Title: Uncertain bottleneck assignment problem using credibility theory

Authors: Debapriya Dey Sarkar; Shyamal Kumar Mondal; Kajla Basu

Addresses: Department of Mathematics, National Institute of Technology Durgapur, Durgapur, India ' Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India ' Department of Mathematics, National Institute of Technology Durgapur, Durgapur, India

Abstract: In this paper, two types of generalised bottleneck assignment problem (BGAP) namely task-BGAP and agent-BGAP have been considered with fuzzy costs, capacities and resources. In reality, most of the data are uncertain or vague in nature. The objective of this paper is to formulate and solve a more realistic model under uncertainty. A robust counterpart of these two BGAP models have been constructed using credibility measure theory to solve these optimal mini-max regret problems. Credibility theory helps the actuaries to understand the risk associated with historical data and try to reduce the losses for any organisation. So, by this approach, chance constrained programming (CCP) models have been developed. Finally, the CCP models are solved to get the optimal solution using LINGO software. The method has been illustrated using a real life application of a production factory in Section 5.

Keywords: trapezoidal fuzzy number; bottleneck assignment problem; confidence interval; credibility measure theory; robust optimisation.

DOI: 10.1504/IJMOR.2023.135549

International Journal of Mathematics in Operational Research, 2023 Vol.26 No.4, pp.502 - 522

Received: 05 Apr 2022
Accepted: 16 Oct 2022
Published online: 18 Dec 2023 *

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