Managing a Customer Following a Target Reverting Policy

We consider a stochastic, capacitated production-inventory model in which the customer provides information about the expected timing of future orders to the supplier. We allow for randomness in customer order arrivals as well as the quantity demanded, but work under the assumption that the customer is making every effort to follow the schedule provided. We term this as a target reverting policy. This gives rise to an interesting nonstationary inventory control model at the supplier. After characterizing the optimal policy, we develop solution procedures to compute the optimal parameters. An extensive computational study provides insights into the behavior of this model at optimality. Further, comparing the cost of the optimal policy to the cost of simple policies that either ignore the customer's information or the capacity constraint, we are able to provide insights as to when these simplifications could be costly.