Joint pricing and inventory control for fresh produce and foods with quality and physical quantity deteriorating simultaneously

A great number of models have been proposed to investigate the deterioration inventory. However, most of models assume that a fixed physical quantity of items deteriorates over time, the quality of items does not decay before their expiration dates. In practice, the quality and physical quantity of many products, including fresh produce and foods, often deteriorate over time. The quality of an item usually plays an important role in influencing the demand for products. In this paper, we consider the pricing and lot-sizing problem for products with quality and physical quantity deteriorating simultaneously. The deterioration rate of quality and physical quantity is taken to be time proportional. The demand rate is assumed to be deterministic and dependent on the quality of an item, the selling price per unit and the on-display stock level. The theory for finding the optimal solution of problem is discussed and numerical examples are used to illustrate the model and the solution procedure. Finally, sensitivity analysis of the optimal solution with respect to price sensitive parameter and values of different deterioration functions is carried out.