Capacity allocation for producing age-based products

Abstract

We consider a firm's production and sales decisions for an age-based product whose value increases with ageing (e.g., whisky, wine, and cheese). The firm has been selling a younger-aged product but is considering introducing a new product by setting some of its production aside to age longer (in the “maturation” process). With a fixed production capacity dictated by the “distilling” process that takes place before the maturation process, the firm needs to decide if and when to sell different aged products as partial substitutes. Specifically, the firm must decide, period by period, how much, if any, of its younger-aged product to set aside for additional ageing. Because the younger product has been selling for some time, the firm knows its market size. For the new product, we consider two scenarios in which the market size is either: (1) known (deterministic) or (2) not yet fully known (stochastic). For the deterministic market size scenario, we provide an analytic solution to the infinite horizon problem and show that the optimal fraction of production reserved for additional ageing increases and converges to a steady-state solution with a closed-form expression. Though our model is dynamic, we show that a static policy, which is easy to compute and is intuitively appealing, performs quite well. For the stochastic market size scenario, we show that a “certainty equivalence” policy is optimal under reasonable conditions, and near-optimal when these conditions do not hold. Hence the stochastic problem is effectively equivalent to the deterministic market size case. We also examine the case when the production process is subject to a deterministic yield loss and obtain similar structural results.