A mixed-integer programming model for a class of assortment problems

The authors consider the problem of placing a set of rectangles of different sizes, in a non-overlapping fashion, within a large rectangle of minimum area. This general problem has several practical applications in location of departments in a minimum area and in two dimensional stock-cutting with the objective of keeping trim-loss at a minimum. The authors formulate the problem as a mixed-integer non-linear programming problem. They present computational results for two special cases of the general problem that reduce to linear integer programs.