Common replenishment cycle order policies for multiple products with capacity expansion opportunities and quantity discounts

Many companies face the challenge of maintaining hundreds, if not thousands, of items in inventory, where each product draws from a common resource (e.g., warehouse space). The introduction of this common resource constraint complicates the traditional lot-sizing problem due to the interdependencies of the lot sizes. This challenge intensifies when the firm can adjust the capacity of the common resource and with the presence of quantity discounts, which may encourage the company to increase lot sizes. This paper develops efficient solutions for a constrained, multi-product lot-sizing problem with a common replenishment cycle, all-units quantity discounts, and a flexible common resource capacity. Historically, the common replenishment cycle (similar to the popular periodic review inventory system) excels in convenience but tends to lag behind in cost effectiveness. We extend the traditional common replenishment cycle approach through the introduction of a refinement policy that allows for more flexibility in the lot-sizing decisions. This modification allows companies to leverage quantity discounts for certain items without detrimental increases to the required common resource capacity (by increasing the cycle length). Via numerical examples and sensitivity analysis, we identify situations where the common replenishment cycle approach with refinement policy outperforms the alternative independent cycles approach in both convenience and cost. Good candidate companies include (1) a growing retailer, (2) a factory with limited storage space, (3) a retailer without secondary warehouse space, (4) a company purchasing bulky items, and (5) a firm located in an expensive city with premium storage space costs.