Robust Bi-Objective Location-Arc Routing Problem with Time Windows: A Case Study of an Iranian Bank

Abstract

In Location-Arc Routing Problems (LARP), unlike the well-known locating-routing problems, demand is on the arc and using deadheading arcs is permitted. Few studies have focused on an arc-routing problem. In this research, a complex bi-objective linear mathematical model for the LARP with time windows under uncertainty is presented. Time windows in the arc-routing problem modeling have complexity since the required arc with time windows becomes a deadheading arc without time windows after service. Furthermore, modeling of the vehicle servicing to multiple required arc with the minimum deadheading arc in route is a feature of this work. The proposed LARP is used for modeling of transforming cash in the bank case study. In this case study, demand has uncertainty with unknown probability distributions and the Bertsimas and Sim’s approach is used for it. The case study problem is a node-basing problem with the closest node and time windows for servicing branches. For this purpose, the Multi-Objective Dragonfly Algorithm (MODA) and Non-dominated Sorting Genetic Algorithm (NSGA-II) are used for locating the cash supply centers of a bank in Tehran. Furthermore, comparing results of robust and deterministic LARP models show that the mean and standard deviation of objective function values in the robust model has better performance in realization.

Keywords

• location-arc routing problem
• time windows
• multiple periods
• robust optimization
• demand uncertainty