A Game Theoretical Analysis of the Quantity Discount Problem for Ameliorating Items

The number of retailers who directly deal with poultry farmers recently increases in Japan. It therefore becomes necessary for the poultry farmers to deliver products to the retailers frequently in accordance with the retailers’ demand. The poultry farmer’s inventory level increases due to the increase in the weight of the fowls, but at the same time, it decreases due to loss of the commercial value of the fowls by the reasons of illness or others. The retailer purchases items as fresh chicken meat from the poultry farmer, the inventory level of the retailer is therefore depleted due to the combined effects of its demand and deterioration. The poultry farmer attempts to increase her profit by controlling the retailer’s ordering schedule through a quantity discount strategy. We formulate the above problem as a Stackelberg game between the poultry farmer and the retailer to analyze the existence of the poultry farmer’s optimal quantity discount pricing policy which maximizes her total profit per unit of time. The same problem is also formulated as a cooperative game. Numerical examples are presented to illustrate the theoretical underpinnings of the proposed formulation.