Abstract

In this paper,we compare different formulations of themulti-depot fleet size

and mix vehicle routing problem (MDFSMVRP). This problem extends the multidepot

vehicle routing problem and the fleet size and mix vehicle routing problem,

two logistics problems that have been extensively studied for many decades. This

difficult vehicle routing problem combines complex assignment and routing decisions

under the objective of minimizing fixed vehicle costs and variable routing costs. We

first propose five distinct formulations to model the MDFSMVRP. We introduce a

three-index formulation with an explicit vehicle index and a two-index formulation in

which only vehicle types are identified. Other formulations are obtained by defining

aggregated and disaggregated loading variables. The last formulation makes use of

capacity-indexed variables. For each formulation, we summarize known and propose

new valid inequalities, including symmetry breaking, lexicographic ordering, routing,

and rounded capacity cuts.We then implement branch-and-cut and branch-and-bound

algorithms for these formulations, and we fed them into a general purpose solver.We

compare the bounds provided by the formulations on a commonly used set of instances

in theMDFSMVRP literature, containing up to nine depots and 360 customers, and on 

newly generated instances.Our in-depth analysis of the five formulations showswhich

formulations tend to perform better on each type of instance. Moreover, our results

have considerably improved available lower bounds on all instances and significantly

improved quality of upper bounds that can be obtained by means of currently available

methods.

Year of Publication
2018
Journal
OR Spectrum 40 (1), 125-157, 2018
Volume
40
Issue
1
Number of Pages
125-157

Alternative formulations and improved bounds for the multi-depot fleet size and mix vehicle routing problem

15-04-2019

Assistant Professor, Department of Operations and Project Management

Citation: Alternative formulations and improved bounds for the multi-depot fleet size and mix vehicle routing problem. OR Spectrum 40 (1), 125-157, 2018. 2018;40(1):125-157.

In: OR Spectrum 40 (1), 125-157, 2018

Published by: R Lahyani, LC Coelho, J Renaud , 2018

Cited by: 35