The assortment problem with dynamic deterministic demands and stationary stocking-substitution policies

We consider multi-period one-dimension assortment problems in which demands for all sizes meet the conditions for a dynamic demand economic lot size problem, the same set of sizes are stocked and the same substitution rules are followed in all periods (stationary stocking-substitution policies), and substitution costs have a 'scrap' component and, possibly, either unit-dependent or unit-independent fixed costs. We develop the form of an optimal solution for certain assumptions about the nature of the cost functions and for the relationships among demand patterns for the different sizes. Solution algorithms are developed for both segmented and quasi-segmented stocking-substitution policies and computation-reduction results are developed.