Dynamic selling of quality‐graded products under demand uncertainties

This paper examines dynamic selling (DS) problems under demand uncertainties. Quality‐graded products with fully downward substitutable demands are considered. Downward demand substitution indicates that demands for lower quality grade products can be fulfilled by either designated or higher quality grade products. In this dynamic selling problem, decision makers need to choose an optimal selling policy in each decision epoch. The objective is to identify an optimal policy for the dynamic selling of quality‐graded inventory. DS problems are formulated as a discrete‐time Markov decision process (MDP) model. In the MDP model, demand type and inventory levels are state variables. The objective is to maximize expected profits. In such a multi‐dimensional dynamic decision problem, computational complexity is a chief concern. This study proves the structure of optimal policies that significantly reduce computational complexity. Performance of optimal dynamic selling policies is evaluated in detailed numerical studies.