A Quantity Discount Problem with One Poultry Farmer and Two Retailers for Ameliorating Items

This study considers a quantity discount problem between a single seller (poultry famer) and two buyers (retailers). The poultry farmer's inventory level increases due to the increase in the weight of the fowls. The retailers purchase fresh chicken meat from the poultry farmer, the inventory levels of the retailers are therefore depleted due to the combined effects of its demand and deterioration. The poultry farmer attempts to increase her/his profit by controlling the retailers' order quantities through a quantity discount strategy. The retailers try to maximize their profits by considering both whether to cooperate with each other and whether to accept the poultry farmer's offer. We formulate the above problem as a Stackelberg game between a single poultry farmer and two retailers to analyze the existence of the poultry farmer's optimal quantity discount pricing policy, which maximizes her/his total profit per unit of time. Numerical examples are presented to illustrate the theoretical underpinnings of the proposed model.