Optimal two-stage lot sizing and inventory batching policies

This paper extends previous studies of two-stage lot sizing problems with finite production rates. We develop various lot sizing and inventory batching (i.e., operation–unit batching (OUB) and unit–unit batching (UUB)) models under different system characteristics and lot sizing and inventory policies. The analysis of the optimality of the lot size ratio between the two stages reveals (1) that both non-increasing and non-decreasing lot sizing policies can be optimal in both OUB and UUB, (2) that a non-integer lot size ratio can be optimal in OUB, and (3) that an integer lot size ratio is always optimal in UUB. We present a simple, easy-to-implement, optimal solution approach to the two-stage lot sizing and inventory batching problem, along with examples.