Assigning slabs to orders: an example of appropriate model formulation

Abstract

An important problem for a steel company is the assigning of slabs, i.e. semi-finished rectangular pieces of steel, to customer orders. Due to its discrete nature, the prolem can be formulated as a zero-one integer programming problem; however, real-world problems are too large (12,000–16,000 zero-one variable) to be solved exactly in a reasonable amount of computer time. In this paper we present a transportation formulation for this problem that can be efficiently solved using a network code of Bertsekas. Then, using rounding heuristics, the transportation solution can be transformed into a practical solution. An example is used to illustrate this approach. Empirical results indicate that excellent (low-cost) practical solutions can be generated for large-scale (300 orders and 3000 slabs) problems in less than 1 min on a 386 PC (25 MHZ).