A continuous review inventory model with the controllable production rate of the manufacturer

Optimal operating policy in most deterministic and stochastic inventory models is based on the unrealistic assumption that lead-time is a given parameter. In this article, we develop an inventory model where the replenishment lead-time is assumed to be dependent on the lot size and the production rate of the manufacturer. At the time of contract with a manufacturer, the retailer can negotiate the lead-time by considering the regular production rate of the manufacturer, who usually has the option of increasing his regular production rate up to the maximum (designed) production capacity. If the retailer intends to reduce the lead-time, he has to pay an additional cost to accomplish the increased production rate. Under the assumption that the stochastic demand during lead-time follows a Normal distribution, we study the lead-time reduction by changing the regular production rate of the manufacturer at the risk of paying additional cost. We provide a solution procedure to obtain the efficient ordering strategy of the developed model. Numerical examples are presented to illustrate the solution procedure.