Warehouse Problem with Multiple Vendors and Generalized Complementarity Constraints

Abstract: We study the warehouse problem, arising in the area of inventory management and production planning. Here, a merchant wants to decide an optimal trading policy that computes quantities of a single commodity to purchase, store and sell during each time period of a finite discrete time horizon. Motivated by recent applications in energy markets, we extend the models by Wolsey and Yaman (2018) and Bansal and G\"unl\"uk (2023) and consider markets with multiple vendors and a more general form of the complementarity constraints. We show that these extensions can capture various practical conditions such as surge pricing and discounted sales, ramp-up and ramp-down constraints and batch pricing. We analyze the extreme points of the underlying non-linear integer program and provide an algorithm that exactly solves the problem. Our algorithm runs in polynomial time under reasonable practical conditions. We also show that the absence of such conditions renders the problem NP-Hard.