A two-stage capacity reservation supply contract with risky supplier and forecast updating

Abstract

We propose a single product two-stage supply contract between a retailer and a main supplier. The retailer buys a number of supply options for a non-refundable price from the main supplier at the beginning of the first decision stage (first period), which can be seen as capacity reservation. At the beginning of the second decision stage (second period), these options can be exercised for a given unit cost and transformed, by the retailer, fully or partially, into orders that are delivered by the supplier immediately. Moreover, the retailer faces a stochastic demand, which is concentrated in the second period and is modeled jointly with a correlated exogenous information using a joint probability distribution. In addition, a second supply opportunity from a risky supplier whose availability is random and modeled using a Bernoulli distribution may be available. At the beginning of the second decision stage, the stochastic exogenous information is revealed and the information about the availability or unavailability of the risky supplier becomes known. Therefore, the demand forecast is updated conditionally to the value of the exogenous information. Thus, if the risky supplier is available, another quantity may be ordered from this supplier by the retailer for a given unit cost and delivered immediately. The end-customer demand occurs during the second period and every satisfied demand is charged a given unit price by the retailer. At the end of the selling season, any remaining units are salvaged by the retailer at a salvage value.We model this problem using a dynamic programming approach and we exhibit some characteristics of the structure of the optimal inventory control policy for the retailer. More specifically, we provide the structure of the second decision stage optimal policy and some analytical insights concerning the first stage optimal policy. Furthermore, through a numerical study, we analyze the effect of some of the model parameters on the optimal policy such as the information quality, the probability of the availability of the risky supply option, and the difference between the costs of the two supply options.