SOLUTION OF A TINNED IRON PURCHASING PROBLEM BY LAGRANGEAN RELAXATION

A tin factory obtains its material from steel works. This consists of sheets of tinned iron which may have very diverging specifications wit h respect to length, width, thickness, and thicknesses of tinfoils. Pr ices per unit of volume vary with width and thickness. For large quant ities of the same size discounts are given. As a consequence of the pr ice structure it is often advantageous for the factory to order sheets of larger sizes than needed and to resell the leftover pieces as scar p. The question is which sizes and quantities one should order if one wishes to minimize total purchase cost. This problem is formulated as a combinatorial optimization problem that is solved by Lagrangean rela xation and subgradient techniques.