Continuous and discrete shipping strategies for the single link problem

We consider the problem of shipping several products from a common origin to a common destination. Each product is offered at the origin and absorbed at the destination at a given constant rate. The objective of the problem is to determine a shipping strategy that minimizes the sum of the transportation and the inventory costs. We present a general framework of analysis from which we derive the known approaches with a continuous frequency and with a set of given frequencies as particular cases. Moreover, we derive from the general framework a new model for the case with discrete shipping times in which a shipment can take place at each discrete time instant. We prove that the optimal solutions of the three models can be ranked and that the distance between the optimal costs can be unlimited in the worst case. Finally, we evaluate, on the basis of a set of randomly generated problem instances, the "average" distance between the optimal solutions of the models.