Multi-period dual-sourcing replenishment problem with option contracts and a spot market

The spot market has been gradually recognized as an important alternative purchasing source. To maintain a flexible replenishment strategy, call, put and bidirectional option contracts, as a risk hedging, are in combined usage with the spot market, respectively. The purpose of this paper is to analyze a finite-horizon replenishment problem with option contracts in the context of a spot market.

Based on stochastic dynamic programming, the firm’s optimal replenishment policy with either call, put or bidirectional option contracts is always shown to be order-up-to type, characterized by an upper threshold and a lower one. The corresponding policy parameters in different cases are calculated through an approximate algorithm. This research highlights the effectiveness of option contracts on the firm’s operational strategies and overall profitability.

This study reveals that the firm is better off with option contracts than without them. When the price parameters are the same for different option contracts, bidirectional option contracts are the best choice among these flexible contracts; otherwise, unilateral option contracts might be either better or worse than bidirectional ones. In addition, if low inventory costs and high spot price volatility are confronted, the firm prefers to call option contracts rather than put ones; otherwise, there exists an opposite conclusion.

In addition to highlight the advantage of option contracts over wholesale price contracts, this paper provides interesting observations with respect to the effect of different option contracts on the firm. Many significant insights derived from this research do not only contribute to the provider’s feasible design of the supply contracts, but also contribute to the user’s rational operational strategies for higher profitability.