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

Abstract

In a variety of discrete manufacturing environments, it is common to experience a nonlinear production rate. In particular, our interest is in the case of an increasing production rate, where learning creates efficiencies. This leads to greater output per unit time as the process continues. However, the advantages of an increasing production rate may be offset by other factors. For examples, JIT policies typically lead to smaller lot sizes, where the value of an increasing production rate is largely lost. We develop a general model that balances the impact of various competing effects. Our research focuses on determining lot sizes that satisfy demand requirements while minimising production and holding costs. We extend our prior work by developing a multi-product, multi-machine method for modelling and solving this class of production problems. The solution method is demonstrated using the production function from the PR#2 grinding process for a production plant in Carlisle, PA. The solution heuristic provides solution times that are on average only 0.22 to 0.55% above optimum as the solution parameters are varied and the ratio of heuristic solution times to optimal solution times varies from 18.16 to 14.15%.

Keywords:

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