Optimum Inventory Control and Warehouse Selection with a Time-Dependent Selling Price

In land-scarce regions, land acquisition and upkeep are becoming more and more expensive as time passes, mainly due to population growth. This eventually will lead most small business owners to rethink their supply chain business models by abandoning owning and running their own warehouses and switching to more lean, flexible, and inexpensive alternatives. In this paper, we consider the alternative of leasing warehouses at the exact required storage capacity. This alternative is analyzed using a mathematical model and a solution algorithm that will help business owners make optimal decisions. The model considers all the available warehousing options, with differing capacities, lease rates, and lease durations for different types of warehouses. The holding cost depends on the number of warehouses leased of each type and their individual lease durations. Since the value of the stored items declines with time, the selling price is assumed to be a linearly decreasing function of the storage duration. The optimization problem is formulated as a nonlinear programing (NLP) model whose objective is to maximize the total profit. An efficient algorithm is proposed that reduces NLP model's nonlinearity to a linear behavior through a combination of neighborhood search and integer programming procedures.