Strict-product-ordering approach in the vertical product-line design problem

We consider a Vertical Product-line Design (VPD) problem for a monopolist where products are designed with quality-type attributes and customer segments exhibit an ordered pattern in the attribute part-worth structure. In this paper, we examine the appropriateness of a strict-product-ordering approach across products in designing a vertical product line. We show that the approach, although used widely in practice, is not a property of an optimal solution and can lead to an arbitrarily bad design. Furthermore, we present a sufficient condition where the strict-product-ordering approach is the property of an optimal solution in a general product line design problem. We also show that the VPD problem with a strict-product-ordering approach is computationally intractable, and develop a greedy heuristic solution procedure that exploits the problem structure. A computational study shows that the heuristic results in an average performance ratio of 98.7% compared with optimal solutions. In addition, our computational study shows that insisting on the strict-product-ordering approach results in on-average 3% less profit for the firm if it is enforced in inappropriate conditions.