TY - JOUR
T1 - Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm
AU - uit het Broek, Michiel A.J.
AU - Schrotenboer, Albert
AU - Jargalsaikhan, Bolor
AU - Roodbergen, Kees Jan
AU - Coelho, Leandro C.
PY - 2021/3/1
Y1 - 2021/3/1
N2 - We present a generic branch-and-cut framework for solving routing problems with multiple depots and asymmetric cost structures, which determines a set of cost-minimizing (capacitated) vehicle tours that fulfill a set of customer demands. The backbone of the framework is a series of valid inequalities with corresponding separation algorithms that exploit the asymmetric cost structure in directed graphs. We derive three new classes of so-called 퐷푘 inequalities that eliminate subtours, enforce tours to be linked to a single depot, and impose bounds on the number of customers in a tour. In addition, other well-known valid inequalities for solving vehicle routing problems are generalized and adapted to be valid for routing problems with multiple depots and asymmetric cost structures. The framework is tested on four specific problem variants, for which we develop a new set of large-scale benchmark instances. The results show that the new inequalities can reduce root-node optimality gaps by up to 67.2% compared with existing approaches. Moreover, the complete framework is very effective and can solve instances of considerably larger size than reported in the literature. For instance, it solves asymmetric multidepot traveling-salesman-problem instances containing up to 400 customers and 50 depots, whereas to date only solutions of instances containing up to 300 customer nodes and 60 depots have been reported.
AB - We present a generic branch-and-cut framework for solving routing problems with multiple depots and asymmetric cost structures, which determines a set of cost-minimizing (capacitated) vehicle tours that fulfill a set of customer demands. The backbone of the framework is a series of valid inequalities with corresponding separation algorithms that exploit the asymmetric cost structure in directed graphs. We derive three new classes of so-called 퐷푘 inequalities that eliminate subtours, enforce tours to be linked to a single depot, and impose bounds on the number of customers in a tour. In addition, other well-known valid inequalities for solving vehicle routing problems are generalized and adapted to be valid for routing problems with multiple depots and asymmetric cost structures. The framework is tested on four specific problem variants, for which we develop a new set of large-scale benchmark instances. The results show that the new inequalities can reduce root-node optimality gaps by up to 67.2% compared with existing approaches. Moreover, the complete framework is very effective and can solve instances of considerably larger size than reported in the literature. For instance, it solves asymmetric multidepot traveling-salesman-problem instances containing up to 400 customers and 50 depots, whereas to date only solutions of instances containing up to 300 customer nodes and 60 depots have been reported.
KW - Asymmetric
KW - Branch-and-cut
KW - Multidepot
KW - Upper-bound procedure
KW - Valid inequalities
KW - Vehicle routing
UR - http://www.scopus.com/inward/record.url?scp=85104127944&partnerID=8YFLogxK
U2 - 10.1287/opre.2020.2033
DO - 10.1287/opre.2020.2033
M3 - Article
VL - 69
SP - 380
EP - 409
JO - Operations Research
JF - Operations Research
SN - 0030-364X
IS - 2
ER -