multiplier and accumulator (MAC) unit using the modified Booth algorithm and parallel self-timed adder (PASTA). The modified Booth algorithm reduces the number of partial products compared to a regular multiplication process, lowering delay. A carry save adder design is also proposed to further improve performance in terms of computation speed, power consumption, and area compared to a conventional design using the modified Booth algorithm. Simulation results show the proposed MAC design with PASTA has better performance and reduced area overhead and critical path delay compared to conventional methods.
REDUCING FREQUENCY OF GROUP REKEYING OPERATIONcsandit
In the past, Ad-hoc networks were used in limited areas which require secure group communication without Internet access, such as the army or emergencies. However, Ad-hoc networks currently are widely used in variety applications like group chat, smart applications, research testbed etc. Ad-hoc network is basically group based network in the absence of access point so it is prevalent to provide group key approach to prevent information leakage. When we use group key approach, we need to consider which group key management method is the most suitable for the architecture because the cost and frequency of the rekeying operation remain as an unresolved issue. In this paper, we present analysis about existing group key management solutions for Ad-hoc network and suggest a new approach to reduce frequency of the rekeying operation.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document proposes an optimized algorithm for parallel bitonic sort on modern coarse-grained parallel machines. The key ideas are:
1) Previous approaches remap data between blocked and cyclic layouts after each stage, but the optimal approach is to remap only after lg(N/P) steps to minimize communication.
2) By analyzing the bit patterns compared in each step, the algorithm derives a data layout that allows lg(N/P) consecutive local steps before the next remap.
3) Experimental results on a 64-node parallel machine show the approach reduces communication and outperforms previous bitonic sort implementations.
Research of 64-bits RISC Dual-core Microprocessor with High Performance and L...TELKOMNIKA JOURNAL
A 64-bits RISC Dual-Core microprocessor with high performance and low power consumption is
presented in this paper. The processor has a symmetric architecture with two cores. Each of them has
three stage pipeline, 64-bit data-path and 64-bit address port. A novel shared register module, redundant
Booth3 algorithm and leapfrog Wallace tree architecture are introduced to the microprocessor, and both
the performance and power consumption of it has been improved enormously. As the FPGA simulation
result indicates, the power consumption is decreased by 14% and the longest data-path is shortened by
25%.
High Speed Signed multiplier for Digital Signal Processing ApplicationsIOSR Journals
This document discusses high speed multiplier architectures for digital signal processing applications. It begins by introducing the importance of fast multiplication in DSP algorithms. It then describes the Vedic multiplication algorithm and how it can be implemented for 4-bit and 8-bit numbers using the Urdhva Tiryakbhyam technique. Next, it introduces the Booth encoding technique for radix-8 multiplication and discusses how it reduces the number of partial products. Simulation results are shown comparing the Vedic and radix-8 multiplier architectures. The radix-8 multiplier is concluded to have better performance in terms of power, delay, and power-delay product, making it well-suited for DSP applications.
11.flow shop scheduling problem, processing time associated with probabilitie...Alexander Decker
The document presents a heuristic algorithm for solving an n-job, 3-machine flow shop scheduling problem where processing times are associated with probabilities involving transportation time, breakdown intervals, job weights, and job block criteria. The algorithm aims to find an optimal or near-optimal sequence that minimizes total elapsed time when considering mean weighted production flow time. It uses Johnson's rule and introduces fictitious machines to handle transportation times, job weights, and job blocks before determining the optimal sequence. The algorithm is demonstrated through a numerical example involving 5 jobs.
Flow shop scheduling problem, processing time associated with probabilities i...Alexander Decker
This document summarizes a research paper that proposes a new heuristic algorithm for solving an n-job, 3-machine flow shop scheduling problem where processing times are associated with probabilities involving transportation time, breakdown intervals, job weights, and job block criteria. The algorithm aims to find an optimal or near-optimal sequence that minimizes the total elapsed time when considering the mean weighted production flow time. Notations used in the model and problem formulation are defined.
Parallel Line and Machine Job Scheduling Using Genetic AlgorithmIRJET Journal
This document summarizes research on using a genetic algorithm to solve a parallel line and machine job scheduling problem. The objective is to minimize the makespan (completion time) of all jobs. A genetic algorithm is applied that represents possible job schedules as chromosomes. The fitness function evaluates schedules based on makespan. Genetic operators like crossover and mutation create new schedules from existing ones. The algorithm was tested on sample job data using a MATLAB program. Results showed the genetic algorithm approach can find optimal job allocations and schedules that minimize makespan for parallel line scheduling problems.
Constrained flow shop scheduling with n jobs, 3-machines, processing time ass...Alexander Decker
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In this paper, a multi-objective based NSGA-II algo
rithm is proposed for dynamic job-shop scheduling
problem (DJSP) with random job arrivals and machine
breakdowns. In DJSP schedules are usually
inevitable due to various unexpected disruptions. T
o handle this problem, it is necessary to select
appropriate key machines at the beginning of the si
mulation instead of random selection. Thus, this pa
per
seeks to address on approach called social network
analysis method to identify the key machines of the
addressed DJSP. With identified key machines, the e
ffectiveness and stability of scheduling i.e., make
span
and starting time deviations of the computational c
omplex NP-hard problem has been solved with propose
d
multi-objective based hybrid NSGA-ll algorithm. Sev
eral experiments studies have been conducted and
comparisons have been made to demonstrate the effic
iency of the proposed approach with classical multi
-
objective based NSGA-II algorithm. The experimental
results illustrate that the proposed method is ver
y
effective in various shop floor conditions
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On linkage of a flow shop scheduling model including job block criteria with a parallel biserial queue network
1. Computer Engineering and Intelligent Systems www.iiste.org
ISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)
Vol 3, No.2, 2012
On Linkage of a Flow Shop Scheduling Model Including Job
Block Criteria with a Parallel Biserial Queue Network
Sameer Sharma1* Deepak Gupta2 Seema Sharma3
3. Department of Mathematics, Maharishi Markandeshwar University, Mullana, Ambala, India
4. Department of Mathematics, Maharishi Markandeshwar University, Mullana, Ambala, India
5. Department of Mathematics, D.A.V.College, Jalandhar, Punjab, India
* E-mail of the corresponding author: samsharma31@yahoo.com
Abstract: This paper is an attempt to establish a linkage between a flowshop scheduling model having job
block criteria with a parallel biserial queue network linked with a common channel in series. The arrival
and service pattern both follows Poisson law in queue network. The generating function technique, law of
calculus and statistical tools have been used to find out the various characteristics of queue. Further the
completion time of jobs in a queue system form the set up time for the first machine in the scheduling
model. A heuristic approach to find an optimal sequence of jobs with a job block criteria with minimum
total flow time when the jobs are processed in a combined system with a queue network is discussed. The
proposed method is easy to understand and also provide an important tool for the decision makers when the
production is done in batches. A computer programme followed by a numerical illustration is given to
justify the algorithm.
Keywords: Queue Network, Mean Queue length, Waiting time, Processing time, Job-block, Makespan,
Biserial Channel
1. Introduction
In flowshop scheduling problems, the objective is to obtain a sequence of jobs which when processed on
the machines will optimize some well defined criteria. Every job will go on these machines in a fixed order
of machines. The research into flow shop problems has drawn a great attention in the last decades with the
aim to increase the effectiveness of industrial production. In queuing theory the objective is to reduce the
waiting time, completion time (Waiting Time + Service Time) and mean queue length of the customers /
jobs which when processed through a queue network. A lot of research work has already been done in the
fields of scheduling and queuing theory separately. The heuristic algorithms for two and three stage
production schedule for minimizing the make span have been developed by Johnson (1954), Ignall &
Scharge (1965) have also developed a branch & bound technique for minimizing the total flow time of jobs
in n x 2 flow shop. Research is also directed towards the development of heuristic and near exact
procedures. Some of the noteworthy heuristics approaches are due to Campbell (1970), Maggu and Das
(1985),, Nawaz et al.(1983), Rajendran (1992), Singh.T.P.(1985) etc. Jackson (1954) studied the time
dependent behavior of queuing system with phase system. O’brien (1954) analyzed the transient queue
model comprised of two queues in series where the service parameter depends upon their queue length.
Maggu (1970) studied a network of two queues in biseries and find the total waiting time of jobs /
customers. Very few efforts have been made so far to combine the study of a production scheduling model
with a queue network. Singh & Kumar (2007, 2008, 2009) made an attempt to combine a scheduling
system with a queue-network.
Kumar (2010) studied linkage of queue network with parallel biserial linked with a common channel to a
flow shop scheduling model. This paper is an attempt to extend the study made by Kumar (2010) by
introducing the idea of Job-Block criteria in scheduling model linked with a queue network having parallel
biserial queues connected with a common channel. The basic concept of equivalent job for a job – block
has been investigated by Maggu & Das (1977) and established an equivalent job-block theorem. The idea
17
2. Computer Engineering and Intelligent Systems www.iiste.org
ISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)
Vol 3, No.2, 2012
of job-block has practical significance to create a balance between a cost of providing priority in service to
the customer and cost of giving service with non-priority. The decision maker may compare the total
production cost in both cases and may decide how much to charge extra from the priority customers. The
objective of the paper is to optimize two phases. In Phase one, the total Completion Time (Waiting time +
Service time), Mean Queue length of the customers / jobs are optimized. In second phase by considering
the completion time as setup time for the first machine, an optimal sequence of the customers / jobs in
order to minimize the makespan including job block is obtained. Thus the problem discussed here is wider
and practically more applicable and has significant results in the process industry.
2. Practical Situation
Many practical situation of the model arise in industries, administrative setup, banking system, computer
networks, office management, Hospitals and Super market etc. For example, in a meal department of mall
shop consisting two parallel biserial sections, one is for drinks and other is for food items and third section
in series common to both is for billing. The customers taking drinks may also take some food items and
vice-versa, then proceed for the billing. After billing the next two machines are for packing of the items and
for the checking the bill and various items purchased. Here the concept of the job block is significant to
give priority of one or more items with respect to others. It is because of urgency or demand of its relative
importance.
Similarly in manufacturing industry, we can consider two parallel biserial channels one for cutting and
other for turning. Some jobs after cutting may go to turning and vice-versa. Both these channels are
commonly connected to the channel for chroming / polishing. After that the jobs has to pass thought two
machine taken as inspection of quality of goods produced and second machine for the final packing. Here
the concept of job block is significant in the sense to create a balance between the cost of providing priority
in service to the customers / jobs and cost of giving services with non-priority customers / jobs. The
decision maker may decide how much to charge extra from priority customers / jobs.
3. Mathematical Model
λ1
S1 P13
P12 P21 M1 M2
S3
S2 S2 P23
λ2
λ1
Phase I
Phase II
Figure 1: Linkage Model
Considered a queue network comprised of three service channels S1, S2 and S3, where the channels S1, S2
are parallel biserial channels connected in series with a common channel S3 and which is further linked
with a flowshop scheduling system of n-jobs and 2-machines M1 and M2. The customers / jobs demanding
service arrive in Poisson streams at the channels S1 and S2 with mean arrival rate λ1 , λ2 and mean service
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rate µ1 and µ2 respectively. Let µ3 be the mean service rate for the server S3. Queues Q1, Q2 and Q3 are
said to be formed in front of the channels S1, S2 and S3 respectively, if they are busy. Customers / Jobs
coming at the rate λ1 either go to the network of channels S1 → S2 → S3 or S1 → S3 with probabilities
p12 , p13 such that p12 + p13 = 1 and those coming at rate λ2 either goes to the network of the channels
S2 → S1 → S3 or S2 → S3 with probabilities p21 , p23 such that p21 + p23 = 1 .Further the completion
time( waiting time + service time) of customers / jobs through Q1, Q2 & Q3 form the setup times for
machine M1.
After coming out from the server S3 .i.e. Phase I, customers / jobs go to the machines M1 and M2(in Phase
II) for processing with processing time Ai1 and Ai2 in second Phase service. Our objective is to develop a
heuristic algorithm to find an optimal sequence of the jobs / customers with minimum makespan in this
Queue-Scheduling linkage system.
4. Assumptions
1. We assume that the arrival rate in the queue network follows Poisson distribution.
2. Each job / customer is processed on all the machines M1, M2, ------- in the same order and pre-
emission is not allowed, .i.e. once a job is started on a machine, the process on that machine can not
be stopped unless job is completed.
3. It is given to a sequence of k jobs i1, i2,--------, ik as a block or group job in the order (i1, i2,-------, ik)
showing the priority of job i1 over i2.
4. For the existence of the steady state behaviour the following conditions hold good:
(i) ρ1 =
( λ1 + λ2 p21 ) < 1
µ1 (1 − p12 p21 )
(ii) ρ 2 =
( λ2 + λ1 p12 ) < 1
µ2 (1 − p12 p21 )
p13 ( λ1 + λ2 p21 ) + p23 ( λ2 + λ1 p12 )
(iii) ρ3 = < 1.
µ2 (1 − p12 p21 )
5. Algorithm
The following algorithm provides the procedure to determine the optimal sequence of the jobs to minimize
the flow time of machines M1 and M2 when the completion time (waiting time + service time) of the jobs
coming out of Phase I is the setup times for the machine M1.
Step 1: Find the mean queue length on the lines of Singh & Kumar (2005, 2006) using the formula
ρ1 ρ2 ρ
L= + + 3
1 − ρ1 1 − ρ 2 1 − ρ3
Here ρ1 =
( λ1 + λ2 p21 ) , ρ = ( λ2 + λ1 p12 ) , ρ = p13 ( λ1 + λ2 p21 ) + p23 ( λ2 + λ1 p12 ) , λ is the mean
µ1 (1 − p12 p21 ) µ2 (1 − p12 p21 ) µ2 (1 − p12 p21 )
2 3 i
arrival rates, µi is the mean service rates, pij are the probabilities.
Step 2: Find the average waiting time of the customers on the line of Little’s (1961) using
L
relation E ( w) = , where λ = λ1 + λ2 .
λ
Step 3: Find the completion time(C) of jobs / customers coming out of Phase I, .i.e. when processed
thought the network of queues Q1, Q2 and Q3 by using the formula
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1
C = E (W ) + .
µ1 p12 + µ1 p13 + µ2 p21 + µ2 p23 + µ3
Step 4: The completion time C of the customers / jobs through the network of queues Q1, Q2 and Q3 will be
the setup time for machine M1. Define the two machines M1, M2 with processing time Ai'1 = Ai1 + C and Ai2.
Step 5: Find the processing time of job block β = ( k , m) on two machines M1 and M2 using equivalent job
block theorem given by Maggu & Das (1977). Find Aβ 1 and Aβ 2 using
Aβ 1 = A'k1 + A'm1 − Min( A'm1 , Ak 2 )
Aβ 2 = Ak 2 + Am 2 − Min( A'm1 , Ak 2 )
Step 6: Define a new reduced problem for machines M1 and M2 with processing time Ai'1 and Ai2 and
replacing the job block ( k, m) by a single equivalent job β with processing time Aβ 1 and Aβ 2 .
Step 7: Apply Johnson’s (1954) procedure to find the optimal sequence(s) with minimum elapsed time.
Step 8: Prepare In-Out tables for the optimal sequence(s) obtained in step 7. The sequence Sk having
minimum total elapsed time will be the optimal sequence for the given problem.
6. Programme
#include<iostream.h>
#include<stdio.h>
#include<conio.h>
#include<process.h>
#include<math.h>
int n1[2],u[3],L[2];
int j[16],n;
float macha[16],machb[16],machc[16],maxv1[16];
float p[4];float r[3];
float g[16],h[16],a[16],b[16];float a1,b1,a2,b2,a3,b3,c1,c2,c3,P,Q,V,W,M;float q1,q2,q3,z,f,c;
void main()
{
clrscr();
int group[16];//variables to store two job blocks
float minval, minv, maxv; float gbeta=0.0,hbeta=0.0;
cout<<"Enter the number of customers and Mean Arrival Rate for Channel S1:";
cin>>n1[1]>>L[1];
cout<<"nEnter the number of customers and Mean Arrival Rate for Channel S2:";
cin>>n1[2]>>L[2]; n=n1[1]+n1[2];
if(n<1 || n>15)
{
cout<<endl<<"Wrong input, No. of jobs should be less than 15..n Exitting";
getch();
exit(0);
}
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for(int d=1;d<=3;d++)
{
cout<<"nEnter the Mean Service Rate for the Channel S"<<d<<":"; cin>>u[d];
}
for(int k=1;k<=4;k++)
{
cout<<"nEnter the value of probability p"<<k<<":";cin>>p[k];
}
for(int i=1;i<=n;i++)
{
j[i]=i;
cout<<"nEnter the processing time of "<<i<<" job for machine A : ";cin>>a[i];
cout<<"nEnter the processing time of "<<i<<" job for machine B : ";cin>>b[i];
}
a1=L[1]+L[2]*p[3];b1=(1-p[1]*p[3])*u[1];
r[1]=a1/b1;a2=L[2]+L[1]*p[1];b2=(1-p[1]*p[3])*u[2];
r[2]=a2/b2;b3=(L[1]+(L[2]*p[3]))*p[2]+(L[2]+(L[1]*p[1]))*p[4];c2=u[3]*(1-(p[1]*p[3]));
c3=b3/c2;r[3]=c1+c3;M=L[1]+L[2];
cout<<"r[1]tt"<<r[1]<<"n";cout<<"r[2]tt"<<r[2]<<"n";cout<<"r[3]tt"<<r[3]<<"n";
if(r[1],r[2],r[3]>1)
{
cout<<"Steady state condition does not holds good...nExitting";
getch();exit(0);
}
Q=(r[1]/(1-r[1]))+(r[2]/(1-r[2]))+(r[3]/(1-r[3]));
cout<<"nThe mean queue length is :"<<Q<<"n";
W=Q/M;
cout<<"nAverage waiting time for the customer is:"<<W<<"n";
z=u[1]*p[1]+u[1]*p[2]+u[2]*p[3]+u[2]*p[4]+u[3];
f=1/z;c= W+f;
cout<<"nnTotal completetion time of Jobs / Customers through Queue Network in Phase 1
:"<<c;
for(i=1;i<=n;i++)
{
g[i]=a[i]+c;h[i]=b[i];
}
for(i=1;i<=n;i++)
{
cout<<"nn"<<j[i]<<"t"<<g[i]<<"t"<<h[i];cout<<endl;
}
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cout<<"nEnter the two job blocks(two numbers from 1 to "<<n<<"):";
cin>>group[0]>>group[1];
//calculate G_Beta and H_Beta
if(g[group[1]]<h[group[0]])
{
minv=g[group[1]];
}
else
{
minv=h[group[0]];
}
gbeta=g[group[0]]+g[group[1]]-minv;hbeta=h[group[0]]+h[group[1]]-minv;
cout<<endl<<endl<<"G_Beta="<<gbeta;cout<<endl<<"H_Beta="<<hbeta;
int j1[16];int f=1;float g1[16],h1[16];
for(i=1;i<=n;i++)
{
if(j[i]==group[0]||j[i]==group[1])
{
f--;
}
else
{
j1[f]=j[i];
}
f++;
}
j1[n-1]=17;
for(i=1;i<=n-2;i++)
{
g1[i]=g[j1[i]];
h1[i]=h[j1[i]];
}
g1[n-1]=gbeta;
h1[n-1]=hbeta;
cout<<endl<<endl<<"displaying original scheduling table"<<endl;
for(i=1;i<=n-1;i++)
{
cout<<j1[i]<<"t"<<g1[i]<<"t"<<h1[i]<<endl;
}
float mingh[16];char ch[16];
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{
cout<<" "<<arr1[i];
}
cout<<endl<<endl<<"In-Out Table is:"<<endl<<endl;
cout<<"Jobs"<<"t"<<"Machine M1"<<"t"<<"t"<<"Machine M2" <<"t"<<endl;
cout<<arr1[1]<<"t"<<time<<"--"<<macha[1]<<" t"<<"t"<<macha[1]<<"--"<<machb[1]<<" t"<<endl;
for(i=2;i<=n;i++)
{
cout<<arr1[i]<<"t"<<macha[i-1]<<"--"<<macha[i]<<""<<"t"<<maxv1[i]<<"--"<<machb[i]<<"
"<<"t"<<endl;
}
cout<<"nnnTotal Elapsed Time (T) = "<<machb[n];
cout<<"nnt***************************************************************";
getch();
}
7. Numerical Illustration
Consider eight customers / jobs are processed through the network of three queues Q1, Q2 and Q3 with the
channels S1, S2 and S3, where S3 is commonly linked in series with each of the two parallel biserial channels
S1 and S2. Let the number of the customers, mean arrival rate, mean service rate and associated
probabilities are given as follows:
S. No No. of Customers Mean Arrival Rate Mean Service Rate Probabilities
1 n1= 5 λ1 = 5 µ1 =12 p12 = 0.4
2 n2= 3 λ2 =4 µ2 = 9 p13 = 0.6
µ3 = 10 p21 = 0.5
p23 = 0.5
Table 1
After completing the service at Phase I jobs / customers go to the machines M1 and M2 with processing
time Ai1and Ai2 respectively given as follows:
Jobs 1 2 3 4 5 6 7 8
Machine M1 (Ai1) 10 12 8 11 9 8 10 11
Machine M2 (Ai2) 13 12 10 9 8 12 7 8
Table 2
Further jobs 2 and 5 are processed as job block β = (2, 5). The objective is to find an optimal sequence of
the jobs / customers to minimize the makespan in this Queue-Scheduling linkage system by considering the
first phase service into account.
Solution: We have
λ1 + λ2 p21 5 + 4 × 0.5 7
ρ1 = = =
(1 − p12 p21 ) µ1 (1 − 0.4 × 0.5)12 9.6
λ2 + λ1 p12 4 + 5 × 0.4 6
ρ2 = = =
(1 − p12 p21 ) µ2 (1 − 0.4 × 0.5)9 7.2
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( λ + λ p ) p + (λ2 + λ1 p12 ) p23 (5 + 4 × 0.5)0.6 + (4 + 5 × 0.4)0.5 7.2
ρ3 = 1 2 21 13 = = .
µ3 (1 − p12 p21 )
11(1 − 0.4 × 0.5) 8.8
ρ1 ρ2 ρ
Mean Queue Length = Average number of Jobs / Customers = L = + + 3 = 12.2692
1 − ρ1 1 − ρ 2 1 − ρ3
L 12.2692
Average waiting time of the jobs / customers = E ( w) = = = 1.3632 .
λ 9
The total completion time of Jobs / Customers when processed through queue network in Phase I
1
= C = E (W ) + .
µ1 p12 + µ1 p13 + µ2 p21 + µ2 p23 + µ3
1
= 1.3632 + = 1.39445 ≈ 1.39.
4.8 + 7.2 + 4.5 + 4.5 + 11
On taking the completion time C = 1.39 as the setup time, when jobs / customers came for processing with
machine M1. The new reduced two machine problem with processing times Ai'1 = Ai1 + C and Ai2 on
machine M1 and M2 is as shown in table 3.
The processing times of equivalent job block β = (2, 5) by using Maggu & Das(1977) criteria are given by
Aβ 1 = A'k1 + A'm1 − Min( A'm1 , Ak 2 ) = 13.39
Aβ 2 = Ak 2 + Am 2 − Min( A'm1 , Ak 2 ) = 9.61
The reduced two machine problem with processing times Ai'1 and Ai2 on machine M1 and M2 with jobs (2,
5) as a job-block β is as shown in table 3.
Using Johnson’s (1954) algorithm, we get the optimal sequence(s)
S1 = 3 – 6 – 1 - β - 4 – 8 – 7 = 3 – 6 – 1 – 2 – 5 - 4 – 8 – 7
S2 = 6 – 3 – 1 - β - 4 – 8 – 7 = 6 – 3 – 1 – 2 – 5 - 4 – 8 – 7.
The In-Out flow table for the sequence S1= 3 – 6 – 1 – 2 – 5 - 4 – 8 – 7 is as shown in table 4.
Therefore, the total elapsed time for sequence S1 = 97.12 units.
The In-Out flow table for the sequence S2= 6 – 3 – 1 – 2 – 5 - 4 – 8 – 7 is as shown in table 5.
Therefore the total elapsed time for sequence S2= 97.12 = the total elapsed time for sequence S1.
Therefore the optimal sequence(s) is S1= 3 – 6 – 1 – 2 – 5 - 4 – 8 – 7 or S2= 6 – 3 – 1 – 2 – 5 - 4 – 8 – 7.
8. Conclusion
The present paper is an attempt to study the queue network model combined with a two stage flowshop
scheduling including job-block criteria with a common objective of minimizing the total elapsed time. A
heuristic algorithm by considering the completion time of queuing network in Phase I as setup time for the
first machine in Phase II. The concept of job-block is introduced to create a balance between the cost of
providing priority in service to the customers / jobs and cost of giving services with non-priority customers
/ jobs. The study may further be extended by introducing various types of queuing models and different
parameters for two and three stage flowshop scheduling models under different constraints.
9. References
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sequencing problem”, Management Science, 16, B630-B637.
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Chander Shekharn, K, Rajendra, Deepak Chanderi (1992),”An efficient heuristic approach to the
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Tables
Table 3: The processing times Ai'1 and Ai2 on machine M1 and M2 is
Jobs 1 2 3 4 5 6 7 8
Machine M1 (A’i1) 11.39 13.39 9.39 12.39 10.39 9.39 11.39 12.39
Machine M2 (Ai2) 13 12 10 9 8 12 7 8
Table 4: The In-Out flow table for the sequence S1= 3 – 6 – 1 – 2 – 5 - 4 – 8 – 7 is
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