Determining of the Optimum Production Quantity in Two-Echelon Production System with Stochastic Demand

In this article, we integrate production and maintenance to two stage lot sizing models with a central warehouse and a manufacturer by adding a new constraint in which the demand is depend on the average percent of product shortage. The central warehouse faces stochastic demand and is controlled by continuous review (R,Q) policy. Additionally, Warehouse ordering cost can be reduced through further investment. In manufacturer system, assembly line needs two types of raw materials before converting them in to the finished product. One of them requires preprocessing inside the facility before the assembly operation and the other comes directly from outside supplier in assembly line. To analyze, we formulate a nonlinear cost function to aggregate all the costs. For doing this, we use Branch and Bound and nonlinear optimization technique– Generalized Reduced Gradient methods and compare the optimal value of these methods. The model is illustrated through numerical examples and sensitivity analyses on cost functions are presented.