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Multistage Production for Stochastic Seasonal Demand

We consider the problem of production planning for a seasonal good which is produced in a multistage manner (e.g., when one or more components must be produced or purchased with a lead time that is long compared to the sales season). During the selling season, lost Bales occur if demand cannot be satisfied; at the end of the season, leftover inventory incurs the usual overage cost. As the season progresses, the forecast of total demand is revised in light of current sales. The problem is to determine production quantities of the various components and assemblies at each period to minimize expected costs of underage and overage. If delivery is not required until the end of the selling (or "order-taking") season, then a dynamic programming formulation can produce the optimal decision rule. However, for the case in which delivery is required during the season, the associated dynamic programming formulation is computationally infeasible. The paper explores four heuristics for the latter problem and compares their cost performance in a numerical example. The most sophisticated heuristic produces expected profits which range from 3.2% to 5.5% of an upper bound on expected profit.