Shared resource capacity expansion decisions for multiple products with quantity discounts

When multiple products compete for the same storage space, their optimal individual lot sizes may need to be reduced to accommodate the storage needs of other products. This challenge is exacerbated with the presence of quantity discounts, which tend to entice larger lot sizes. Under such circumstances, firms may wish to consider storage capacity expansion as an option to take full advantage of quantity discounts. This paper aims to simultaneously determine the optimal storage capacity level along with individual lot sizes for multiple products being offered quantity discounts (either all-units discounts, incremental discounts, or a mixture of both). By utilizing Lagrangian techniques along with a piecewise-linear approximation for capacity cost, our algorithms can generate precise solutions regardless of the functional form of capacity cost (i.e., concave or convex). The algorithms can incorporate simultaneous lot-sizing decisions for thousands of products in a reasonable solution time. We utilize numerical examples and sensitivity analysis to understand the key factors that influence the capacity expansion decision and the performance of the algorithms. The primary characteristic that influences the capacity expansion decision is the size of the quantity discount offered, but variability in demand and capacity per unit influence the expansion decision as well. Furthermore, we discover that all-units quantity discounts are more likely to lead to capacity expansion compared to incremental quantity discounts. Our analysis illuminates the potential for significant savings available to companies willing to explore the option of increasing storage capacity to take advantage of quantity discount offerings for their purchased products.