Optimal admission policy in make-to-stock/make-to-order production systems

This paper analyses the performances of a supplier who, besides his own products, has the possibility to accept or not the production of a personalized product for a customer who may be a new one. The contract with this customer specifies the demand arrival rate, the sale price and the backorder cost. Face to this proposition, the supplier has to decide whether to accept or not the contract and how to manage his production system: which products must be produced according to make-to-order policy? Which quantity of finished goods must be kept in the stock for those to produce under make-to-stock policy? We characterize analytically and through numerical examples the structure of the optimal decision with regard to the questions quoted above. We extend the analysis to the case where the supplier can choose between several new product proposals.