A Greedy Network Flow Algorithm for A Warehouse Leasing Problem

In this paper we consider the problem of a firm which must lease warehouse space over a finite planning horizon. Demand for space in each time period is a random variable with known density function. The firm contracts for warehouse space for each time period at the beginning of the planning horizon via a primary contract. If demand exceeds space in any period, additional space can be obtained via a secondary contract. The leasing problem is shown to be equivalent to a linear programming problem under reasonable assumptions. The dual to the linear program is shown to be equivalent to a network flow problem which can be solved via a greedy algorithm, and admits a rather simple primal variable recovery procedure. Computational evidence indicates that dual problems with some 200,000 arcs can be solved efficiently.