Optimal sales and production rollover strategies under capacity constraints

Firms regularly replace their old product generation by a newer generation to sustain and increase their market share and profit. The product rollover problem of deciding on the number of old products to be pre-produced before the introduction of the new generation, and then deciding on the prices, sales volumes, and production volumes of the old and the new generation during the introduction under capacity constraint is considered. Production capacity limitations are common during the introduction period of a new product. We provide the first study that examines how a production capacity constraint affects the optimal decisions. The optimal decisions for a deterministic period-based model are provided in closed-form. A single sales/production rollover strategy implies that the sales/production of the old generation is discontinued before introducing the new generation. With a dual sales/production rollover strategy, the old and the new generation are sold/produced simultaneously. Depending on the capacity shortage, there are two types of mitigation actions: (i) increasing the prices, (ii) changing the sales and/or production rollover strategies with pre-production while adjusting the prices accordingly. If the capacity is unlimited, aligned sales and production rollover strategies are always optimal. We establish the conditions under which limited capacity leads to a combination of a single production rollover with a dual sales rollover strategy. We show that the selection of optimal rollover strategies is non-monotone in the available capacity. This implies that a change in the rollover strategy in response to limiting capacity has to be revoked for more severe capacity shortages.