This paper deals with a problem of production planning of manufacturing system under withdrawal and leasing constraints. We have developed a production policy for a manufacturing system composed by several identical machines mounted in parallel. The problem consists on a production system, unable to satisfy a random demand over a finite time horizon under given service level and take into account the product returned. In order to assure an economical production planning a best combination of leased machines number, production rate and inventory level is made which minimize the total production, holding costs. The key of this study is to consider the influence of the product returned (withdrawal right) on the optimal production planning. An analytical study and a numerical example are presented in order to prove the developed approach.

Production plannin, Random demand, Service level, Multi parallel machine, withdrawal.