Optimal dynamic pricing for perishable foods with quality and quantity deteriorating simultaneously under reference price effects

Empirical evidences demonstrate that food quality and reference prices have great impacts on consumers' purchasing decisions. In practice, the physical quantitative and qualitative deterioration of perishable foods usually occur simultaneously. However, the extant literature of perishable items largely focuses on quantitative deterioration. In this paper, we propose a dynamic pricing model for perishable foods with quality and quantity deteriorating simultaneously under reference price effects. An optimal control model is formulated to maximise the total profit, where the demand depends on the sales price, the quality and the reference price. The optimal dynamic pricing strategy is obtained by solving the optimal control model based on Pontryagin's maximum principle. Additionally, numerical examples and sensitivity analysis are implemented. Finally, some managerial insights are presented.