Scheduling in a Multistage Production System with Set-up and Inventory Costs

This paper considers a multistage production system with constant known demand rate across an infinite horizon. A unit of product passes through the stages sequentially, so each stage draws from the in-process inventory of the previous stage. Each stage of the process is assumed to produce at a fixed, known, finite rate greater than the demand rate, so that it must be shut down and restarted periodically. Different stages may produce at different rates. This paper describes a procedure to find the start-up and shut-down schedule of each production stage which minimizes the sum of inventory costs and set-up costs for the system. This problem is solved using dynamic programming.