A Bi objective uncapacitated multiple allocation p-hub median problem in public administration considering economies of scales

Abstract

This paper addresses uncapacitated multiple allocation p-hub median problems, which deals with both the constructors’ and the users’ objectives in order to obtain an economically sustainable system. One objective is maximizing the overall investment return in road and hub construction and the users’ satisfaction is translated by minimization of the overall usage cost. The problem is formulated in a way that can cover three possible policies as: Governmental requirement, constructor’s break-even point and predefined make span. To make these models more pragmatic, variable discount factors are used in preference to fixed ones. Accordingly, a comprehensive discussion about discount factors and their components has been included to justify the use of variable discount factors. Then some meta-heuristic algorithms like the Imperialist competitive algorithm (ICA), and an enhanced variation of a well-known multi-objective genetic algorithm called nondominated sorting genetic algorithm II (NSGA-II) are developed and applied to solve the problem. The performance of algorithms is compared to each other by utilizing some indicators such as hypervolume, ε-indicator, spacing metric, and CPU time. Computational experiments emphasize the need for using stated assumptions and the variable discount factor. It also confirms the efficiency of the proposed ICA.