Optimal dynamic order scheduling under capacity constraints given demand-forecast evolution

We consider a manufacturer without any frozen periods in production schedules so that it can dynamically update the schedules as the demand forecast evolves over time until the realization of actual demand. The manufacturer has a fixed production capacity in each production period, which impacts the time to start production as well as the production schedules. We develop a dynamic optimization model to analyze the optimal production schedules under capacity constraint and demand-forecast updating. To model the evolution of demand forecasts, we use both additive and multiplicative versions of the martingale model of forecast evolution. We first derive expressions for the optimal base stock levels for a single-product model. We find that manufacturers located near their market bases can realize most of their potential profits (i.e., profit made when the capacity is unlimited) by building a very limited amount of capacity. For moderate demand uncertainty, we also show that it is almost impossible for manufacturers to compensate for the increase in supply–demand mismatches resulting from long delivery lead times by increasing capacity, making lead-time reduction a better alternative than capacity expansion. We then extend the model to a multi-product case and derive expressions for the optimal production quantities for each product given a shared capacity constraint. Using a two-product model, we show that the manufacturer should utilize its capacity more in earlier periods when the demand for both products is more positively correlated.