Mixed integer programming: A historical perspective with Xpress-MP

Abstract

The mathematical programming system Xpress-MP, Dash Optimization (2006), was first released in 1983 as a tool for modeling and solving linear programming (LP) models on a PC, and it was extended in 1986 to deal with mixed integer programming (MIP) models. Its initial authors, Bob Daniel and I, had previously worked on Scicon’s (now part of EDS) mathematical programming system for Univac mainframes and mini computers such as DEC’s VAX series. Although Xpress-MP was originally designed as a simple tool that every OR Analyst should have on his desk, by 1990 an Intel 486 based PC had as much power as an IBM 3090 mainframe for the numerical work required by mathematical programming and Xpress on such a PC ran faster in elapsed time than IBM’s industry standard MPSX package, IBM (1988), on a typical 3090. From that point onward desktop computers running Xpress-MP were, from a practical point-of-view, as powerful a tool for solving industrial MP problems as software on any standard mini or mainframe computer. My career in mathematical programming was motivated by an early experience of its impact on a British engineering business. With two of my students, I built a simple model of a wire-pulling factory in Liverpool. The factory took as input 8 mm copper rods, which it drew through dies and coated in varnish, to produce electrical wire that was mainly used by electric motor manufacturers. When we started work in 1987, the factory was losing around £800,000 per year and closure seemed imminent. Our simple model looked at a years’ worth of orders, what was required to process them, and their machine requirements. From just looking at the orders’ reduced costs we saw that different customers were placing orders for similar quantities of similar products at vastly different prices. The reason