On the best number of different standard lengths to stock for one-dimensional assortment problems

This paper considers the one-dimensional assortment problem (1D-AP) which includes the determination of the number of different sizes of standard lengths to be maintained as inventory and to be used to fulfill a set of cutting orders. Keeping two or more types of stock lengths in inventory is generally a better practice with respect to the total material cost, when compared to a single type of stock lengths. However, a greater variety in the number of different stock lengths results in increased complexity of operations, stocking and handling. The purpose of this paper is therefore to evaluate the possible savings in the total material cost which can be realized by using an assortment with two or more types of stock lengths, compared to an assortment with a single type of stock lengths. By investigating a large number of problem instances of different classes of the 1D-AP, it is shown that there exist problem classes for which it is possible to realize substantial savings in the total material cost by using an assortment with two, three or four types of standard lengths. However, the results of the computational study also reveal that there are other problem classes for which it is not possible to realize savings of more than 0.5%, even when an assortment with five or more different stock sizes can be used.