Optimising lot sizing with nonlinear production rates in a multi-product single-machine environment

Abstract

We model a nonlinear production process at CTS Reeves, a manufacturing firm in Carlisle, PA, using a linear approximation model and heuristic methods to find a near optimal solution to determining lot sizes when learning effects are present. In a nonlinear manufacturing process, the average time to produce a part varies based upon the lot size, and typically, the average time to produce a part decreases as the lot size increases owing to a learning effect. Our linear approximation model uses discrete time periods to represent production lots. The amount of production is known for any discrete period, and as the length of the period increases, the production amounts increase at the nonlinear rate. The discrete time periods enable a production schedule to be determined that minimises production and holding costs. We build upon our prior method, which successfully addressed the single-product, single-machine environment. In this work, we expand the method to the multiple product and single machine environment. Our method constructs a feasible production schedule with total production and holding costs close to those in the optimal linear approximation model. The viability of the heuristic method is verified with testing on 50, 100, 200, 500, 1500, and 3000 period models.

Keywords:

• mathematical programming
• production scheduling
• non-linear production rates
• mixed-integer programming
• learning effect