Title: Sensitivity analysis of the optimum solution to perturbations of the profit of an item in the multiple-choice knapsack problem

Authors: Luay Aljasim; Ferhan Al-Maliky

Addresses: Department of Mathematics, University of Basrah, Basrah, Iraq ' Department of Mathematics, University of Basrah, Basrah, Iraq

Abstract: Sensitivity analysis of an optimisation problem is the task of studying the stability of a given optimal solution due to the modifications in the parameters data. In this paper, we study the sensitivity analysis for the optimum to the multiple-choice knapsack problem (MCKP), according to the perturbation of the profit of an arbitrary item. We study how much the profit of an arbitrary item in the original problem can vary without changing the optimal solution structure. The range of variations can be represented by the so-called sensitivity intervals that consist of lower and upper values (limits). The obtained results are explained through a simple example. Furthermore, the performance of the proposed methods is evaluated on a set of problem instances.

Keywords: knapsack; multiple choice; optimality; optimisation; perturbation; sensitivity analysis.

DOI: 10.1504/IJMOR.2024.138902

International Journal of Mathematics in Operational Research, 2024 Vol.28 No.2, pp.147 - 162

Received: 12 Feb 2023
Accepted: 12 Mar 2023
Published online: 03 Jun 2024 *

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