Extreme-Point Search Heuristics for Solving Interval-Flow Transshipment Networks Richard S. Barr * Robert H. Jones † June, 2012 Abstract Interval-flow networks are a special class of network models that can include minimum-flow requirements on some or all active arcs in a feasi- ble solution. While this extension expresses constraints often encountered in practice, the resulting NP-hard problems are challenging to solve by standard means. This work describes a heuristic that explores adjacent extreme-point solutions to quickly find high-quality feasible solutions to large-scale instances of this problem class. Computer software implement- ing this approach is tested on problems with up to 40,000 nodes and 1 million arcs, giving solution speeds over 400 times faster than a leading commercial optimizer. 1 Introduction This paper describes solution methods for interval-flow transshipment networks, a relatively new class of network flow models in which disjunctive constraints restrict each arc’s flow to be either zero or within a stated interval. As de- tailed below, the traditional pure network formulation is extended by including conditional lower bounds to require minimum flow levels on arcs with activity. The addition of minimum-use activity levels expands the applicability of the popular network-flow models to include quantity discounts, economic viability thresholds, lot-sizing considerations, and demand triggers for technology deci- sions. A familiar examples would be minimum class sizes for a college course to be offered (see Figure 1) and minimum purchase amounts to receive a lower price. Figure 2 depicts a software licensing model that provides quantity dis- counts for bulk purchases and costs of delaying and expediting license renewals to take advantage of the lower prices. Interval-flow modeling enhances logistics networks [9, 18] such as trucking, shipping, or road toll planning [10] by requiring a minimum shipment size for * Department of Engineering Management, Information, and Systems, Lyle School of En- gineering, Southern Methodist University, Dallas, TX 75275, USA, barr@smu.edu † Oncor Electric Delivery, Dallas, TX, USA, robert.jones@oncor.com 1