Minimizing transportation and inventory costs for several products on a single link

This paper deals with the problem of determining the frequencies at which several products have to be shipped on a common link to minimize the sum of transportation and inventory costs. A set of feasible shipping frequencies is given. Transportation costs are supposed to be proportional to the number of journeys perfromed by vehicles of a given capacity. Vehicles may or may not be supposed to carry out completely all materials available, and products assigned to different frequencies may or may not share the same truck. Integer and mixed integer linear programming models are formulated for each of the resulting four situations, and their properties are investigated. In particular, the authors show that allowing products to be split among several shipping frequencies makes trucks traveling at high frequencies to be filled up completely. In this situation, trucks may always be loaded with products shipped at the same frequency.