On Computational Procedures for Optimising an Omni-Channel Inventory Control Model

Abstract

Dynamic programming (DP) and specifically Markov Decision Problems (MDP) are often seen in inventory control as a theoretical path towards optimal policies, which are (often) not tractable due to the curse of dimensionality. A careful bounding of decision and state space and use of resources may provide the optimal policy for realistic instances despite the dimensionality of the problem. We will illustrate this process for an omni-channel inventory control model where the first dimension problem is to keep track of the outstanding ordered quantities and the second dimension is to keep track of items sold online that can be returned.