A multi-warehouse inventory model under hybrid-price-stock dependent demand and a bulk release pattern

In retailing, sales may determinatively depend on both selling price and how much stock is displayed before customers. However, when high logistics costs are incurred at the point of sale, nearby rented warehouses may be arranged as an economic stock point in-between, and partially in lieu of, external orders. Likewise, a simplified ordering process can be attained via modular logistics, a practice considered in different competitive markets. The objective of the present paper is to develop a deterministic modular replenishment model with multiple warehouses (an own warehouse, OW, and rented warehouses, RW, of custom capacities), assuming price- and stock-dependent demand, and a bulk release pattern. The global optimal selling price, order-up-to level, reorder level, and the number and capacity of warehouses conducive to profit maximisation are then determined. To this end, theoretical research in extension of multi-warehouse and hybrid-price-stock dependent demand inventory models is conducted together with computer-assisted numerical studies. Findings show that 1) optimal selling price and displayed stock level may increase with market size, 2) displayed-stock demand elasticity can improve market efficiency, 3) partial use of existing fixed OW capacity may prove optimal as demand decreases, 4) successive RWs may increase profit, yet at a decreasing rate, 5) joint warehouse/price optimisation can be most profitable as demand decreases. From the above, it follows that modular downstream warehousing, jointly with displayed stock-based marketing practices, may constitute an effective tool toward industry profitability and supply - demand alignment, specially during contractionary periods, where price-reducing regulatory efforts may, in turn, become partly dispensable.