Batch sizing and scheduling on a volatile production line through the usage of linear optimisation

Abstract

This report examines and determines the optimisation solution to a complex batch sizing problem. A mix of low- and high-volume production causes complexity in batch sizing and scheduling at Mecalc Manufacturing. Prototyping and a volatile demand forecast only adds to the intricacy. After in-depth analyses of the production problem, it is determined that the main restriction of the optimal solution is parameter control. Various Industrial Engineering techniques that relate to batch sizing and operations research are studied in the report. With the control and determination of the production variables being the most crucial factor, the literature study is summarised into three main models. The first model that is considered, is an economic manufacturing quantity (EMQ) with random breakdowns (Lin & Kroll 2007). Stochastic programming is then studied, from which the next two models originate – The recourse model with a multi-stage problem and the probabilistically constrained model. These two are very similar in results, working with production and variable scenarios. After comprehensive comparisons between the models researched, it is decided to formulate both stochastic-type models. The reason for this is the unpredictability of Mecalc’s production parameters and data. Both models are programmed on Python giving results that are not satisfactory for Mecalc’s unique production process. The multi-stage model is chosen as the base for the solution model and adjustments are made accordingly. The final solution formulation is clearly laid out with all its elements, explanations, and interpretations. Variables are analysed, and complexities are determined. The data frames that function as the input, are explained with some of the variables’ simulations. Validation of the solution and the sensitivity analysis thereof is evaluated nearing the end of the report. Some analyses of which resulted in determining the parameters in which the model works and doesn’t work. Variables such as inventory quantities, maximum batch sizes, and reliability factors are assessed. Finally the report is concluded with the proposed implementation with some recommendations for Mecalc.