Analysis of the Hiring Cost Impact with a Bi-objective Model for the Multi-depot Open Location Routing Problem

Abstract

This paper investigates the effect of the hiring cost over transportation cost and the capacity utilization for the vehicles used. This analysis is conducted on a multi-depot open location-routing problem. The problem consists of determining the optimal number of depots to open, as well as the design of the open routes in order to satisfy the demand for all of the customers while seeking the best trade-off between the total traveling and opening cost. To solve the problem, we propose a bi-objective mixed-integer linear model, which is solved using two different approaches: the augmented epsilon constraint 2 (AUGMECON2) method and the weighting revised multi-choice goal programming (WRMCGP) method. Both approaches are implemented, solving benchmark instances and comparing the quality of the Pareto fronts in terms of multi-objective metrics. Accordingly, the results indicate that AUGMECON2 performs better than WRMCGP concerning the quality of the Pareto Front and the elapsed CPU time, for instances with a homogeneous fleet. However, the WRMCGP reported the best solution time in the heterogeneous instances. In summary, considering heterogeneous fleets, the results demonstrate that the hiring cost can be reduced up to 85%, with 73% more vehicle utilization on average.