Optimising lot sizing and order scheduling with non-linear production rates

This research focuses on developing an optimum production schedule in a process with a non-linear production rate. Non-linear production processes may exhibit an increasing production rate as the lot size increases, which results in increasing efficiency in per-unit production. The degree to which this learning is carried forward into the next lot varies by process. Sometimes the learning effect experiences a 100% carryover into the next lot, but other times some learning is forgotten and there is less than a 100% carryover. We consider processes in which the learning effect is completely forgotten from lot to lot. In practice non-linear processes are often treated as linear. That is, the production data are collected and aggregated over time and an average production rate is calculated which leads to inaccuracies in the production schedule. Here we use a discretised linear model to approximate the non-linear process. Production occurs in discrete time periods within which the amount produced is known. This enables a production schedule to be determined that minimises production and holding costs. A dynamic programming model that starts with the latest demand and progresses towards the earliest demand is used to solve the single-product single-machine problem. The model is tested using the production function from the PR#2 grinding process at CTS Reeves, a manufacturing firm in Carlisle, Pa. Solution times are determined for 50, 100, 200, 500, 1500, and 3000 periods.