Some Explicit Results for the Distribution Problem of Stochastic Linear Programming

Ansaripour, Afrooz; Mata, A. Hernández; Nourazari, Sara; Kumin, Hillel L.

doi:10.4236/ojop.2016.54014

Cited by 6 publications

(4 citation statements)

References 11 publications

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“…At step (6), these coefficients are updated after changing the temperature with the factor of (1+δ1) and (1+δ2), respectively. In addition, one can use the new techniques presented by Ansaripour et al [2], to deal with the stochastic aspects of the problem when it arises. This approach would be very helpful to find a close form expression for the cumulative distribution function of the maximum value of the objective function which is not very easy to solve by other existing solutions in the literature!…”

Section: Explanation Of the Main Steps 1 Solution Representation And ...mentioning

confidence: 99%

An Augmented Variable Neighborhood Search to Solve the Capacitated Location-Routing Problem

Mohamadi-Shad

Niakan

Manzour

2021

EJENG

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In this paper we proposed a new variable neighborhood search (VNS) for solving the location- routing problem with considering capacitated depots and vehicles. A set of capacitated vehicles, a set of depots with restricted capacities, and associated opening costs, and a set of customers with deterministic demands are given. The problem aims to determine the depots to be opened, fleet assignment to each depot, and the routes to be performed to satisfy the demand of the customers. The objective is to minimize the total costs of the open depots, the setup cost associated with the used vehicles, and transportation cost. We proposed a new VNS which is augmented with a probabilistic acceptance criterion as well as a set of efficient local searches. The computational results implemented on four well-known data sets demonstrate that the proposed algorithm is competitive with other well- known algorithms while reaching many best-known solutions and updating six best new results with reasonable computational time. Conclusions and future research avenues close the paper.

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Section: Explanation Of the Main Steps 1 Solution Representation And ...mentioning

confidence: 99%

An Augmented Variable Neighborhood Search to Solve the Capacitated Location-Routing Problem

Mohamadi-Shad

Niakan

Manzour

2021

EJENG

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“…This model did not take into account the uncertainty or fuzziness or imperfect information inherent in some of the dynamic parameters like merchant capacities, their budget distributions etc. Afrooz Ansaripour et al , 2016 [4] carried out technique developed for finding a closed form expression for the cumulative distribution function of the maximum value of the objective function in a stochastic linear programming problem, where either the objective function coefficients or the right hand side coefficients are continuous random vectors with known probability distributions. This is the "wait and see" problem of stochastic linear programming.…”

Section: Literature Reviewmentioning

confidence: 99%

Comparison between Goal Programming and other Linear Programming Methods

Tiwari¹

2018

IJRASET

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Linear Programming (LP) widely used mathematical technique designed to help operation manager's plan and make the decision necessary to allocate resources. It is often desirable to find production level that will produce maximum profit and minimum cost. The production process can be described with a set of linear inequalities which is called as Constraints. The profit and cost function to be maximize or minimize is called as Objective Function. The process of finding optimal level with the set of linear inequalities is called as Linear Programming. In manufacturing problem LP problem determines the number of units of different products which should be produced and sold by firm when each product requires fixed manpower, machine hour, labour hour per unit of product, warehouse space per unit of output etc. in order to make maximum profit. The scope of current study is to determine appropriate method among various LP problems by comparing any LP problem and Goal Programming (GP) problem. Keywords: LPP( Linear Programming Problems), GP(Goal Programming), ILP(Integer Linear Programming), Simplex Method, Dynamic Programming Model. I. INTRODUCTIONThe purpose of this paper is to give the brief introduction of Linear Programming Problem (LPP) and to look at the three methods say; Integer Linear Programming, Simplex method and Transportation method in solving Linear Programming Problem and find out the method that will maximize profit and increase the productivity. Linear programming (LP) is a tool for solving optimization problems. It is a mathematical modelling "System" which has found widespread uses in providing decision maker with an efficient means for resolving complex operational alternatives. It is applicable to the general category of problems that require the optimization of a linear objective function subject to linear constraints. Linear Programming is a technique used to determine the best utilization of limited resources to reach a desired objective of either maximizing the benefit (Profit) or minimizing the costs. There are many ways to solve linear programming basics but starts from Simplex Method and Big-M Method. After the advancement in operation research field and considering demand in companies there are many other quit types to solve linear programming for single objective problem as well as we can solve for multi-objective problem like Integer Programming (Gomory's cutting plane method), Sensitivity Analysis, Dynamic Programming, Stochastic Programming, Goal Programming and etc. Integer programming techniques have gained a lot of interest in our practical life, we come across many business and production industries which have to usually face problems of economics optimization such as cost minimization of non-economic items that are most vital to the existence of their firms. Integer Linear Programming (ILP) problems belong to a particular class of Linear Programming Problems (LPP). In LPP, the decision variables are assumed to be continuous, but in ILP the decision variables are restricte...

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“…In conventional multi-objective optimization problems, weighted LP and NLP algorithms yield a single optimal point based on the random or fixed weights [17,18]. In singleobjective optimization models and multi-objective problems, the endeavor is to find a set of optimal solutions for conflicting objectives which are not necessarily superior corresponding to all objectives, called the non-dominated Pareto optimal solutions [19][20][21]. Utilizing evolutionary algorithms such as Non-dominated Sorting Genetic Algorithm (NSGA) [22][23][24][25], Multi-Colony ACO (MOACO) [26], and Multi-Objective Particle Swarm Optimization (MOPSO) [27,28], establishes a set of solutions which are subject to decision-makers' selection from the optimum.…”

Section: Introductionmentioning

confidence: 99%

Integrated Preventive Maintenance Scheduling Model with Redundancy for Cutting Tools on a Single Machine

Tavassoli¹,

Sakhavand²,

Fazeli³

2020

Eng. Technol. Appl. Sci. Res.

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In this paper, we present an integrated multi-objective framework of a single machine for a single cutting tool problem. Our maintenance policy is based on performing minimal repairs in case of a minor failure and Preventive Maintenance (PM) to avoid a major failure that results in the replacement of the tool. This framework allows simultaneous optimization of the two conflicting time and cost objectives. A redundant system is proposed as a part of the model to assist the production line under a major failure. In addition, the tool’s preventive maintenance time is synchronized with the completion of the machine tool’s work cycle to reduce the machine’s set-up time. The model was optimized using a customized Non-dominated Sorting Genetic Algorithm (NSGA-II). An experimental study based on real-market data was conducted and the results were compared with the ones obtained from classical methods.

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Some Explicit Results for the Distribution Problem of Stochastic Linear Programming

Cited by 6 publications

References 11 publications

An Augmented Variable Neighborhood Search to Solve the Capacitated Location-Routing Problem

An Augmented Variable Neighborhood Search to Solve the Capacitated Location-Routing Problem

Comparison between Goal Programming and other Linear Programming Methods

Integrated Preventive Maintenance Scheduling Model with Redundancy for Cutting Tools on a Single Machine

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