Convex hull results for the warehouse problem

Given an initial stock and a capacitated warehouse, the warehouse problem aims to decide when to sell and purchase to maximize profit. This problem is common in revenue management and energy storage. We extend this problem by incorporating fixed costs and provide convex hull descriptions as well as tight compact extended formulations for several variants. For this purpose, we first derive unit flow formulations based on characterizations of extreme points and then project out the additional variables using Fourier-Motzkin elimination. It turns out that the nontrivial inequalities are flow cover inequalities for some single node flow set relaxations.