Integrated Routing and Job-Shop Scheduling Model under Uncertainty

Abstract

The present study was conducted with the aim of developing an integrated mathematical model to address the routing and job-shop scheduling problem under uncertainty while considering system reliability and maintenance operations. In terms of purpose, this research is applied, and in terms of methodology, it follows a descriptive–analytical approach. The required data were collected through library-based and computational methods. In the first stage, the dimensions of the problem and its associated constraints were defined, and a multi-objective mathematical model was developed to simultaneously minimize costs, maximize reliability, and efficiently manage production resources. Subsequently, the proposed model was solved for small-scale instances using the GAMS software package in order to obtain exact solutions. Considering the combinatorial nature of the problem, its NP-hard complexity, and the exponential growth of the search space in large-scale instances, the multi-objective Non-dominated Sorting Genetic Algorithm II (NSGA-II) was employed to solve the model at realistic scales, and its implementation was carried out in the MATLAB environment. The results demonstrated that the NSGA-II algorithm, with a deviation of less than 3% from the exact solutions obtained by GAMS, was capable of generating high-quality solutions while maintaining an appropriate balance among conflicting objectives. A comparison of the performance of NSGA-II with the Multi-Objective Simulated Annealing (MOSA) algorithm under uncertain conditions also indicated its robustness and satisfactory accuracy in managing complex and dynamic scenarios. Furthermore, computational time analysis revealed that NSGA-II solved large-scale instances in less than one minute, exhibiting significantly faster and more efficient performance than the exact solution approach. In the largest test instance, the solution time of GAMS exceeded 7,200 seconds. The sensitivity analysis further confirmed the significant influence of key parameters, such as failure rate and maintenance duration, on solution outcomes and overall model performance. Overall, the findings indicate that the proposed integrated mathematical model, together with the NSGA-II algorithm, can serve as an effective decision-support tool for production planning, resource optimization, and the management of industrial systems under uncertainty. Moreover, it provides practical guidance for industrial managers seeking to reduce costs and enhance operational efficiency.