Inventory Management with Advance Supply Contracts Across Multiple Replenishment Periods

In this paper, we study optimal procurement policies with advance contracting option over a finite multi-period horizon for a seasonal product. In this setting, each period is defined by the time between two consecutive inventory replenishment stages where demand is not stationary across periods. Demand for the product in each period is stochastic whose probabilistic distribution is a function of the market signal received right before the beginning of the selling season. The firm receives price discounts by making quantity contracts in advance of the selling season and thus, before the realization of the market signal. Replenishment costs vary across periods during the selling season. We investigate optimal combination of advance contracting and expedited replenishment policies using stochastic dynamic programming. Our research is primarily motivated by applications in the cruise line industry where contracts are made before the final number of bookings is realized and additional purchases can be made at ports of call with varying local prices. Our results show that optimal replenishment policies follow order-up-to policies and there is a unique advance contract amount that minimizes the expected costs over the planning horizon. We provide a numerical sensitivity analysis to investigate the effects of replenishment prices, demand volatility, and disparity between periods in terms of demand on the advance contract amount, replenishments from the spot markets, service levels, and the overall expected cost.