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Showing 15 results for Nonlinear Programming

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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.


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 .


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.
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.
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.
Yahia Zare Mehrjerdi,
Volume 25, Issue 3 (7-2014)
Abstract

Abstract It is the purpose of this article to introduce a linear approximation technique for solving a fractional chance constrained programming (CC) problem. For this purpose, a fuzzy goal programming model of the equivalent deterministic form of the fractional chance constrained programming is provided and then the process of defuzzification and linearization of the problem is started. A sample problem is presented for clarification purposes.
Mr Aliakbar Hasani, Mr Seyed Hessameddin Zegordi,
Volume 26, Issue 1 (3-2015)
Abstract

In this study, an optimization model is proposed to design a Global Supply Chain (GSC) for a medical device manufacturer under disruption in the presence of pre-existing competitors and price inelasticity of demand. Therefore, static competition between the distributors’ facilities to more efficiently gain a further share in market of Economic Cooperation Organization trade agreement (ECOTA) is considered. This competition condition is affected by disruption occurrence. The aim of the proposed model is to maximize the expected net after-tax profit of GSC under disruption and normal situation at the same time. To effectively deal with disruption, some practical strategies are adopted in the design of GSC network. The uncertainty of the business environment is modeled using the robust optimization technique based on the concept of uncertainty budget. To tackle the proposed Mixed-Integer Nonlinear Programming (MINLP) model, a hybrid Taguchi-based Memetic Algorithm (MA) with an adaptive population size is developed that incorporates a customized Adaptive Large Neighborhood Search (ALNS) as its local search heuristic. A fitness landscape analysis is used to improve the systematic procedure of neighborhood selection in the proposed ALNS. A numerical example and computational results illustrate the efficiency of the proposed model and algorithm in dealing with global disruptions under uncertainty and competition pressure.
Mr. Mohammad Rohaninejad, Dr. Amirhossein Amiri, Dr. Mahdi Bashiri,
Volume 26, Issue 3 (9-2015)
Abstract

This paper addresses a reliable facility location problem with considering facility capacity constraints. In reliable facility location problem some facilities may become unavailable from time to time. If a facility fails, its clients should refer to other facilities by paying the cost of retransfer to these facilities. Hence, the fail of facilities leads to disruptions in facility location decisions and this problem is an attempt to reducing the impact of these disruptions. In order to formulate the problem, a new mixed-integer nonlinear programming (MINLP) model with the objective of minimizing total investment and operational costs is presented. Due to complexity of MINLP model, two different heuristic procedures based on mathematical model are developed. Finally, the performance of the proposed heuristic methods is evaluated through executive numerical example. The numerical results show that the proposed heuristic methods are efficient and provide suitable solutions.

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Adeleh Behzad, Mohammadali Pirayesh, Mohammad Ranjbar,
Volume 28, Issue 3 (9-2017)
Abstract

In last decades, mobile factories have been used due to their high production capability, carrying their equipment and covering rough and uneven routes. Nowadays, more companies use mobile factories with the aim of reducing the transportation and manufacturing costs. The mobile factory must travel between the suppliers, visit all of them in each time period and return to the initial location of the mobile factory. In this paper, we present an integer nonlinear programming model for production scheduling and routing of mobile factory with the aim of maximization of profit. This problem is similar to the well-known Traveling Salesman Problem (TSP) which is an NP-hard problem. Also at each supplier, the scheduling problem for production is NP-hard. After linearization, we proposed a heuristic greedy algorithm. The efficiency of this heuristic algorithm is analyzed using the computational studies on 540 randomly generated test instances. Finally, the sensitivity analysis of the production cost, transportation cost and relocation cost was conducted.


Amin Saghaeeian, Reza Ramezanian,
Volume 28, Issue 4 (11-2017)
Abstract

This study considers pricing, production and transportation decisions in a Stackelberg game between three-stage, multi-product, multi-source and single-period supply chains called leader and follower. These chains consist of; manufacturers, distribution centers (DCs) and retailers. Competition type is horizontal and SC vs. SC. The retailers in two chains try to maximize their profit through pricing of products in different markets and regarding the transportation and production costs. A bi-level nonlinear programming model is formulated in order to represent the Stackelberg game. Pricing decisions are based on discrimination pricing rules, where we can put different prices in different markets. After that the model is reduced to single-level nonlinear programming model by replacing Karush-Kuhn-Tucker conditions for the lower level (follower) problem. Finally, a numerical example is solved in order to analyze the sensitivity of effective parameters on price and profit.


Mojtaba Torkinejad, Iraj Mahdavi, Nezam Mahdavi-Amiri, Mirmehdi Seyed Esfahani,
Volume 28, Issue 4 (11-2017)
Abstract

Considering the high costs of the implementation and maintenance of gas distribution networks in urban areas, optimal design of such networks is vital. Today, urban gas networks are implemented within a tree structure. These networks receive gas from City Gate Stations (CGS) and deliver it to the consumers. This study presents a comprehensive model based on Mixed Integer Nonlinear Programming (MINLP) for the design of urban gas networks taking into account topological limitations, gas pressure and velocity limitations and environmental limitations. An Ant Colony Optimization (ACO) algorithm is presented for solving the problem and the results obtained by an implementation of ACO algorithm are compared with the ones obtained through an iterative method to demonstrate the efficiency of ACO algorithm. A case study of a real situation (gas distribution in Kelardasht, Iran) affirms the efficacy of the proposed approach.
 
Sina Nayeri, Ebrahim Asadi-Gangraj, Saeed Emami,
Volume 29, Issue 1 (3-2018)
Abstract

Natural disasters, such as earthquakes, tsunamis, and hurricanes cause enormous harm during each year. To reduce casualties and economic losses in the response phase, rescue units must be allocated and scheduled efficiently, such that it is a key issues in emergency response. In this paper, a multi-objective mix integer nonlinear programming model (MOMINLP) is proposed to minimize sum of weighted completion times of relief operations as first objective function and makespan as second objective with considering time-window for incidents. The rescue units also have different capability and each incident just can be allocated to a rescue unit that has the ability to do it. By assuming the incidents and rescue units as jobs and machine, respectively, the research problem can be formulated as a parallel-machine scheduling problem with unrelated machines. Multi-Choice Goal programming (MCGP) is applied to solve research problem as single objective problem. The experimental results shows the superiority of the proposed approach to allocate and schedule the rescue units in the natural disasters.


Shadan Sadighbehzadi, Zohreh Moghaddas, Amirreza Keyghobadi, Mohsen Vaez-Ghasemi,
Volume 29, Issue 4 (12-2018)
Abstract

Natural disasters and crisis are inevitable and each year impose destructive effects on human as injuries and damage to property. In natural  disasters and after the outbreak of the crisis, demand for logistical goods and services increase. Effective distribution of emergency aid could have a significant role in minimizing the damage and fatal accident. In this study, a three-level relief chain including a number of suppliers in fixed locations, candidate distribution centers and affected areas at certain points are considered. For this purpose a mixed integer nonlinear programming model is proposed for open transportation location routing problem by considering split delivery of demand. In order to solve a realistic problem, foregoing parameters are considered as fuzzy in our proposed mode. The objectives of the proposed model include total cost minimization, minimization of the maximum travel time of
vehicles and minimization of unmet demands. In order to solve the problem of the proposed model, fuzzy multi-objective planning is used. For efficiency and effectiveness of the proposed model and solution approach, several numerical examples are studied. Computational results show the effectiveness and efficiency of the model and the proposed approach.
Hamiden Abdelwahed Khalifa,
Volume 29, Issue 4 (12-2018)
Abstract

This paper deals with multi- objective nonlinear programming problem having rough intervals in the constraints. The problem is approached by taking maximum value range and minimum value range inequalities as constraints conditions, reduces it into two classical multi-objective nonlinear programming problems, called lower and upper approximation problems.  All of the lower and upper approximation problems may be solved using the weighting method, where an optimal rough interval solution is obtained. The stability set of the first kind corresponding to the optimal rough interval solution is determined. An illustrative numerical example is given to clarify the obtained results.

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