Reactive capacity and inventory competition under demand substitution

An important component of any accurate response program is the creation of extra reactive capacity that can effectively respond to uncertain demand. While the idea of using reactive capacity to reduce the mismatch between supply and demand is well known and the benefit well documented, it has not been studied in a competitive environment. In this paper the competition between two firms that rely on initial inventory as well as reactive capacity to fill uncertain demand is studied. Some customers may switch if they cannot get their first-choice product, so the two firms compete on product availability. Two models are considered. In the first model, reactive capacity is given and the firms compete only on choosing initial inventory. In the second model, the firms compete on both initial inventory and reactive capacity, appropriate for situations where the firms can change reactive capacity temporarily. It is shown that under some mild conditions, a unique Nash equilibrium exists in both models. Attention is focused on the reactive capacity (in the first model) or the cost of reactive capacity (in the second model) and the cost of inventory. Additional reactive capacity or a lower cost of reactive capacity has a positive competitive effect on a firm but a negative effect on the competitor. The effects of inventory cost depend on how the firms compete. In the first model, a lower inventory cost creates a positive competitive effect for a firm but a negative effect for the competitor. In the second model, however, under some reasonable conditions on costs, inventory cost plays no role in the competition; it only affects how the firms use inventory and reactive capacity to fill demand.