Integer Linear Programming Applied to Production Planning

Abstract

The Job-Shop Scheduling Problem (JSSP) is a classic optimization problem that has been a focal point in the field of operational research for decades. As industries advance into Industry 4.0, optimizing production planning becomes increasingly cru cial to enhance efficiency and competitiveness. This thesis explores the application of Integer Linear Programming (ILP) to an extended version of the JSSP, intro ducing new constraints and utilizing a heuristic when solving the problem. In this work, we present our mathematical formulation for the extended job-shop schedul ing problem. Our approach embeds additional constraints and variables that reflect real-world production scenarios more accurately than traditional JSSP models. The performance of our formulation is evaluated by comparing our results against two benchmarks, where the first benchmark compares the results to a scheduler solely based on heuristics, and the other compares the result to a lower bound of the optimal solution. These comparisons provide insight into the performance of our proposed model. Furthermore, we discuss difficulties associated with solving this NP problem. Expressing the complications of computational complexity and its ef fects on our extension. This research not only advances the theoretical understand ing and exploration of different useful techniques regarding job-shop scheduling but also provides practical tools and insights for optimizing production planning in the era of Industry 4.0.