The model presented in this paper assumes that a constant lot size is produced through a fixed sequence of manufacturing stages, with a single set-up and without interruption at each stage. Transportation of partial lots, called batches, is allowed between stages. Equal or unequal sized batches can be shipped from one stage to the next, and the total number of batches may differ across stages. A heuristic procedure is developed to determine the economic lot size and the batch sizes for each stage. The computational method for solving the model is illustrated by an example.

This paper describes a model for a multi-stage production/inventory system where lots may be of different sizes. In addition, either completed lots or partial lots, called batches, may be transported to succeeding stages. The model incorporates constraints on lot and batch-sizes and thus provides a rather comprehensive set of possibilities for organizing a production/inventory system. A heuristic solution procedure is developed and is shown to be ‘close to optimal’ by bounding.

The objective of this paper is to show that the models suggested in the literature for optimizing the packaging frequency of jointly replenished items are invalid when the material to be packaged is processed in a multi-stage production/inventory system. Two basic models are presented for the case in which the internally manufactured material is packaged into two items of different size on the same packaging facility. Deterministic and constant demand and production rates, as well as fixed (set-up) costs and linear inventory unit holding costs, are assumed over an infinite time horizon. The ratio of the packaging frequency of the two items is restricted to be an integer and no back-logging of packaged items is allowed. A quite simple solution method and a computational example are given for each model.

It has been suggested in the literature that unequal sub-batch sizes yield a lower cost than equal sub-batch sizes, for the same problem parameters. It is shown in this paper that the cost comparison that led to this conclusion is invalid because it is based on the same lot size and number of sub-batches for both cases. The two models would not necessarily yield identical optimal lot sizes and numbers of sub-batches. Perhaps more importantly, the effect of the relaxed batch-size constraint on transportation costs was ignored in comparing the costs.