A fast algorithm for assortment optimization problems

Abstract

Assortment optimization problems intend to seek the best way of placing a given set of rectangles within a minimum-area rectangle. Such problems are often formulated as a quadratic mixed 0–1 program. Many current methods for assortment problems are either unable to find an optimal solution or being computationally inefficient for reaching an optimal solution. This paper proposes a new method which finds the optimum of assortment problem by solving few linear mixed 0–1 programs. Numerical examples show that the proposed method is more computationally efficient than current methods. Scope and purpose Assortment optimization problems aim at cutting given rectangular pieces from a larger rectangle where the wasteful area is minimized. Current assortment optimization methods (Chen et al., European Journal of Operational Research 1993; 63: 362–67; Li and Chang, European Journal of Operational Research 1998; 105: 604–12) are either unable to find optimal solution or being computationally inefficient for reaching the optimal solution. This paper proposes a fast algorithm which only requires to solve three linear programs. Numerical examples demonstrate that the proposed algorithm is much faster than current methods. By utilizing this algorithm, many practical cutting programs in industries could be solved efficiently.