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Showing 7 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.


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.
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.
Pegah Rahimian, Sahand Behnam,
Volume 31, Issue 3 (9-2020)
Abstract

In this paper, a novel data driven approach for improving the performance of wastewater management and pumping system is proposed, which is getting knowledge from data mining methods as the input parameters of optimization problem to be solved in nonlinear programming environment. As the first step, we used CART classifier decision tree to classify the operation mode -number of active pumps- based on the historical data of the Austin-Texas infrastructure. Then SOM is applied for clustering customers and selecting the most important features that might have effect on consumption pattern. Furthermore, the extracted features will be fed to Levenberg-Marquardt (LM) neural network which will predict the required outflow rate of the period for each operation mode, classified by CART. The result show that F-measure of the prediction is 90%, 88%, 84% for each operation mode 1,2,3, respectively. Finally, the nonlinear optimization problem is developed based on the data and features extracted from previous steps, and it is solved by artificial immune algorithm. We have compared the result of the optimization model with observed data, and it shows that our model can save up to 2%-8% of outflow rate and wastewater, which is significant improvement in the performance of pumping system.
Mohsen Khezeli, Esmaeil Najafi, Mohammad Haji Molana, Masoud Seidi,
Volume 32, Issue 2 (6-2021)
Abstract

One of the most important fields of logistic network is transportation network design that has an important effect on strategic decisions in supply chain management. It has recently attracted the attention of many researchers. In this paper, a multi-stage and multi-product logistic network design is considered.
This paper presents a hybrid approach based on simulation and optimization (Simulation based optimization), the model is formulated and presented in three stages.  At first, the practical production capacity of each product is calculated using the Overall Equipment Effectiveness (OEE) index, in the second stage, the optimization of loading schedules is simulated. The layout of the loading equipment, the number of equipment per line, the time of each step of the loading process, the resources used by each equipment were simulated, and the output of the model determines the maximum number of loaded vehicles in each period. Finally, a multi-objective model is presented to optimize the transportation time and cost of products. A mixed integer nonlinear programming (MINLP) model is formulated in such a way as to minimize transportation costs and maximize the use of time on the planning horizon. We have used Arena simulation software to solve the second stage of the problem, the results of which will be explained. It is also used GAMS software to solve the final stage of the model and optimize the transporting cost and find the optimal solutions. Several test problems were generated and it showed that the proposed algorithm could find good solutions in reasonable time spans.
Mohsen Khezeli, Esmaeil Najafi, Mohammad Haji Molana, Masoud Seidi,
Volume 33, Issue 2 (6-2022)
Abstract

Nowadays, supply chain management (SCM) is an interesting problem that has attracted the attention of many researchers. Transportation network design is one of the most important fields of SCM. In this paper, a logistics network design is considered to optimize the total cost and increase the network stability and resiliency. First, a mixed integer nonlinear programming model (MINLP) is formulated to minimize the transportation time and transportation cost of products. The proposed model consists of two main stages.
One is a normal stage that minimizes the transportation and holding costs, all manufacturers are also assumed to be healthy and in service. In this stage, the quantity of customer demand met by each manufacturer is eventually determined.
The second is the resilience stage. A method is presented by creating an information network in this supply chain for achieving the resilient and sustainable production and distribution chain that, if some manufacturers break down or stop production, Using the Restarting and load sharing scenarios in the reactive approach to increase resilience with accepting the costs associated with it in the supply network and return to the original state in the shortest possible time, the consequences of accidental failure and shutdown of production units are managed.
Two capacities are also provided for each manufacturer
  • Normal capacity to meet the producer's own demand
  • Load sharing capacity, Determine the empty capacity and increase the capacity of alternative units to meet the out-of-service units demand
In order to solve the model, we used GAMS & Matlab software to find the optimal solutions. A hybrid priority-based Non-dominated Sorting Genetic Algorithms (NSGA-II) and Sub-population Genetic Algorithm (SPGA- II) is provided in two phases to find the optimal solutions. The solutions are represented with a priority matrix and an Allocated vector. To compare the efficiency of two algorithms several criteria are used such as NPS, CS and HV. Several Sample problems are generated and solved that show the Sub-population Genetic Algorithm (SPGA- II) can find good solutions in a reasonable time limit.

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