Interactive approach to bi-level integer multi-objective fractional programming problem

Emam, O. E.

doi:10.1016/j.amc.2013.07.085

Cited by 44 publications

(33 citation statements)

References 11 publications

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“…Even when all the functions involved are linear, the problem is NP-hard. Several heuristic methods have been proposed to solve the bi-level programming problems (Bard and Moore 1990;Lu et al 2007;Emam 2013;Hansen et al 1992).…”

Section: Solution Methodologymentioning

confidence: 99%

Optimizing decentralized production–distribution planning problem in a multi-period supply chain network under uncertainty

et al. 2017

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Decentralized supply chain management is found to be significantly relevant in today's competitive markets. Production and distribution planning is posed as an important optimization problem in supply chain networks. Here, we propose a multi-period decentralized supply chain network model with uncertainty. The imprecision related to uncertain parameters like demand and price of the final product is appropriated with stochastic and fuzzy numbers. We provide mathematical formulation of the problem as a bi-level mixed integer linear programming model. Due to problem's convolution, a structure to solve is developed that incorporates a novel heuristic algorithm based on Kth-best algorithm, fuzzy approach and chance constraint approach. Ultimately, a numerical example is constructed and worked through to demonstrate applicability of the optimization model. A sensitivity analysis is also made.

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Section: Solution Methodologymentioning

confidence: 99%

Optimizing decentralized production–distribution planning problem in a multi-period supply chain network under uncertainty

et al. 2017

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“…To solve the TLLSILP by adopting the three-planner stackelberg game [10], the FLDM gives the satisfactory solutions that are reasonable in rank order to the SLDM, and after that the SLDM takes the satisfactory solutions of the FLDM to get the solutions, and to gradually get the preferred solution of the FLDM. The satisfactory solutions of the FLDM and the SLDM are conveyed to the TLDM who will get the solutions, and to gradually get the preferred solution of the SLDM.…”

Section: An Interactive Model For the Tllsilpmentioning

confidence: 99%

“…The clue of this approach provides a learning process, whereby DM can figure out how to perceive a preferred solution. This approach utilizes the concepts of satisfactoriness at each level [10,11].…”

Section: Introductionmentioning

confidence: 99%

An Interactive Model for Fully Rough Three Level Large Scale Integer Linear Programming Problem

Emam¹,

Fathy²,

Abohany³

2016

IJCA

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The motivation behind this paper is to focus on the solution of Fully Rough Three Level Large Scale Integer Linear Programming (FRTLLSILP) problem, in which all decision parameters and decision variables in the objective functions and the constraints are rough intervals, and have block angular structure of the constraints. The optimal values of decision rough variables are rough integer intervals. The proposed model is based on interval method and slice-sum method in an interactive model to find a compromised solution for the problem under consideration. Furthermore, the concepts of satisfactoriness are advanced as the upper level decisionmakers' preferences until the preferred solution is obtained.

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“…Usually, this kind of problems can be solved by using different mathematical programming techniques ( [8], [11]). Most studies in multilevel field are focused on bi-level problem ( [10,13,14,15,16,17]). In [10], Emam proposed an algorithm for solving bi-level integer multi-objective fractional programming problem.…”

Section: Introductionmentioning

confidence: 99%

“…Most studies in multilevel field are focused on bi-level problem ( [10,13,14,15,16,17]). In [10], Emam proposed an algorithm for solving bi-level integer multi-objective fractional programming problem. At the first phase of the solution algorithm, it begin by finding the convex hull of its original set of constraints then simplifying the equivalent problem by transforming it into a separate multi-objective decision-making problem and finally solving the resulted problem by using the ε-constraint method.…”

Section: Introductionmentioning

confidence: 99%

A Decomposition Algorithm for Solving a Three Level Large Scale linear Programming Problem

Sultan¹,

Emam²,

Abohany³

2014

Appl. Math. Inf. Sci.

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This paper presents a three level large scale linear programming problem in which the objective functions at every level are to be maximized. A three level programming problem can be thought as a static version of the Stackelberg strategy. An algorithm for solving a three planner model and a solution method for treating this problem are suggested. At each level we attempt to optimize its problem separately as a large scale programming problem using Dantzig and Wolfe decomposition method. Therefore, we handle the optimization process through a series of sub problems that can be solved independently. Finally, a numerical example is given to clarify the main results developed in this paper.

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Interactive approach to bi-level integer multi-objective fractional programming problem

Cited by 44 publications

References 11 publications

Optimizing decentralized production–distribution planning problem in a multi-period supply chain network under uncertainty

Optimizing decentralized production–distribution planning problem in a multi-period supply chain network under uncertainty

An Interactive Model for Fully Rough Three Level Large Scale Integer Linear Programming Problem

A Decomposition Algorithm for Solving a Three Level Large Scale linear Programming Problem

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