The Discrete Two-Dimensional Assortment Problem

• Published in: Operations research Vol. 36; no. 2; pp. 324 - 332
• Main Author: Pentico, David W
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01-03-1988; Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: 112 dynamic programming applications; 334 inventory/production deterministic models; 344 inventory/production operating characteristics; Applied sciences; Average fixed cost; Capital costs; Cost functions; Dynamic programming; Exact sciences and technology; Fixed costs; Heuristic; Heuristics; Inventory control, production control. Distribution; Inventory management; Mathematical analysis; Mathematical theorems; Minimization of cost; Operational research and scientific management; Operational research. Management science; Operations research; Optimization; Optimization techniques; Rectangles; Techniques; Variable costs; Stockpile control; Costs; Substitution; Deterministic model; Quality; Selection; Size; Heuristic method; Cost function; Two dimensional model; Dynamic programming; Mathematical programming
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.36.2.324

In the two-dimensional assortment problem, a unit of product that is larger or better on two measurements or qualities may be used to substitute, at some cost, for a unit of demand that is smaller or inferior on both measurements or qualities. The problem is to determine which dimensional combinations to stock in order to minimize the combined stocking and substitution costs. Characteristics of the optimal stocking pattern are presented, and three heuristic solution procedures are compared with an optimization technique under a variety of conditions for demand and cost characteristics.