Inventory control on sequences of links with given transportation frequencies

This paper deals with the problem of minimizing the sum of the inventory and transportation costs in the multi-products logistic network with one origin, some intermediate nodes and one destination when a set of possible shipping frequencies is given. The problem is to determine for each link a periodic shipping strategy in order to minimize the total cost. We first propose a mixed integer linear programming model; then we present two more compact formulations of the problem obtained by computing the inventory cost through the aggregation of the inventory over time or over nodes. Finally, we present heuristic algorithms based either on the decomposition of the sequence or on the solution of a simpler problem through dynamic programming techniques.