A sequential lot sizing heuristic with optimal average performance

The classical dynamic lot size problem without backlogging is in practice usually solved with the aid of various heuristics. Most heuristics are sequential techniques, i.e. the future demand is considered period for period, and a decision whether to have a set-up or not in a certain period is taken without regarding the future demand. The average performance of a lot sizing heuristic will depend on the demand process. The paper assumes that a typical demand will look like a sequence of independent identically distributed random numbers, and it derives a sequential lot sizing rule with optimal average performance under such circumstances. The optimal decision rule is compared to the Silver-Meal heuristic. The paper also analyzes the situation when the decision rule is allowed to look ahead one period.