Multi-item inventory systems with joint ordering and transportation decisions

In many practical situations joint determination of ordering and transportation decisions for a family of items may lead to a considerable cost saving. This paper considers a multi-item inventory system with a freight rate schedule that is a function of the volume shipped and the capacity of a standard container. Orders for the family of items are all triggered by a coordinated periodic (R,S) policy. Economies of scale exist because of the reduced freight rates when ordering a full-container load instead of a less-than-container load. A full-container load can be achieved by enlarging the initial order quantities. A heuristic is proposed to decide whether an initial order should be enlarged or not. The heuristic is based on a comparison of the expected saved shipping cost, the expected saved ordering cost and the expected extra holding cost, caused by an enlargement. Some numerical examples show that the heuristic works quite satisfactorily.