Optimal shipment consolidation and dynamic pricing policies for perishable items

Considering a firm who operates multiple stores to sell perishable items with limited inventory, we build a multi-location inventory model to explore the optimal dynamic pricing and shipment consolidation policies. The optimal consolidation and continuous-time dynamic pricing policies are obtained by solving the corresponding optimization problem based on optimal control theory. The optimal strategies derived show that the firm should take penetration pricing policy and select a subset of stores with high market potentials. Compared to cases of static pricing and non-consolidation, both dynamic pricing and shipment consolidation policies can enhance the firm's profitability, while they exert substitutable effects. Furthermore, the heterogeneity of stores, price sensitivity of demands, deteriorating property of items, holding cost and delivery cost all highlight the importance of consolidation. Additionally, the optimal dynamic price exhibits non-monotonicity with respect to deterioration rate and holding cost.