An optimization framework for pricing and delivery in competing retail supply chains with strategic consumers

In retail supply chains where products differ in quality and delivery times are quoted in advance, consumers often behave strategically by delaying purchases to benefit from future discounts or faster service. This paper studies a retail competition scenario in which two firms offer products of different quality levels and compete on both price and delivery time. A two-period model is developed to capture strategic consumer decisions based on valuation, patience, and sensitivity to delivery time. Retailers commit to prices and delivery times at the beginning of the selling season, and consumers decide whether, when, and from whom to make a purchase. The interaction is formulated as a Generalized Nash Equilibrium Problem and solved numerically using a Gauss-Seidel-based algorithm. The model considers both uniform and product-specific levels of consumer patience. Results show that an equilibrium exists when consumers are equally or more patient toward the low-quality product, while no equilibrium arises when patience favors the high-quality product. Higher patience for high-quality products reduces demand and profitability for both firms. Under low competition, the high-quality retailer tends to quote longer delivery times; as competition intensifies, both firms shorten their delivery commitments. The model provides analytical insights into how pricing and delivery strategies align with strategic consumer behavior in competitive retail supply chains.