The Weber Problem in Logistic and Services Networks under Congestion

TL;DR

This paper addresses a complex logistics problem involving location, fleet sizing, and routing under congestion, proposing a model that integrates these decisions to optimize throughput and robustness.

Contribution

It introduces a novel integrated decision model for location, fleet size, and routing under congestion, reducing the location problem to a weighted Weber problem and analyzing its robustness.

Findings

Location decision reduces to a weighted Weber problem.

Joint location and fleet size decisions are separable.

Location robustness against parameter perturbations.

Abstract

We investigate a location-allocation-routing problem where trucks deliver goods from a central production facility to a set of warehouses with fixed locations and known demands. Due to limited capacities congestion occurs and results in queueing problems. The location of the center is determined to maximize the utilization of the given resources (measured in throughput), and the minimal number of trucks is determined to satisfy the overall demand generated by the warehouses. Main results for this integrated decision problem on strategic and tactical/operational level are: (i) The location decision is reduced to a standard Weber problem with weighted distances. (ii) The joint decision for location and fleet size is separable.(iii) The location of the center is robust against perturbations of several system parameters on the operational/tactical level. Additionally, we consider minimization of travel times as optimization target.