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Fuzzy programming for multi-choice bilevel transportation problem

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ARORA R., GUPTA K.
Operations Research and Decisions
|
2021
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vol. 31
|
issue 3
5-21
XX
Multi-choice programming problems arise due to the diverse needs of people. In this paper, multi-choice optimization has been applied to the bilevel transportation problem. This problem deals with transportation at both the levels, upper as well as lower. There are multiple choices for demand and supply parameters. The multi-choice parameters at the respective levels are converted into polynomials which transmute the defined problem into a mixed integer programming problem. The objective of the paper is to determine a solution methodology for the transformed problem. The significance of the formulated model is exhibited through an example by applying it to the hotel industry. The fuzzy programming approach is employed to obtain a satisfactory solution for the decision-makers at the two levels. A comparative analysis is presented in the paper by solving the bilevel multi-choice transportation problem with goal programming mode as well as by the linear transformation technique. The example is solved using computing software.
2
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Robust bi-level optimization for an opportunistic supply chain network design problem in an uncertain and risky environment

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GOLPÎRA H.
Operations Research and Decisions
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2017
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vol. 27
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issue 1
21-41
EN
This paper introduces the problem of designing a single-product supply chain network in an agile manufacturing setting under a vendor managed inventory (VMI) strategy to seize a new market oppor-tunity. The problem addresses the level of risk aversion of the retailer when dealing with the uncertainty of market related information through a conditional value at risk (CVaR) approach. This approach leads to a bilevel programming problem. The Karush–Kuhn–Tucker (KKT) conditions are employed to trans-form the model into a single-level, mixed-integer linear programming problem by considering some relaxations. Since realizations of imprecisely known parameters are the only information available, a data-driven approach is employed as a suitable, more practical, methodology of avoiding distribu-tional assumptions. Finally, the effectiveness of the proposed model is demonstrated through a numer-ical example.
3
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Branch and bound algorithm for discrete multi- level linear fractional programming problem

100%
ARORA R., GUPTA K.
Operations Research and Decisions
|
2018
|
vol. 28
|
issue 2
5-21
EN
An algorithm is proposed to find an integer solution for bilevel linear fractional programming problem with discrete variables. The method develops a cut that removes the integer solutions which are not bilevel feasible. The proposed method is extended from bilevel to multilevel linear fractional programming problems with discrete variables. The solution procedure for both the algorithms is elucidated in the paper.
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