Optimal production and selling policies with fixed-price contracts and contingent-price offers

This paper investigates optimal production and selling decisions for a single supplier with two types of customers. Specifically, risk‐averse buyers would rather pay higher fixed prices with guaranteed supply contracts whereas risk‐prone buyers prefer to secure remaining stocks and pay lower contingent prices. This study formulized this problem with a dynamic programming model and analyzed it further using successive approximations. Theoretical results indicate that no controls are needed for fixed‐price orders. However, thresholds exist for manufacturing and contingent‐price ordering policies. These two types of threshold planes increased with the addition of waiting customers. Furthermore, a sensitivity analysis of seasonal factors revealed that the optimal threshold plane shifts upward during high demand periods.