TY - JOUR
T1 - The vehicle-routing problem with delivery and back-haul options
AU - Anily, Shoshana
PY - 1996/4
Y1 - 1996/4
N2 - In this article we consider a version of the vehicle-routing problem (VRP): A fleet of identical capacitated vehicles serves a system of one warehouse and N customers of two types dispersed in the plane. Customers may require deliveries from the warehouse, back hauls to the warehouse, or both. The objective is to design a set of routes of minimum total length to serve all customers, without violating the capacity restriction of the vehicles along the routes. The capacity restriction here, in contrast to the VRP without back hauls is complicated because amount of capacity used depends on the order the customers are visited along the routes. The problem is NP-hard. We develop a lower bound on the optimal total cost and a heuristic solution for the problem. The routes generated by the heuristic are such that the back-haul customers are served only after terminating service to the delivery customers. However, the heuristic is shown to converge to the optimal solution, under mild probabilistic conditions, as fast as N-0.5. The complexity of the heuristic, as well as the computation of the lower bound, is O(N3) if all customers have unit demand size and O(N3 log N) otherwise, independently of the demand sizes.
AB - In this article we consider a version of the vehicle-routing problem (VRP): A fleet of identical capacitated vehicles serves a system of one warehouse and N customers of two types dispersed in the plane. Customers may require deliveries from the warehouse, back hauls to the warehouse, or both. The objective is to design a set of routes of minimum total length to serve all customers, without violating the capacity restriction of the vehicles along the routes. The capacity restriction here, in contrast to the VRP without back hauls is complicated because amount of capacity used depends on the order the customers are visited along the routes. The problem is NP-hard. We develop a lower bound on the optimal total cost and a heuristic solution for the problem. The routes generated by the heuristic are such that the back-haul customers are served only after terminating service to the delivery customers. However, the heuristic is shown to converge to the optimal solution, under mild probabilistic conditions, as fast as N-0.5. The complexity of the heuristic, as well as the computation of the lower bound, is O(N3) if all customers have unit demand size and O(N3 log N) otherwise, independently of the demand sizes.
UR - http://www.scopus.com/inward/record.url?scp=0000204415&partnerID=8YFLogxK
U2 - 10.1002/(SICI)1520-6750(199604)43:3<415::AID-NAV7>3.0.CO;2-C
DO - 10.1002/(SICI)1520-6750(199604)43:3<415::AID-NAV7>3.0.CO;2-C
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AN - SCOPUS:0000204415
VL - 43
SP - 415
EP - 434
JO - Naval Research Logistics
JF - Naval Research Logistics
SN - 0894-069X
IS - 3
ER -