Mixed-Integer Linear Programming Model for the Dual-Resource Flexible Job-Shop Scheduling Problem

Abstract

Scheduling is a vital function for efficiently operating flexible job-shop systems. Traditionally, that function considers assigning jobs to machines and their sequence. However, machines need to be operated by another set of resources (i.e., workers). Due to the fact that operators are skilled workers, the available pool is limited. Hence, the interaction of machines and humans needs to be studied in an integral manner to address the scheduling problem. In this article, a novel precedence variable-based, mixed-integer linear programming model is developed for the dual-resource flexible job-shop problem. The mathematical formulation deals with the optimal assignment of machines and workers to operations and the operation sequence in both resources by minimizing the makespan. The model gives an exact solution by solving both the assignment and the sequencing problems concurrently. The model was implemented in Docplex and was run on three instances of varying sizes. The model solved the three introduced examples, including a large instance involving 20 operations with 4 workers and 4 machines, using only 1662 variables and 5217 constraints in 156.43 seconds, indicating that the proposed model is adequate. The model can be used to label training examples for machine learning-based techniques as well as help track and compare models developed using heuristics.