The Assortment Problem with Nonlinear Cost Functions

The early work done on the assortment problem assumed a linear production cost and a substitution cost based only on the difference in value of the item used and the item required. The research reported in this paper extends the analysis by considering concave production cost functions and substitution cost functions that add either a unit fixed cost or a unit-independent fixed charge to the previously considered “scrap” cost. The form of an optimal stocking policy is developed for each case and horizon theorems are proved to aid in the computations. Algorithms for finding optimal policies are described.