A study on capacity allocation scheme with seasonal demand

This paper studies a game-theoretical capacity allocation problem in a two-echelon supply chain comprised of one supplier and N retailers. With demand fluctuating seasonally and significantly, supply is sufficient in low-demand periods but is insufficient in high-demand periods, especially when the supplier’s capacity decreases in high-demand periods. Retailers compete for the supplier’s capacity in high-demand periods, but do not want to absorb the supplier’s redundant capacity in low-demand periods. A turn-and-earn allocation scheme is proposed to encourage retailers to increase their order quantity in low-demand periods. Under the turn-and-earn allocation scheme, in high-demand periods, the supplier is willing to offer a guaranteed portion of supply capacity for the primary retailer. The remaining capacity in high-demand periods is allocated based on orders retailers placed in low-demand periods. In response, the retailers will decide how much they should order in low-demand periods. Then, a competitive game based on Nash equilibrium among the supplier and her retailers is analysed. In order to solve the problem of unreasonable distribution of interest caused by competition, a contract is designed to make it possible for subsidy to be transferred from the supplier to the retailers. Usually, the supplier and her primary retailer can both be better off under turn-and-earn allocation compared with fixed allocation, and the system efficiency in Nash solution is close to it in optimal solution. A numerical study is also conducted to discuss the parties’ sensitivity to different demand level and guaranteed allocation portion of capacity.