Linear and Non-Linear Models for Master Scheduling of Dynamic Resources Product Mix

TL;DR

This paper develops and compares linear and non-linear models for master scheduling in product mix problems under dynamic resource availability, considering raw material supply variability and optimizing profit, costs, and utilization.

Contribution

It introduces new integer linear and non-linear models that account for dynamic raw material supply in master scheduling, extending prior static resource assumptions.

Findings

Models outperform static approaches in profit and resource utilization

Non-linear models better capture supply variability effects

Comparative analysis shows trade-offs between models' complexity and accuracy

Abstract

The literature on master production scheduling for product mix problems under the Theory of Constraints (TOC) was considered by many previous studies. Most studies assume a static resources availability. In this study, the raw materials supplied to the manufacturer is considered as dynamic depending on the results of the problem. Thus, an integer linear heuristic, an integer non-linear optimization model, and a basic non-linear model are developed to find a good solution of the problem. The results of the three models were compared to each other in terms of profit, raw materials costs, inventory costs and raw materials utilization. Recent studies in the field are reviewed and conclusions are drawn.