Implicit Treatment of "Zero or Range" Constraints in a Model for Minimum Cost Foundry Alloys

A major problem in foundries is to select scrap alloys and pure metals in order to produce at minimum cost alloy of specified composition. We show that such problems, of realistic size, can be solved optimally by mixed-integer programming. Constraints are that the content of the alloys in various metals must be within given ranges and that the selected amount of each scrap alloy must be either zero or within a given range. The latter "zero or range" constraints can be treated implicitly in a similar way as lower and upper bounds are treated implicitly in bounded variables linear programming. Computation times for representative problems are thus reduced by a factor of three.