Exact and heuristic solutions for a shipment problem with given frequencies

We consider the problem of shipping several products from an origin to a destination when a discrete set of shipping frequencies is available, in such a way that the sum of the transportation and inventory costs is minimized. This problem, which is known to be NP-hard, has applications in transportation planning and in location analysis. In this paper we derive dominance rules for the problem solutions that allow a tightening of the bounds on the problem variables and improve the efficiency of a known branch-and-bound algorithm. Moreover, we present some heuristics and compare them with two different modifications of an EOQ-type algorithm for the solution of the problem with continuous frequencies.