Who benefits from postponement in multi-period supply channel optimization?

Abstract

Duopolistic price-setting supply channels competing in a bilevel framework have been extensively studied in single-period (static) settings. However, such supply channels typically face uncertain and time-varying demand; and thus require a dynamic analysis. Dynamic channel optimization while addressing uncertain demand has received limited attention due to the highly nested structure of the ensuing equilibrium problems. The level of complexity rises when demand is dependent on current and previous prices. We consider a decentralized (non-cooperative) supply channel whose members, a manufacturer and a retailer, competing in a Stackelberg framework, must address the demand for a perishable commodity within a multi-period discrete-time setting. In the first part of the paper, we propose a constructive theorem providing an explicit solution algorithm to obtain equilibrium states at each period. Next, we prove that the resulting equilibria are subgame perfect. In the second part, we allow the retailer (follower) to postpone the supply and pricing decisions until demand uncertainty is resolved in each period. Using subgame perfection of the equilibria, we propose solution algorithms that use the delayed information obtained by the postponement. Our comparative theorems and simulated scenarios indicate that postponement strategies are always beneficial for the follower, and, for a centralized (cooperative) channel. Whereas in a decentralized channel, due to vertical competition, there may be scenarios wherein postponement strategies, i.e., access to extra information, turn out to be detrimental to the manufacturer (leader).