Stochastic Analytical Models

Cohen and Lee (1988) develop a model for establishing a material requirements policy for all materials for every stage in the supply chain production system. In this work, the authors use four different cost-based sub-models (there is one stochastic sub-model for each production stage considered). Each of these sub-models is listed and described below:

• Material Control: Establishes material ordering quantities, reorder intervals, and estimated response times for all supply chain facilities, given lead times, fill rates, bills of material, cost data, and production requirements.
• Production Control: Determines production lot sizes and lead times for each product, given material response times.
• Finished Goods Stockpile (Warehouse): Determines the economic order size and quantity for each product, using cost data, fill rate objectives, production lead times, and demand data.
• Distribution: Establishes inventory ordering policies for each distribution facility, based on transportation time requirements, demand data, cost data, network data, and fill rate objectives.

Each of these sub-models is based on a minimum-cost objective. In the final computational step, the authors determine approximate optimal ordering policies using a mathematical program, which minimizes the total sum of the costs for each of the four sub-models.