Capacity Allocation for Producing Age-Based Products

Abstract

We consider a firm's production and sales decisions for an age-based product (e.g. whiskey, wine, or cheese) whose value increases with aging. The firm has been selling only a younger aged product but is considering introducing a new product by setting some of its production aside to age longer. The firm has a fixed production capacity and the differently aged products are partial substitutes. As such, the firm must decide, period by period, how much, if any, of that period's production to set aside for additional aging.

While the currently available younger product faces a stable and known demand, we consider scenarios in which the demand of the new product is either (1) deterministic or (2) stochastic.

In the deterministic demand scenario, we provide an analytic solution to the infinite horizon problem and show that the optimal fraction of production reserved for additional aging increases to a steady state solution. Though our model is dynamic, we show that a static policy, which is easy to compute and intuitively appealing, performs quite well. For the stochastic-demand scenario, we show that, under reasonable conditions, a "certainty equivalence'' policy is optimal. Hence the stochastic problem is effectively equivalent to the deterministic demand case.