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Showing 43 results for Linear Programming

Dr. Zahra Esfandiari, Prof. Mahdi Bashiri, Prof. Reza Tavakkoli-Moghaddam,
Volume 0, Issue 0 (3-2020)
Abstract

One of the major risks that can affect supply chain design and management is the risk of facility disruption due to natural hazards, economic crises, terrorist attacks, etc. Static resiliency of the network is one of the features that is considered when designing networks to manage disruptions, which increases the network reliability. This feature refers to the ability of the network to maintain its operation and connection in the lack of some members of the chain. Facility hardening is one of the strategies used for this purpose. In this paper, different reliable capacitated fixed-charge location allocation models are developed for hedging network from failure. In these proposed models, hardening, resilience, and hardening and resilience abilities are considered respectively. These problems are formulated as a nonlinear programming models and their equivalent linear form are presented. The sensitivity analysis confirms that the proposed models construct more effective and reliable network comparing to the previous networks. A Lagrangian decomposition algorithm (LDA) is developed to solve the linear models. Computational results show that the LDA is efficient in computational time and quality of generated solutions for instances with different sizes. Moreover, the superiority of the proposed model is confirmed comparing to the classical model.
M. Kargari, Z. Rezaee, H. Khademi Zare ,
Volume 18, Issue 3 (11-2007)
Abstract

 Abstract : In this paper a meta-heuristic approach has been presented to solve lot-size determination problems in a complex multi-stage production planning problems with production capacity constraint. This type of problems has multiple products with sequential production processes which are manufactured in different periods to meet customer’s demand. By determining the decision variables, machinery production capacity and customer’s demand, an integer linear program with the objective function of minimization of total costs of set-up, inventory and production is achieved. In the first step, the original problem is decomposed to several sub-problems using a heuristic approach based on the limited resource Lagrange multiplier. Thus, each sub-problem can be solved using one of the easier methods. In the second step, through combining the genetic algorithm with one of the neighborhood search techniques, a new approach has been developed for the sub-problems. In the third step, to obtain a better result, resource leveling is performed for the smaller problems using a heuristic algorithm. Using this method, each product’s lot-size is determined through several steps. This paper’s propositions have been studied and verified through considerable empirical experiments.

 


, , ,
Volume 20, Issue 1 (5-2009)
Abstract

  The problem of lot sizing, sequencing and scheduling multiple products in flow line production systems has been studied by several authors. Almost all of the researches in this area assumed that setup times and costs are sequence –independent even though sequence dependent setups are common in practice. In this paper we present a new mixed integer non linear program (MINLP) and a heuristic method to solve the problem in sequence dependent case. Furthermore, a genetic algorithm has been developed which applies this constructive heuristic to generate initial population. These two proposed solution methods are compared on randomly generated problems. Computational results show a clear superiority of our proposed GA for majority of the test problems.


Mahmood Rezaei Sadrabadi , Seyed Jafar Sadjadi,
Volume 20, Issue 1 (5-2009)
Abstract

Multiple Objective Programming (MOP) problems have become famous among many researchers due to more practical and realistic implementations. There have been a lot of methods proposed especially during the past four decades. In this paper, we develop a new algorithm based on a new approach to solve MOP problems by starting from a utopian point (which is usually infeasible) and moving towards the feasible region via stepwise movements and a plain continuous interaction with Decision Maker (DM). We consider the case where all objective functions and constraints are linear. The implementation of the proposed algorithm is demonstrated with two numerical examples.
Jafar Mahmudi, Soroosh Nalchigar , Seyed Babak Ebrahimi,
Volume 20, Issue 1 (5-2009)
Abstract

Selection of an appropriate set of Information System (IS) projects is a critical business activity which is very helpful to all organizations. In this paper, after describing real IS project selection problem of Iran Ministry of Commerce (MOC), we introduce two Data Envelopment Analysis (DEA) models. Then, we show applicability of introduced models for identifying most efficient IS project from 8 competing projects. Then, in order to provide further insight, results of two introduced models are compared. It is notable that using basic DEA models -CCR and BCC- decision maker is not able to find most efficient Decision Making Unit (DMU) since these models identify some of DMUs as efficient which their efficiency scores equal to 1. As an advantage, the applied models can identify most efficient IS (in constant and variable return to scale situations) by solving only one linear programming (LP). So these models are computationally efficient. It is while using the basic DEA models requires decision maker to solve a LP for each IS.
Masoud Narenji, Ahmad Makui, Mehdi Fathi ,
Volume 20, Issue 4 (4-2010)
Abstract

Nowadays, interval comparison matrices (ICM) take an important role in decision making under uncertainty. So it seems that a brief review on solution methods used in ICM should be useful. In this paper, the common methods are divided into four categories that are Goal Programming Method (GPM), Linear Programming Method (LPM), Non-Linear Programming Method (NLPM) and Statistic Analysis (SA). GPM itself is divided also into three categories. This paper is a review paper and is written to introduce the mathematical methods and the most important applications of ICM in decision making techniques.
Mohammad Najafi Nobar, Mostafa Setak,
Volume 21, Issue 1 (6-2010)
Abstract

In nowadays world competitive market, on account of the development of electronic media and its influence on shortening distances, companies require some core competencies in order to be able to compete with numerous competitors in industry and sustain their situation in such a market. In addition companies achieve this target are those which their processes perform great and exploit from competitive price, quality, guarantee, etc. Since some parameters such as price and quality are so dependent on the performance of company supply chain management, so the results can highly impress the final price and quality of products. One of the main processes of supply chain management is supplier selection process which its accurate implementation can dramatically increase company competitiveness. In presented article two layers of suppliers have been considered as a chain of suppliers. First layer suppliers are evaluated by two groups of criteria which the first one encompasses criteria belongs to first layer suppliers features and the second group contains criteria belong to the characteristics of second layer suppliers. One of the criteria is the performance of second layer suppliers against environmental issues. Then the proposed approach is solved by a method combined of concepts of fuzzy set theory (FST) and linear programming (LP) which has been nourished by real data extracted from an engineering design and supplying parts company. At the end results reveal the high importance of considering second layer suppliers features as a criteria for selecting the best supplier.
Mohammad Mahdavi Mazdeh, Ali Khan Nakhjavani , Abalfazl Zareei,
Volume 21, Issue 2 (5-2010)
Abstract

  This paper deals with minimization of tardiness in single machine scheduling problem when each job has two different due-dates i.e. ordinary due-date and drop dead date. The drop dead date is the date in which jobs’ weights rise sharply or the customer cancels the order. A linear programming formulation is developed for the problem and since the problem is known to be NP-hard, three heuristic algorithms are designed for the problem based on Tabu search mechanism. Extensive numerical experiments were conducted to observe and compare the behavior of the algorithms in solving the problem..


M. S Jabalameli, B. Bankian Tabrizi, M. Moshref Javadi ,
Volume 21, Issue 4 (12-2010)
Abstract

  The problem of locating distribution centers (DCs) is one of the most important issues in design of supply chain. In previous researches on this problem, each DC could supply products for all of the customers. But in many real word problems, DCs can only supply products for customers who are in a certain distance from the facility, coverage radius. Thus, in this paper a multi-objective integer linear programming (MOILP) model is proposed to locate DCs in a two-echelon distribution system. In this problem, customers who are in the coverage radius of the DCs can be supplied. Moreover, we suppose that the coverage radius of each DC can be controlled by decision maker and it is a function of the amount of money invested on the DC. Finally, a random generated problem is used to verify the model and the computational results are presented .


F. Khaksar-Haghani, N. Javadian, R. Tavakkoli-Moghaddam , A. Baboli , R. Kia,
Volume 22, Issue 3 (9-2011)
Abstract

 

  Dynamic cellular manufacturing systems,

  Mixed-integer non-linear programming,

  Production planning, Manufacturing attributes

 

This paper presents a novel mixed-integer non-linear programming model for the design of a dynamic cellular manufacturing system (DCMS) based on production planning (PP) decisions and several manufacturing attributes. Such an integrated DCMS model with an extensive coverage of important design features has not been proposed yet and incorporates several manufacturing attributes including alternative process routings, operation sequence, processing time, production volume of parts, purchasing machine, duplicate machines, machine depot, machine capacity, lot splitting, material flow conservation equations, inflation coefficient, cell workload balancing, budget constraints for cell construction and machine procurement, varying number of formed cells, worker capacity, holding inventories and backorders, outsourcing part-operations, warehouse capacity, and cell reconfiguration. The objective of the integrated model is to minimize the total costs of cell construction, cell unemployment, machine overhead and machine processing, part-operations setup and production, outsourcing, backorders, inventory holding, material handling between system and warehouse, intra-cell and inter-cell movements, purchasing new machines, and machine relocation/installation/uninstallation. A comprehensive numerical example taken from the literature is solved by the Lingo software to illustrate the performance of the proposed model in handling the PP decisions and to investigate the incorporated manufacturing attributes in an integrated DCMS .


Mahdi Karbasian, Saeed Abedi ,
Volume 22, Issue 4 (12-2011)
Abstract

One of the main principles of the passive defense is the principle of site selection. In this paper, we propose a multiple objective nonlinear programming model that considers the principle of the site selection in terms of two qualitative and quantitative aspects. The purpose of the proposed model is selection of the place of facilities of a system in which not only it observes the dispersion principle but also reduces the system transportation costs. Moreover, the proposed model tries to select the sites that can fulfill other elements of site selection as well as dispersion in a way that it increases the trustworthiness of the selected network .


Mostafa Setak, Samaneh Sharifi,
Volume 22, Issue 4 (12-2011)
Abstract

In recent years, Supplier evaluation and selection, an important element in supply chain management, has been gaining attention in both academic literature and industrial practice. The Mixed integer multi-Objective non-Linear programming model (MIMONLP) presented in this paper aimed to evaluate and select the appropriate set of suppliers considering quantitative and qualitative criteria and in addition to selecting the first layer's suppliers which relate directly to the organization, analyses the characteristics of second-layers suppliers, and design a network to determine the flow rate of products and materials between buyers and best suppliers in both layers. Another important feature of this model is considering holding costs of different products over the planning horizon and quantity discounts for the first layer's suppliers at the same time. Finally, the model is solved by using goal programming approach and numerical examples are presented to test the performance of proposed model.


Yahia Zare Mehrjerdi,
Volume 23, Issue 1 (3-2012)
Abstract

An interactive heuristic approach can offer a practical solution to the problem of linear integer programming (LIP) by combining an optimization technique with the Decision Maker’s (DM) judgment and technical supervision. This is made possible using the concept of bicriterion linear programming (BLP) problem in an integer environment. This model proposes two bicriterion linear programs for identifying a feasible solution point when an initial infeasible solution point is provided by the decision maker or when the searching process leaves the region of feasibility seeking for a better pattern to improve the objective function. Instructions regarding the structure of such BLP problems are broadly discussed. This added property offers a great degree of flexibility to the decision making problem solving process.

The heuristic engine is comprised of four algorithms: Improve, Feasible, Leave, and Backtrack. In each iteration, when a selected algorithm has been terminated, the DM is presented with the results and asked to reevaluate the solution process by choosing an appropriate algorithm to follow. It is shown that the method converges to the optimal solution for most of the time. A solution technique for solving such a problem is introduced with sufficient details.


Mahdi Karbasian, Saeed Abedi,
Volume 23, Issue 1 (3-2012)
Abstract

One of the main principles of the passive defense is the principle of site selection. In this paper, we propose a multiple objective nonlinear programming model that considers the principle of the site selection in terms of two qualitative and quantitative aspects. The purpose of the proposed model is selection of the place of key production facilities of a system in which not only it observes the dispersion principle but also reduces the system transportation costs. Moreover, the proposed model tries to select the sites that can fulfill other elements of site selection as well as dispersion in a way that it increases the trustworthiness of the selected network. For solving the proposed model we used the Genetic Algorithm integrated with TOPSIS method.
, , ,
Volume 23, Issue 2 (6-2012)
Abstract

Design of a logistics network in proper way provides a proper platform for efficient and effective supply chain management. This paper studies a multi-period, multi echelon and multi-product integrated forward-reverse logistics network under uncertainty. First, an efficient complex mixed-integer linear programming (MILP) model by considering some real-world assumptions is developed for the integrated logistics network design to avoid the sub-optimality caused by the separate design of the forward and reverse networks. Then, the stochastic counterpart of the proposed MILP model is used to measure the conditional value at risk (CVaR) criterion, as a risk measure, that can control the risk level of the proposed model. The computational results show the power of the proposed stochastic model with CVaR criteria in handling data uncertainty and controlling risk levels.
Ali Yahyatabar Arabi, Abdolhamid Eshraghnia Jahromi, Mohammad Shabannataj,
Volume 24, Issue 2 (6-2013)
Abstract

Redundancy technique is known as a way to enhance the reliability and availability of non-reparable systems, but for repairable systems, another factor is getting prominent called as the number of maintenance resources. In this study, availability optimization of series-parallel systems is modelled by using Markovian process by which the number of maintenance resources is located into the objective model under constraints such as cost, weight, and volume. Due to complexity of the model as nonlinear programming , solving the model by commercial softwares is not possible, and a simple heuristic method called as simulated annealing is applied. Our main contribution in this study is related to the development of a new availability model considering a new decision variable called as the number of maintenance resources. A numerical simulation is solved and the results are shown to demonstrate the effecienct of the method.
Jafar Bagherinejad, Maryam Omidbakhsh,
Volume 24, Issue 3 (9-2013)
Abstract

Location-allocation of facilities in service systems is an essential factor of their performance. One of the considerable situations which less addressed in the relevant literature is to balance service among customers in addition to minimize location-allocation costs. This is an important issue, especially in the public sector. Reviewing the recent researches in this field shows that most of them allocated demand customer to the closest facility. While, using probability rules to predict customer behavior when they select the desired facility is more appropriate. In this research, equitable facility location problem based on the gravity rule was investigated. The objective function has been defined as a combination of balancing and cost minimization, keeping in mind some system constraints. To estimate demand volume among facilities, utility function(attraction function) added to model as one constraint. The research problem is modeled as one mixed integer linear programming. Due to the model complexity, two heuristic and genetic algorithms have been developed and compared by exact solutions of small dimension problems. The results of numerical examples show the heuristic approach effectiveness with good-quality solutions in reasonable run time.
Mahdi Bashiri, Masoud Bagheri,
Volume 24, Issue 3 (9-2013)
Abstract

The quality of manufactured products is characterized by many controllable quality factors. These factors should be optimized to reach high quality products. In this paper we try to find the controllable factors levels with minimum deviation from the target and with a least variation. To solve the problem a simple aggregation function is used to aggregate the multiple responses functions then an imperialist competitive algorithm is used to find the best level of each controllable variable. Moreover the problem has been better analyzed by Pareto optimal solution to release the aggregation function. Then the proposed multiple response imperialist competitive algorithm (MRICA) has been compared with Multiple objective Genetic Algorithm. The experimental results show efficiency of the proposed approach in both aggregation and non aggregation methods in optimization of the nonlinear multi-response programming.
Yahia Zare Mehrjerdi,
Volume 24, Issue 4 (12-2013)
Abstract

Stochastic Approach to Vehicle Routing Problem: Development and Theories Abstract In this article, a chance constrained (CCP) formulation of the Vehicle Routing Problem (VRP) is proposed. The reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. Knowing that reliable computer software for large scaled complex nonlinear programming problem with 0-1 type decision variables for stochastic vehicle routing problem (SVRP) is not easily available merely then the value of an approximation technique becomes imperative. In this article, theorems which build a foundation for moving toward the development of an approximate methodology for solving SVRP are stated and proved. Key Words: Vehicle Routing Problem, Chance Constrained Programming, Linear approximation, Optimization.

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