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.
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.
The main objective of this study is to increase the productivity against the demand. The Quality related issue regarding material&
material shortage online is not in the scope of this study. Taking a value stream perspective means working on the big picture, nota just
individual process; and not a just optimization but an actual improvement. It covers value adding as well as non-value-adding activities. This
study also includes layout improvement and time study report.
This research shows marking benefit associated with the implementation of lean program because this project shows an industrial case
study of MCCB manufacturing Assembly line.
In the competitive and economic market, Industries needs shorter lead time, low cost and high customer demand satisfaction. So such industries face cost reduction and efficiency challenges. To sustain and stabilize market industries have to find out ways to reduce production time, cost and elimination of waste to improve operating performance and product quality. Value stream mapping technique maps material flow, information flow, activities and other process elements that are part of supply chain. The visual picture simplifies lean approach by identifying the value-added and non-value added stages. The primary objective of this study is to increase the productivity against the demand. The Quality related issue regarding material & material shortage online is not in the scope of this study. A value stream means working on the big picture,
not a just individual process; and not a just optimization but an actual improvement. It covers value adding as well as non-value-adding activities
his research shows benefit associated with the implementation of the lean program. This case study shows a manufacturing industry case study.
This paper considers a flow shop scheduling problem. The flow shop scheduling is
characterized “n” jobs and “m” machines in series with unidirectional flow of work with
variety of jobs being processed sequentially in a single pass manner. Most real world
problems are NP-hard in nature. The essential complexity of the problem necessitates the
use of meta-heuristics for solving flow shop scheduling problem. The paper addresses the
flow shop scheduling problem to minimize the makespan time with specific batch size
using Particle Swarm Optimization (PSO) and comparing the results with an real time
company production sequence.
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.
The main objective of this study is to increase the productivity against the demand. The Quality related issue regarding material&
material shortage online is not in the scope of this study. Taking a value stream perspective means working on the big picture, nota just
individual process; and not a just optimization but an actual improvement. It covers value adding as well as non-value-adding activities. This
study also includes layout improvement and time study report.
This research shows marking benefit associated with the implementation of lean program because this project shows an industrial case
study of MCCB manufacturing Assembly line.
In the competitive and economic market, Industries needs shorter lead time, low cost and high customer demand satisfaction. So such industries face cost reduction and efficiency challenges. To sustain and stabilize market industries have to find out ways to reduce production time, cost and elimination of waste to improve operating performance and product quality. Value stream mapping technique maps material flow, information flow, activities and other process elements that are part of supply chain. The visual picture simplifies lean approach by identifying the value-added and non-value added stages. The primary objective of this study is to increase the productivity against the demand. The Quality related issue regarding material & material shortage online is not in the scope of this study. A value stream means working on the big picture,
not a just individual process; and not a just optimization but an actual improvement. It covers value adding as well as non-value-adding activities
his research shows benefit associated with the implementation of the lean program. This case study shows a manufacturing industry case study.
This paper considers a flow shop scheduling problem. The flow shop scheduling is
characterized “n” jobs and “m” machines in series with unidirectional flow of work with
variety of jobs being processed sequentially in a single pass manner. Most real world
problems are NP-hard in nature. The essential complexity of the problem necessitates the
use of meta-heuristics for solving flow shop scheduling problem. The paper addresses the
flow shop scheduling problem to minimize the makespan time with specific batch size
using Particle Swarm Optimization (PSO) and comparing the results with an real time
company production sequence.
Automation of Material Handling: Design & Analysis of Bucket System on an Inc...IJRES Journal
Material handling systems are widely used in the industry for transportation of raw material, finished
product, storage and retrieval of materials. The increase cost of labor and manual work or operation is now
replaced by semiautomatic or automatic system. These low cost systems are not only cost efficient but also
enhance productivity & address the issues related to labor problem. Material handling equipment is designed
such that they make simple, economical, fast and safe loading and unloading with less human intervention. The
research work is related to develop an automated material Handling system MHS in the chemical Industry
where the bulk material transportation is done manually. The successful completion of this research work has
generated design and analysis of an automated bucket on inclined rail system for the chemical industry, which is
quick, efficient and safety to labor.
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.
MCDM Techniques for the Selection of Material Handling Equipment in the Autom...IJMER
Abstract: Material Handling Equipments are utilized in different shops of an automobile industry.
For culling congruous Material Handling Equipment, it is felt that some Multi Criteria Decision
Making Methods must be used due to their ability of converting an intricate quandary to a paired
comparison. These methods are predicated on some relative Criteria and Sub-criteria. Certain
methods such as; Analytic Hierarchy Process (AHP), Fuzzy Analytic Hierarchy Process (FAHP), and
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) Method have to be utilized
for solving the quandary of Material Handling Equipment cull in different shops of automobile
industry. For solving these quandaries, some criteria (Material, Move, and Method) are culled.
The main conclusions drawn from this study are that, Method criteria is more consequential for
culling Material Handling Equipment, and Conveyor System is more efficient and precise Equipment
for Handling the Material in shop floor of any automobile industry. The focus of this research is in
the area of Cull of Material Handling Equipment in automobile industry. Cull of congruous Material
Handling Equipment is very paramount for reducing manufacturing cycle time, and cost of
manufacturing.
Designing Unbalanced Assembly Lines: A Simulation Analysis to Evaluate Impact...IJERA Editor
This article investigates the impact of controlled imbalance levels on assembly lines, and its effects on two
important performance indicators: throughput and work in process (WIP) level. Using a five workstations line
simulation, with different degrees of imbalance and different configurations, we could conclude that there is a
relationship between extra capacity added to non-constraints and average WIP level and line throughput.
Simulation revealed that, using bowl shape configuration, the higher the imbalance, the higher the throughput,
with less WIP. These results allow proposing new studies to create a framework for evaluating the feasibility of
investments in extra capacity vis-a-vis those gains in resources efficiency.
Which of the following is not a problem definition tooljohann11374
FOR MORE CLASSES VISIT
www.ops571help.com
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
Modelling of Vendor Selection Problem for Radial Drilling Column by Fuzzy Inf...IJSRD
Like many complex supply chain problems, vendor selection problems are not so well defined which can be handed over completely to computers, whereas many human characteristics are also essential to the issues. In this paper attention is given to the fuzzy System helps Vendor Selection Problem (VSP) for Radial Drilling Column (RDC). It required expert’s view, conversion it into fuzzy term, making 8 rule base Model with implementing Fuzzy System using MATLAB. At ending point, conclusions and likely areas of Fuzzy in selecting vendors are present.
Which of the following approaches to service designjohann11372
FOR MORE CLASSES VISIT
www.ops571help.com
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
Which of the following basic types of production layoutjohann11372
FOR MORE CLASSES VISIT
www.ops571help.com
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
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.
Vendor Selection Problem for Radial Drilling Arm by Fuzzy Inference Decision ...IJSRD
Like many complex supply chain problems, vendor selection problems are not so well defined which can be handed over completely to computers, whereas many human characteristics are also essential to the issues. In this paper attention is given to the fuzzy System helps Vendor Selection Problem (VSP) for Radial drilling Arm (RDA). It required expert’s view, conversion it into fuzzy term, making 8 rule base Fuzzy System. At ending point, conclusions and likely areas of Fuzzy in selecting vendors are present.
Comparative Analysis of Metaheuristic Approaches for Makespan Minimization fo...IJECEIAES
This paper provides comparative analysis of various metaheuristic approaches for m-machine no wait flow shop scheduling (NWFSS) problem with makespan as an optimality criterion. NWFSS problem is NP hard and brute force method unable to find the solutions so approximate solutions are found with metaheuristic algorithms. The objective is to find out the scheduling sequence of jobs to minimize total completion time. In order to meet the objective criterion, existing metaheuristic techniques viz. Tabu Search (TS), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are implemented for small and large sized problems and effectiveness of these techniques are measured with statistical metric.
Which of the following is a total measure of productivityjohann11373
FOR MORE CLASSES VISIT
www.ops571help.com
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
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Automation of Material Handling: Design & Analysis of Bucket System on an Inc...IJRES Journal
Material handling systems are widely used in the industry for transportation of raw material, finished
product, storage and retrieval of materials. The increase cost of labor and manual work or operation is now
replaced by semiautomatic or automatic system. These low cost systems are not only cost efficient but also
enhance productivity & address the issues related to labor problem. Material handling equipment is designed
such that they make simple, economical, fast and safe loading and unloading with less human intervention. The
research work is related to develop an automated material Handling system MHS in the chemical Industry
where the bulk material transportation is done manually. The successful completion of this research work has
generated design and analysis of an automated bucket on inclined rail system for the chemical industry, which is
quick, efficient and safety to labor.
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.
MCDM Techniques for the Selection of Material Handling Equipment in the Autom...IJMER
Abstract: Material Handling Equipments are utilized in different shops of an automobile industry.
For culling congruous Material Handling Equipment, it is felt that some Multi Criteria Decision
Making Methods must be used due to their ability of converting an intricate quandary to a paired
comparison. These methods are predicated on some relative Criteria and Sub-criteria. Certain
methods such as; Analytic Hierarchy Process (AHP), Fuzzy Analytic Hierarchy Process (FAHP), and
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) Method have to be utilized
for solving the quandary of Material Handling Equipment cull in different shops of automobile
industry. For solving these quandaries, some criteria (Material, Move, and Method) are culled.
The main conclusions drawn from this study are that, Method criteria is more consequential for
culling Material Handling Equipment, and Conveyor System is more efficient and precise Equipment
for Handling the Material in shop floor of any automobile industry. The focus of this research is in
the area of Cull of Material Handling Equipment in automobile industry. Cull of congruous Material
Handling Equipment is very paramount for reducing manufacturing cycle time, and cost of
manufacturing.
Designing Unbalanced Assembly Lines: A Simulation Analysis to Evaluate Impact...IJERA Editor
This article investigates the impact of controlled imbalance levels on assembly lines, and its effects on two
important performance indicators: throughput and work in process (WIP) level. Using a five workstations line
simulation, with different degrees of imbalance and different configurations, we could conclude that there is a
relationship between extra capacity added to non-constraints and average WIP level and line throughput.
Simulation revealed that, using bowl shape configuration, the higher the imbalance, the higher the throughput,
with less WIP. These results allow proposing new studies to create a framework for evaluating the feasibility of
investments in extra capacity vis-a-vis those gains in resources efficiency.
Which of the following is not a problem definition tooljohann11374
FOR MORE CLASSES VISIT
www.ops571help.com
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
Modelling of Vendor Selection Problem for Radial Drilling Column by Fuzzy Inf...IJSRD
Like many complex supply chain problems, vendor selection problems are not so well defined which can be handed over completely to computers, whereas many human characteristics are also essential to the issues. In this paper attention is given to the fuzzy System helps Vendor Selection Problem (VSP) for Radial Drilling Column (RDC). It required expert’s view, conversion it into fuzzy term, making 8 rule base Model with implementing Fuzzy System using MATLAB. At ending point, conclusions and likely areas of Fuzzy in selecting vendors are present.
Which of the following approaches to service designjohann11372
FOR MORE CLASSES VISIT
www.ops571help.com
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
Which of the following basic types of production layoutjohann11372
FOR MORE CLASSES VISIT
www.ops571help.com
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
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.
Vendor Selection Problem for Radial Drilling Arm by Fuzzy Inference Decision ...IJSRD
Like many complex supply chain problems, vendor selection problems are not so well defined which can be handed over completely to computers, whereas many human characteristics are also essential to the issues. In this paper attention is given to the fuzzy System helps Vendor Selection Problem (VSP) for Radial drilling Arm (RDA). It required expert’s view, conversion it into fuzzy term, making 8 rule base Fuzzy System. At ending point, conclusions and likely areas of Fuzzy in selecting vendors are present.
Comparative Analysis of Metaheuristic Approaches for Makespan Minimization fo...IJECEIAES
This paper provides comparative analysis of various metaheuristic approaches for m-machine no wait flow shop scheduling (NWFSS) problem with makespan as an optimality criterion. NWFSS problem is NP hard and brute force method unable to find the solutions so approximate solutions are found with metaheuristic algorithms. The objective is to find out the scheduling sequence of jobs to minimize total completion time. In order to meet the objective criterion, existing metaheuristic techniques viz. Tabu Search (TS), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are implemented for small and large sized problems and effectiveness of these techniques are measured with statistical metric.
Which of the following is a total measure of productivityjohann11373
FOR MORE CLASSES VISIT
www.ops571help.com
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
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Job-shop manufacturing environment requires planning of schedules for the systems of low-volume having numerous variations. For a job-shop scheduling, ‘k’ number of operations and ‘n’ number of jobs on ‘m’ number of machines processed through an assured objective function to be minimized (makespan). This paper presents a capable genetic algorithm for the job-shop scheduling problems among operating parameters such as random population generation with a population size of 50, operation based chromosome structure, tournament selection as selection scheme, 2-point random crossover with probability 80%, 2-point mutation with probability 20%, elitism, repairing of chromosomes and no. of iteration is 1000. An algorithm is programmed for job shop scheduling problem using MATLAB 2009 a 7.8. The proposed genetic algorithm with certain operating parameters is applied to the two case studies taken from literature. The results also show that genetic algorithm is the best optimization technique for solving the scheduling problems of job shop manufacturing systems evolving shortest processing time and transportation time due to its implications to more practical and integrated problems.
In industries, the completion time of job problems in the manufacturing unit has risen significantly. In several types of current study, the job's completion time, or makespan, is reduced by taking straight paths, which is time-consuming. In this paper, we used an Improved Ant Colony Optimization and Tabu Search (ACOTS) algorithm to solve this problem by precisely defining the fault occurrence location in order to rollback. We have used a short-term memory-based rollback recovery strategy to minimise the job's completion time by rolling back to its own short-term memory. The recent movements in Tabu quest are visited using short term memory. As compared to the ACO algorithm, our proposed ACOTS-Cmax solution is more efficient and takes less time to complete.
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.
Optimization Approach of Vehicle Routing By a Milk-Run Material Supply Systemijsrd.com
Material handling is one of the most crucial issues that should be taken into account for eliminating waste and reducing the cost. The purpose of this research is to develop a mathematical model, which will be helpful to construct the routes and determine the service period for the design of milk-run material supply system. The material supply by this system occurs on a just-in-time basis from a central warehouse to several stations. Milk-run material supply system is the round trips are either goods collected from several suppliers and transported to one customer, or goods collected from one supplier and transported to several customers. Besides, it's intends to construct routes based on an initial service period value and attempts to improve the solution by considering different period values. The most suitable solution is decided on the basis of the least total material handling and inventory holding cost. The objective of the mathematical model is the minimization of the total material handling and inventory holding cost. These saving could be either use for reduction of the product cost, which will boost up the sales or to lift the company profit margin.
Hybridizing guided genetic algorithm and single-based metaheuristics to solve...IAESIJAI
This paper focuses on solving unrelated parallel machine scheduling with
resource constraints (UPMR). There are j jobs, and each job needs to be
processed on one of the machines aim at minimizing the makespan. Besides
the dependence of the machine, the processing time of any job depends on the
usage of a rare renewable resource. A certain number of those resources (Rmax)
can be disseminated to jobs for the purpose of processing them at any time,
and each job j needs units of resources (rjm) when processing in machine m.
When more resources are assigned to a job, the job processing time minimizes.
However, the number of resources available is limited, and this makes the
problem difficult to solve for a good quality solution. Genetic algorithm shows
promising results in solving UPMR. However, genetic algorithm suffers from
premature convergence, which could hinder the resulting quality. Therefore,
the work hybridizes guided genetic algorithm (GGA) with a single-based
metaheuristics (SBHs) to handle the premature convergence in the genetic
algorithm with the aim to escape from the local optima and improve the
solution quality further. The single-based metaheuristics replaces the mutation
in the genetic algorithm. The evaluation of the algorithm performance was
conducted through extensive experiments.
Optimization of Assembly Line and Plant Layout in a Mass Production Industry...inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
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.
Solving Assembly Line Balancing Problem Using A Hybrid Genetic Algorithm With...inventionjournals
In this paper, we propose a hybrid genetic algorithm to solve assembly line balancing problem. We put into the optimization framework of maximizing assembly line efficiency and minimizing total idle time simultaneously. The model is able to deal with more realistic situation of assembly line balancing problem such as zoning constraints. The genetic algorithm may lack the capability of exploring the solution space effectively, so we aim to provide its exploring capability by sequentially hybridizing the well-known assignment rules heuristics with genetic algorithm.
Solving Assembly Line Balancing Problem Using A Hybrid Genetic Algorithm With...inventionjournals
In this paper, we propose a hybrid genetic algorithm to solve assembly line balancing problem. We put into the optimization framework of maximizing assembly line efficiency and minimizing total idle time simultaneously. The model is able to deal with more realistic situation of assembly line balancing problem such as zoning constraints. The genetic algorithm may lack the capability of exploring the solution space effectively, so we aim to provide its exploring capability by sequentially hybridizing the well-known assignment rules heuristics with genetic algorithm
Scheduling By Using Fuzzy Logic in ManufacturingIJERA Editor
This paper represents the scheduling process in furniture manufacturing unit. It gives the fuzzy logic application in flexible manufacturing system. Flexible manufacturing systems are production system in furniture manufacturing unit. FMS consist of same multipurpose numerically controlled machines. Here in this project the scheduling has been done in FMS by using fuzzy logic tool in Matlab software. The fuzzy logic based scheduling model in this paper will deals with the job and best alternative route selection with multi-criteria of machine. Here two criteria for job and sequencing and routing with rules. This model is applicable to the scheduling of any manufacturing industry.
SIMULATION-BASED OPTIMIZATION USING SIMULATED ANNEALING FOR OPTIMAL EQUIPMENT...Sudhendu Rai
The paper describes a software toolkit that enables the data-driven simulation-based optimization of print shops It enables quick modeling of complex print production environments under the cellular production framework. The software toolkit automates several steps of the modeling process by taking declarative inputs from the end-user and then automatically generating complex simulation models that are used to determine improved design and operating points. This paper describes the addition of another layer of automation consisting of simulation-based optimization using simulated-annealing that enables automated search of a large number of design alternatives in the presence of operational constraints to determine a cost-optimal solution. The results of the application of this approach to a real-world problem are also described.
Text Mining in Digital Libraries using OKAPI BM25 ModelEditor IJCATR
The emergence of the internet has made vast amounts of information available and easily accessible online. As a result, most libraries have digitized their content in order to remain relevant to their users and to keep pace with the advancement of the internet. However, these digital libraries have been criticized for using inefficient information retrieval models that do not perform relevance ranking to the retrieved results. This paper proposed the use of OKAPI BM25 model in text mining so as means of improving relevance ranking of digital libraries. Okapi BM25 model was selected because it is a probability-based relevance ranking algorithm. A case study research was conducted and the model design was based on information retrieval processes. The performance of Boolean, vector space, and Okapi BM25 models was compared for data retrieval. Relevant ranked documents were retrieved and displayed at the OPAC framework search page. The results revealed that Okapi BM 25 outperformed Boolean model and Vector Space model. Therefore, this paper proposes the use of Okapi BM25 model to reward terms according to their relative frequencies in a document so as to improve the performance of text mining in digital libraries.
Green Computing, eco trends, climate change, e-waste and eco-friendlyEditor IJCATR
This study focused on the practice of using computing resources more efficiently while maintaining or increasing overall performance. Sustainable IT services require the integration of green computing practices such as power management, virtualization, improving cooling technology, recycling, electronic waste disposal, and optimization of the IT infrastructure to meet sustainability requirements. Studies have shown that costs of power utilized by IT departments can approach 50% of the overall energy costs for an organization. While there is an expectation that green IT should lower costs and the firm’s impact on the environment, there has been far less attention directed at understanding the strategic benefits of sustainable IT services in terms of the creation of customer value, business value and societal value. This paper provides a review of the literature on sustainable IT, key areas of focus, and identifies a core set of principles to guide sustainable IT service design.
Policies for Green Computing and E-Waste in NigeriaEditor IJCATR
Computers today are an integral part of individuals’ lives all around the world, but unfortunately these devices are toxic to the environment given the materials used, their limited battery life and technological obsolescence. Individuals are concerned about the hazardous materials ever present in computers, even if the importance of various attributes differs, and that a more environment -friendly attitude can be obtained through exposure to educational materials. In this paper, we aim to delineate the problem of e-waste in Nigeria and highlight a series of measures and the advantage they herald for our country and propose a series of action steps to develop in these areas further. It is possible for Nigeria to have an immediate economic stimulus and job creation while moving quickly to abide by the requirements of climate change legislation and energy efficiency directives. The costs of implementing energy efficiency and renewable energy measures are minimal as they are not cash expenditures but rather investments paid back by future, continuous energy savings.
Performance Evaluation of VANETs for Evaluating Node Stability in Dynamic Sce...Editor IJCATR
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http://sandymillin.wordpress.com/iateflwebinar2024
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This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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Solving Multi-level, Multi-product and Multi-period Lot Sizing and Scheduling Problem in Permutation Flow Shop
1. International Journal of Science and Engineering Applications
Volume 2 Issue 6, 2013, ISSN-2319-7560 (Online)
www.ijsea.com 130
Solving Multi-level, Multi-product and Multi-period Lot
Sizing and Scheduling Problem in Permutation Flow
Shop
M. Babaei
Department of
Industrial
Engineering
Kharazmi University
Karaj, Iran
M. Mohammadi
Department of
Industrial
Engineering,
Kharazmi University
Karaj, Iran
S. M. T. Fatemi
Ghomi
Department of
Industrial
Engineering,
Amirkabir
University, Iran
M. A. Sobhanallahi
Department of
Industrial
Engineering,
Kharazmi University
Karaj, Iran
Abstract: 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.
Keywords: permutation flow shop; evolutionary algorithms; lot sizing and scheduling
1. INTRODUCTION
The multilevel lot sizing problem concerns how to determine
the lot size for producing or procuring an item at each and
sequencing is to determine job ordering on each level. The
objective of lot sizing and sequencing generally is to
minimize the sum of the total setup cost and inventory holding
cost. Lot sizing and sequencing problem plays an important
role in the efficient operation of modern manufacturing and
assembly processes.
The flow shoplot sizing has been a very extensively
researched area since the seminal paper of Johnson [1]. In the
flowshop problem (FSP) a set ofunrelated jobs are to be
processed on a set of machines. These machines are disposed
in series and each job has to visit all of them in the same
order. A special case of flow shop that assumes the same order
of products in all machines is called permutation flow shop. In
this paper we consider a permutation flow shop problem with
setup carryover, setup sequence-dependent and backlogging.
In highly capacitated environments as well as in many real-
life situations, the inclusion of back orders is crucial because
otherwise, no feasible plan would exist and the respective
result that no feasible solution can be found is of minor
importance in practical settings. On the other hand, in many
real-life manufacturing environment the capacity of the
machines are limited, or for cost saving reasons, it might be
useful to produce a product volume in a period other than its
demand period to save setup time and costs. In traditional lot
sizing models producing of a product in a period before its
delivery to the customer is permitted. In this case, inventory
cost occurs. In our case, it is also possible that the product
cannot be delivered on time. It is then backlogging occurs and
backlogging costs are incurred for every unit at period of the
delay. While only few lot sizing approaches consider the
possibility of back ordering, it is of great importance in
practical settings: If capacity is limited, some productsmay
have to be backlogged [2].
Quadt and Kuhn [3] investigated a capacitated lot sizing and
scheduling problem with setup times, setup carryover,
backorders, and parallel machines. They formulated a mixed
integer formulation of the problem and a new solution
procedure. The solution procedure was based on a novel
“aggregate model” which uses integer instead of binary
variables. Song and Chan [4] considered a single item lot
sizing problem with backlogging on a single machine at a
finite production rate. The objective function was to minimize
the total cost of setup, stockholding and backlogging to satisfy
a sequence of discrete demands.Other researchers have
considered backlogging including Wolsey and Pochet [5],
Cheng et al. [6]and Karimi et al.[7].
Graham et al. [8] showed that the permutation flow shop
scheduling problem is strongly NP-complete. Since then many
researches have been attracted to develop heuristic and
metaheuristic algorithms for these problems. Among
researchers that employed metaheuristic we can cite to
Mohammadi et al. [9]. They employed a GA as a solution
approach. Their proposed algorithm was used for a
simultaneous lot sizing and sequencing problem in
permutation flow shops involving sequence-dependent setups
and capacity constraints. Ruiz et al. [10]proposed new genetic
algorithms for solving the permutation flow shop scheduling.
The minimization of the total completion time or
makespanwas considered as theoptimization criterion. They
used new genetic operators, advanced techniques like
hybridization with local search and an efficient population
initialization as well as a new generational scheme. The
2. International Journal of Science and Engineering Applications
Volume 2 Issue 6, 2013, ISSN-2319-7560 (Online)
www.ijsea.com 131
following is brief review of studies that have considered GA
as a solution approach for a permutation flow shop problem.
The authors employed their proposed GA for different
optimization criteria. A GA was used inAllada and Ruiz
[11]study with total tardiness minimization criterion. Tseng
and Lin [12]have minimized makespan in a permutation flow
shop problem.TavakkoliMoghaddam et al. [13]employed a
GA to minimize the makespan. Goren [14]provided an
overview of recent advances in the field in order to highlight
the many ways GAs can be applied to various lot sizing
models.
Despite the fact that GA is one of the most popular
algorithm,other metaheuristic algorithms have been used
broadly by authors. Among metaheuristics, ICA is a novel
population-based evolutionary algorithm proposed by
Atashpaz-Gargari and Lucas [15].ICA is a novel socio-
politically motivated metaheuristic algorithm inspired by
imperialist competition. The results show that the algorithm
performs significantly better than existing algorithms like
genetic algorithm (GA), simulated annealing (SA), tabu
search (TS), and particle swarm optimization (PSO) [16].So
we propose a novel imperialist algorithm (ICA) that employed
some genetic operators during local search.Many researchers
have employed ICA as a solution approach for flow shops. As
instances, Attar et al. [17]proposed a novel imperialist
competitive algorithm to solve flexible flow shop scheduling
problem the optimization criterion was minimization
maximum completion time.Shokrollahpour et al. [18] used
ICA for a two-stage assembly flow shop scheduling problem
with minimization of weighted sum of makespan and mean
completion time as the objective function. Rajabioun et al.
[19],Khabbazi et al. [20],Kaveh and Talatahari [21] Lucaset
al. [22],Nazari-Shirkouhi et al. [23] andSarayloo and
Tavakkoli-Moghaddam[24] are other related study that
employed ICA.
In literature, other metaheuristics have been employed by
researchers. The following shows recent studies about using
different kind of metaheuristics in permutation flow shop.
Quan et al. [25]used PSO in permutation flow shop with
makespan criterion. Ant Colony Optimization is employed
byUdomsakdigool and Khachitvichyanukul [26].
As mentioned above, despite backlogging importance in
practical settings, only few researchers have addressed
capacitated lot sizing problems with back ordering especially
in case of permutation flow shop. To the best of our
knowledge, this is the first paper that deals with setup
sequence-dependent, setup carryover and backlogging in a
multi-level, multi-machine and multi-period permutation flow
shop environment and proposes two metaheuristics to solve
the model and develops a lower bound to compare algorithms.
This paper is organized as follows:in next section, notations
used in the formulation are described and a lower bound is
presented. In section 3 the genetic algorithm and in section 4
imperialist algorithm are proposed. In subsequence section,
the algorithms are calibrated by Taguchi method and
theperformance of proposed algorithms is evaluated. Finally,
Section 6 is devoted to conclusions and recommendation for
future studies.
2. PROBLEM FORMULATION
The following notations are used in the model:
2.1. Notations and assumptions
2.1.1 Indices
, , Index of production type
Index of product type
Designation for a specific setup number
Index of level of production
Index of period
2.1.2 Parameters
Planning horizon
Number of different products
Number of production levels/number of machines
A large real number
, Available capacity of machine min period t (in time
units)
, External demand for product j at the end of period t
(in units of quantity)
ℎ , Storage costs unit rate for product j in level m.
ℎ , Shortage costs unit rate for product j at the end of
period t.
, Capacity of machine m required to produce a unit of
product (or shadow product) j (in time units per
quantity units).
, , Production costs to produce one unit of product j on
machine m at period t (in money unit per quantity
unit).
, , Sequence-dependent setup time for the setup of the
machine m from production of product i to
production of product j (in time units); for ≠
, , , ≥ 0and = , . . = 0.
, , Sequence-dependent setup cost for the setup of the
machine m from production of product i to
production of product j (in money units); for
≠ , , , ≥ 0 and = , . . = 0.
The starting setup configuration on machine m.
2.1.3 Decision variables
, , Stock of product j at level m at the end of period t.
, Shortage of product j at the end of period t.
, , Binary variable, which indicates whether the nth
setup on machines at period t isfrom product i to
product j ( , , = 1) or not ( , , = 0).
, , Quantity of product j produced after nth setup on
machine m at period t.
3. International Journal of Science and Engineering Applications
Volume 2 Issue 6, 2013, ISSN-2319-7560 (Online)
www.ijsea.com 132
, , Shadow product: the gap (in quantity units) between
nth setup (to product j) on machine m at period t and
its related production in order to ensure that direct
predecessor of this product (production of product j
on machine m at period t) has been completed.
To formulate this model the following assumptions are
considered:
Several products are produced in a flow shop environment
and each product can be produced only on one machine at the
same time,
Inventory cost incurred when a product unit is hold between
a particular period,
If the product cannot be delivered on time shortage cost is
incurred,
Setup times reducing machine capacity and each machine is
constrained in capacity
Setups are sequence-dependent and must be complete in a
period.
There must be precisely N (number of products) setups in
each period on each machine, even if a setup is just from a
product to itself, with respect to this issue that setup time (and
cost) from a product to itself is zero
The mathematical model in this paper is described on the
basis of the above assumptions and notations
2.1. Mathematical formulation
Capacitated lot sizing focuses on how to make lot sizing
planning and sequencing focuses on the order of each product
should be produced to minimize total cost. The objective
function is to find an optimal lot sizing and sequencing that
minimize setup, inventory, production and backlogging costs.
, , . . , + , , . , , + ℎ , . , , + ℎ , . , (1)
Subject to
, = , , + , , − , , − , + , ; = 1, …, , = 1,… , (2)
, , + , , = , , + , , ; = 1, …, , = 1, …, − 1, = 1,… , (3)
, , . , , + , . , , + , . , , ≤
, , . , , + , . , , + , . , , ; = 1,. . . , , = 1, . . . , − 1,
= 1, . . . ,
(4)
, , . , , + , . , , + , . , , ≤ , ; = 1, . . . , , = 1, .. . , (5)
, , ≤
,
,
. , ,
, ( ( )
, = 1, . . ., , = 1, . . . , , = 1, . . . , , = 1, . . . ,
(6)
, , ≤
,
,
. , , , = 1,. . . , , = 1, . . . , , = 1, . . . , , = 1, .. . , (7)
, , = 0 ≠ , = 1, . . . , (8)
, , = 1, (9)
, , = , , = 1, . . . , , = 1,. . . , − 1, = 1, . . . , , = 1, . . . , (10)
, , = 0 1 (11)
4. International Journal of Science and Engineering Applications
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, , , , , , , , , , ≥ 0 (12)
, , = 0, = 1, . . . , , = 1, . . . , (13)
In this model, the objective function is Equation (1). The
backlogging or storage at the end of each period is considered
by Equation (2). Constrain (3) ensures total of in-flows to
each node is equal to of out-flows from that node. Equation
(4) ensures within one period each typical product j one
machine m is produced before its direct successor. The
capacity constraints of machines are considered by Equation
(5). Equation (6) respects setups in production process.
Equation (7) indicates the relationship between shadow
products and setups. Constraints (8) and (9) ensure that for
each machine, the first setup at the beginning of the planning
horizon is from a defined product. Equation (10) represents
the relationship between successive setups. The type of
variables is defined by Equations (11) and (12) and finally
Equation (13) indicates that at the end of planning horizon
there is no on-hand inventory.
2.3. Lower bound
In this section we present a lower bound that developed by
Mohammadi et al. [27]. We first relax binary variables to
continuous variables that fall in [0, 1].
Then we add following equation to relaxed model:
, , + , ,
,
= , (14)
In this equation , is binary variable.
Equation (14) was proved that is valid to model. We refer the
proof of this equation to Mohammadi et al [27].
3. GENETIC ALGORITHM
GAs are probabilistic search optimization algorithms that
were inspired by the process of natural evolution and the
principles of survival of the fittest [28].Genetic Algorithms
(GAs) can be employed to find a near-optimal solution for
NP-hard problems. GAs evolves a population of individuals
according to the progress of algorithm to reach a good
solution. Genetic operators (such as natural selection,
mutation, and cross over) manipulate individuals in a
population of solution over several iterations to improve their
fitness.The algorithm generates a new candidate pool of
solutions iteratively from the presently available solutions and
replaces some or all of the existing members of the current
solution tool with the newly created feasible solutions.
We first present a simple and effective heuristic to generate
initial solution and then discuss the issue of encoding in our
case aninteger array representation. We then turn to the
evolutionary stages of the algorithm and the specific genetic
operators that have been designed to increase search
efficiency.
Initial Population
A genetic algorithm starts with popularly an initial population
of feasible solutions. Initial population can affectsthe
performance of GAs. So that a simple and effect heuristic is
used for = 1to and is described as follows:
(1) The products are sorted in the decreasing order of , =
∑ , , ; = 1, . .. , .
(2) Let [ ] indicate the th product in an ordered sequence in
this heuristic.
For [ ] = 1 to :
(a) Consider inserting product [ ] into every position.
(b) Calculate the sum of setup costs for all products scheduled
so far using the actual setup costs.
(c) Place product i in the position with the lowest resultant
sum of setup costs.
With using this method, different initial populations is
produced (for = 1,. . ., ), the remaining initial
populations have been generated randomly.In this way, binary
variables are coded in the form of matrices with ×
dimensions.
In Figure1 a sample chromosome with T =3, N =3 is depicted.
Figure 1. A chromosome representation
In Figure 1 an encoded binary variables have been shown.
The corresponding decoded binary variablesin this
chromosomeduring period T=1 are, , , = , , = , , =
1 and the corresponding decoded binary variables to this
chromosome during period T=2 are, , , = , , = , , =
1and finally for period T=3, , , = , , = , , = 1and
other binary variables would get value 0.With encoding of the
binary variables, we are able to employ crossover and
mutation operators more efficientlyand more effectively than
noncoding chromosomes.
Fitness function
The fitness value of each chromosome has been calculated by
solving the corresponding problem.
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Selection operator
The requirement parents for using of crossover have been
obtained by one of the five selection method, Deterministic
Sampling (A), Random Sampling (B), Roulette Wheel (C),
Ranking (D) andTournament(E).
Crossover operation and mutation operator
Several crossover operators have been proposed in reference
[29]. Similar job two point crossover has been used in this
research. In order to produce small perturbations on
chromosomes to promote diversity of the population, a shift
mutation operator has been used in this article.Crossover and
mutation probability must be determined during parameters
calibration.
Population replacement
Chromosomes for the next generation are selectedfrom the
enlarged population. The best pop_sizechromosomes of the
enlarged population have beenselected for the next generation.
Termination criterion
The algorithm must terminate according to a criterion. This
criterion is specified by reaching to maximum number of
iteration it_max.
4. IMPERIALIST COMPETITIVE
ALGORITHM
ICA is a novel population-based evolutionary algorithm
proposed by Atashpaz-Gargari and Lucas [15]. The ICA
initiates with an initial population, like most evolutionary
algorithms. Each individual of the population is called a
‘country’ equivalent ‘chromosome’ in GA. Some of the most
powerful countries are chosen to be the imperialiststates and
the other countries constitute the colonies of theseimperialists.
All the colonies of initial countries are partitioned among the
mentioned imperialists based on theirpower. Equivalent of
fitness value in the GA, the power ofeach country, is
conversely proportional to its cost. Anempire is constituted
from the imperialist states with theircolonies [30].
After all empires were formed, the competition between
countries starts. First, the colonies in each of empires start
moving toward their imperialist. During this movement, if the
colony gets better cost function than its imperialist does, they
will exchange their positions and the algorithm will continue
with the new imperialist. The power of each empire is
calculated by imperialist cost function and colonies. The
empire which is weaker than the others loses its colonies.
Each imperialist attempts to gain the colonies of other
empires. The most powerful empires have a more chance to
gain the colonies from the weakest empires. The more
powerful an empire is, the more likely it will possess the
weakest colony of the weakest empire (Imperialistic
competition)
During the competition weak imperialists will lose their
weakest colony gradually. When an empire loses all of its
colonies, it will be eliminated from the population. In fact the
empire collapses. The final level of imperialist rivalry is when
there is only one empire in the world. The main steps of ICA
are described as follows:
Step 1 Generating of Initial countries
Each individual of the population is called a ‘country’
equivalent ‘chromosome’ in GA. Each country denotes a
socio-political characteristic in that country such as culture,
language, business, economic policy and etc. The socio-
political characteristic in countries is the same different type
of variables. There are two different types of variables,
continuous variables ( , , , ) and binary variables ( ).
Each country consists of five variables, , , , and
where all of these variables must be optimized.
Initial values of continuous variables are generated randomly
by uniform distribution function. To generate initial value for
binary variable, we use a simple and effective heuristic which
has been presented by Mohammadi et al. [27].
Step 2 Generating of Initial imperials
A set of the most powerful countries form imperialists and the
rest weaker countries are colonies of imperialists. The power
of each country is calculated based on the objective function.
Step 3 Assimilation of colonies
Assimilation has been modeled by moving all the colonies
toward the imperialist. Each country (colony) has different
socio-political characteristics (variables), so every socio-
political characteristic (variables) could moves toward the
related socio-political of imperialist in different ways.
Continuous variables of colonies move toward related
continuous variables of its imperialist and binary variables
move toward binary variables of its imperialist.
The assimilation of continuous variables is modeled by
moving the colony toward the imperialist by xunits
~ (0, × ). Where > 1and ~ (− , ). is distance
between colony and the its imperialist.
The movement of binary variables is accomplished by
crossover operation, like crossover operator in genetic
algorithms. Crossover allows exchanging information
between different solutions (chromosomes) so it is useful to
assimilate binary variables.
Step 4 Revolution
The revolution increases the exploration of the algorithm and
prevents the early convergence of countries to local
minimums. A very high value of revolution decreases the
exploitation power of algorithm and can reduce its
convergence rate [31].In each iteration, some of the colonies
are chosen and their positions are exchanged. This mechanism
is similar to mutation process in genetic algorithm for
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creatingdiversification in solutions. Mutation increases the
variety in the population, so this operator is used for creating a
revolution in binary variables.
Step 5 Exchange the colony with imperialist
During assimilation and revolution, a colony may get to a
situation with lower cost than the imperialist. In this case, the
imperialist and the colony change their positions.
Step 6 Imperialistic competition
To start the competition, after selecting the weakest colony,
the possession probability of each empire must be found. The
normalized total cost of an empire is simply obtained by
= − max { }
Where, and are the total cost and the normalized
total cost of th empire, respectively.
The total power of an empire is mainly contributed by the
power of imperialist country. It is clear that the power of an
empire includes the imperialist power and their colonies.
= { } +
∗ { ( )}
Where is a positive small number.The possession
probability of each empire is given by
=
∑
Roulette wheel method was used for assigning the mentioned
colony to empires.
Step 7 Elimination of powerless empires.
During the competition weak imperialists will lose their
weakest colony gradually. When an empire loses all of its
colonies, it collapses. At the end just one imperialist will
remain. This is the optimum point.
Step 8 Stop criterion
In such an ideal new world, all the colonies will have the
same positions and same costs and they will be controlled by
an imperialist with the same position and cost as themselves.
In such a world, there is no difference not only among
colonies, but also between colonies and imperialist [32]in this
situation; the algorithm has reached the global solution.
Stopping criterion in proposed algorithm is to get the
maximum decades (maximum iteration).
5.PARAMETER CALIBRATION AND
COMPUTATIONAL TESTING
Parametercalibration andcomputationalexperiments are key
steps in the developmentof any algorithm.Conventionally,
setting parameters relies on a trial and-error procedure.
However, this procedure cannot determine optimal parameter
settings and consumes considerable time [33]. In this paper,
we employed the Taguchi Methodology to optimize the
parameters of the algorithms via systematic experiments.
5.1. Parameter calibration
Taguchi [34] developed a family of fractional factorial
experiment (FFE) matrices that ultimately lessens the number
of experiments, but still provides adequate information. Full
fractional experiment is not an effective approach when the
number of factors becomes large, so in our case because of the
large number of factors and few levels for each factor we use
Taguchi method to calibrate the parameters.
A transformation of the repetition data is created toanother
value by Taguchi which is the measure of variation. The
transformation is the signal-to-noise (S/N) ratio. The S/N ratio
is obtained by following equation:
= −10log( )
Where “signal” describes the desirable value, in our study we
use the following performance measure as desirable value.
⎝
⎜
⎛ ∑ ℎ −
× 100
⎠
⎟
⎞
15
Where ℎ is the obtained solution by the
algorithm (GA or ICA) and is the solution obtained by the
lower bound. Note that each problem runs 15 times and the
average of this runs consider as corresponding desirable value
for the problem. It is obvious that the smaller value of the
performance measurement shows that the metaheuristic is
more efficient.
The term “noise” specifies the undesirable value (standard
deviation). The S/N ratioindicates the amount of variation
present in the response variable. Here, maximization of the
signal-to-noise ratio isdesirable (i.e., is the goal).
In order to calibrate the parameters of the algorithms we
determine the level of each parameter. Table 1 shows the level
of each parameter for two metaheuristics. Since increase in
number of products (N) leads to polynomial increase in
computational timeso that to make a fair calibration, we
divide number of population and maximum iteration
bynumber of products (N).
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Table 1. Factor levels
Parameter Level Level 1 Level 2 Level 3 Level 4 Level 5
GA
Selection Type A B C D E
Crossover Probability 0.1 0.2 0.3 0.4 .5
Mutation Probability 0.05 .10 .15 .20 .25
Number of Population 500/N 600/N 750/N 900/N 1000/N
Maximum Iteration 500/N 600/N 750/N 900/N 1000/N
ICA
Number of Population 500/N 600/N 750/N 900/N 1000/N
Number of Imperialist 5 7 10 12 15
Maximum Iteration 0.5 0.7 1 1.2 1.5
Revolution Probability 500/N 600/N 750/N 900/N 1000/N
0.1 0.2 0.3 0.4 0.5
In this case, Taguchi method needs 25 experiments for each
algorithm.As mentioned above, for each 25 experiment 15
independent runs are carried. The termination criterion of
maximum elapsed CPU time ist=7200S [9]The required
parameters for these problems are extracted from the
following uniform distributions: ≈ (5,10), ≈
(0.5,1), ℎ ≈ (0.05, 0.1), ℎ ≈ (1,5), ≈
(0.02, 0.04), ≈ (0.02, 0.04), ≈ (100,1100)
In order to conduct the experiments, we implemented GA and
ICA examples in MATLAB run on a PC with a 2.27 GHz
Intel Core i5 processor and 3 GB RAM memory and analyzed
the result by Minitab 16 software.Figure2 and 3 show the
average S/N ratio obtained at each level for ICA and GA.
According to Figure 2 and Figure 3 the optimal levels of
factors have been indicated in Table 2.
Figure 2. Main effect plot for S/N ratios for GA Figure 3. Main effect plot for S/N ratios for ICA
Table 2. The optimal levels of factors
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Parameter Level Optimum
GA
Selection Type C
Crossover Probability 0.7
Mutation Probability 0.10
Number of Population 900/N
Maximum Iteration 900/N
ICA
Number of Population 750/N
Number of Imperialist 7
Maximum Iteration 750/N
Revolution Probability 0.25
0.7
5.2. Comparison of the algorithms
In this section, in order to evaluate and compare the
performance of two proposed, we consider different problem
sizes.
For each problem set, 15 independent instances are randomly
generated (225 problems) and the required parameters for
these problems are extracted from the following uniform
distributions:
≈ (5,10), ≈ (0.5, 1),ℎ ≈ (0.05, 0.1),ℎ
≈ (1, 5), ≈ (0.02, 0.04),
≈ (0.02, 0.04), ≈ (100, 1100)
For each of the 15 instances, 15 independent runs are carried
out for each algorithm within a reasonable CPU time, 7200
s.We obtain the mean of 15 instances as the response variable
of each instance. This response is used to compare two
algorithms. Problems have been solved in MATLAB run on a
PC with a 2.27 GHz Intel Core i5 processor and 3 GB RAM
memory.The computed results are reported in Table 3.
Table 3. Computational results
Problem set
Dimension of
problems
( × × )
GA ICA
1 2 × 2 × 2 16.72% 9.66%
2 3 × 3 × 3 16.76% 9.42%
3 4 × 4 × 4 9.38% 6.46%
4 5 × 5 × 5 15.01% 11.69%
5 6 × 6 × 6 15.02% 8.55%
6 7 × 7 × 7 15.84% 7.48%
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7 8 × 8 × 8 14.85% 10.07%
8 9 × 9 × 9 13.71% 9.20%
9 10 × 10 × 10 14.04% 10.12%
10 11 × 11 × 11 10.95% 6.97%
11 12 × 12 × 12 10.32% 6.60%
12 13 × 13 × 13 12.17% 6.92%
13 14 × 14 × 14 11.76% 8.99%
14 15 × 15 × 15 13.41% 8.58%
15 16 × 16 × 16 15.08% 8.07%
We are now employing a 95% confidence level and we are
using Tukey HSD confidence intervals to compare algorithms
with Minitab 16 Software. The result has been showed in
Figure 4. From the Figure 4 it is clear that the proposed ICA
algorithm is statistically better than the proposed GA
algorithm.
Figure 4:Tukey HSD confidence intervals
6. CONCLUSION
This paper studies the permutation flow shop lo sizing and
scheduling problem and developed a new model for the
problem under sequence-dependent and carryover setups with
considering backlogging.
To solve the problem, two metaheuristics was proposed
namely, GA and ICA. Since the parameters of any algorithm
has significant effect onalgorithms performance, we use a
fractional factorial experiment namely, Taguchi method. In
order to evaluate the effectiveness and robustness of the
proposed GA and ICA, we carried out a comparison between
the algorithms. In this context, we presenteda lower bound
and compared the algorithms against it. The distance
betweenthe algorithms and the lower bound was calculated.
Base on the results, Tukey HSD confidence intervals was
employed to determine which algorithm is statistically
superior to the other one. The results showed the ICA
outperforms the GA.
As a direction for future research, it would be interesting to
develop other metaheuristic, like Particle Swarm
Optimization, Harmony Search and Honey Bee Algorithm. As
an additional contribution, developing of the single objective
into multi objective models can be considered.
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