Abstract
AbstractIn the inventory routing problem (IRP) inventory management and route optimization are combined. The traveling salesman problem (TSP) is a special case of the IRP, hence the IRP is NP‐hard. We investigate how other aspects than routing influence the complexity of a variant of the IRP. We first study problem variants on a point and on the half‐line. The problems differ in the number of vehicles, the number of days in the planning horizon and the service times of the customers. Our main result is a polynomial time dynamic programming algorithm for the variant on the half‐line with uniform service times and a planning horizon of 2 days. Second, for nearly any problem in the class with nonfixed planning horizon, we show that the complexity is dictated by the complexity of the pinwheel scheduling problem, for which the complexity is a long‐standing open research question. Third, NP‐hardness is shown for problem variants with nonuniform servicing times. Finally, we prove strong NP‐hardness of a Euclidean variant with uniform service times and an easily computable routing cost approximation, avoiding immediate NP‐hardness via the TSP.
Highlights
This article studies the computational complexity of special cases of a variant of the inventory routing problem (IRP), in which a set of customers is supplied over a given time horizon by identical vehicles from a central depot
We study problem variants of the IRP in which customers are located on a point or on the half-line
We provide a concise description of the problem variants we study in this article, in much the same spirit as done for scheduling problems in Graham et al [22] and later for dial-a-ride problems in de Paepe et al [18]
Summary
This article studies the computational complexity of special cases of a variant of the inventory routing problem (IRP), in which a set of customers is supplied over a given time horizon by identical vehicles from a central depot. Each customer has a storage capacity, a fixed demand per day, a latest delivery day at the start of the planning horizon and a service time. The metrics that underlie the customer locations do not immediately imply intractability because of routing aspects. We consider the problem in which all customers are located in a single point, on a half-line and in the Euclidean plane, but the latter under a specific approximation of the tour length. The vehicles have a tour duration constraint which limits the number of time units per day (traveling plus service time). The objective is to minimize the total time spent by all vehicles over all days
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
