Note—On the Optimality of Sub-Batch Sizes for a Multi-Stage EPQ Model—A Rejoinder

Goyal [Goyal, S. K. 1976. Note on ‘Manufacturing cycle time determination for a multi-stage economic production quantity model’. Management Sci.23 (3, November) 332–333.] suggests an extension of the EPQ model described in [Szendrovits, A. Z. 1975. Manufacturing cycle time determination for a multi-stage economic production quantity model. Management Sci.22 (3, November) 298–308.]. His simultaneous optimization of both the lot size (Q) and the number of sub-batches (b) is valid provided that the transportation cost of sub-batches through all stages can be established and that the transportation cost function is of the form he suggests. We should, however, examine the basic nature of transportation costs in a plant and their usual allocation. In practice, any system of transportation equipment and personnel must be designed to cope flexibly with unscheduled activities. The timing of transport operations and the variability in loading the equipment have a great influence on costs. In addition, this transportation system must handle a whole spectrum of products, and it is difficult to allocate the costs of the system to particular product lots. As a consequence, transportation costs in a plant are usually regarded as sunk costs and are treated accordingly in most of the multi-stage inventory models.