Managing Inventory with Cash Register Information: Sales Recorded but Not Demands

Inventory inaccuracy is common in many businesses. While retailers employ cash registers to enter incoming orders and outgoing sales, inaccuracy arises because they do not record invisible demand such as spoilage, damage, pilferage, or returns. This setting results in incomplete inventory and demand information. An important inventory control problem therefore is to maximize the total expected discounted profit under this setting. Allowing for dependence between demand and invisible demand, we obtain the associated dynamic programming equation with an infinite-dimensional state space, and reduce it to a simpler form by employing the concept of unnormalized probability. We develop an analytical upper bound on the optimal profit as well as an iterative algorithm for an approximate solution of the problem. We compare profits of the iterative solution and the myopic solution, and then to the upper bound. We see that the iterative solution performs better than the myopic solution, and significantly so in many cases. Furthermore, it gives a profit not far from the upper bound, and is therefore close to optimal. Using our results, we also discuss meeting inventory service levels.