Impacts of Inventory Record Inaccuracy on Retailers’ Internal Operations

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We present a continuous-time stochastic formulation of the standard Economic Order Quantity (EOQ) model incorporating all major costs incurred in carrying a product, including the cost of restocking, the cost of auditing the shelf stock level, the opportunity cost of capital, the cost of loss process, and the costs caused by not serving demand. In this formulation, the loss process is an unobservable point process while the demand point process is observed only when the item is in stock. The retailer’s control problem is reduced to an optimal stopping problem (corresponding to the restocking time) during which the shelf stock level can be audited finite number of times. The solution to the Hamilton-Jacobi-Bellman (HJB) equation of this stopping problem is fully characterized and constructed by applying a differential operator finite number of times. In particular, a closed-form expression for the optimal value function is obtained when auditing is infeasible or suboptimal. It is proved that the optimal restocking policy is a threshold policy in a three-dimensional state space that defines the Bayesian belief dynamics of the shelf stock level. Complete comparative statics analysis of this probability threshold along with its corresponding stopping time equivalent in the time domain are provided. We show that the jointly optimal auditing policy is not a threshold-based policy, that is the state trajectory can enter and leave the optimal audit region, leading to a finite time window during which auditing is optimal. We present a numerical example to illustrate the functional form of the optimal solution and estimate the impacts of inventory record inaccuracy on increasing the net present value of the expected total cost of carrying a product. The performance of the optimal policy is also compared with the best performing threshold-based heuristic policies in both time and probability domains. We show in this example that when the distribution of the shelf stock level is dynamically tracked, auditing the shelf stock level has a negligible impact on reducing the net present value of the expected total cost of carrying a product.