Development of a new mathematical model and meta-heuristic algorithm for dual resource constrained hybrid flow-shop scheduling problem with job rejection

In the real world, businesses with hybrid flow-shop manufacturing environment have faced the constraints in machinery, human resource constraints and increasing salary and have tried to use their human resource better. Given the limitations of these resources, customer delivery requirements have made the job rejection essential in order to meet distinct customer requirements. Therefore, this paper considers the dual resource constrained hybrid flow-shop scheduling problem with job rejection in order to minimize the total net cost (the sum of the sum of costs obtained from rejected jobs and total penalty cost) which has high practical and operational relevance in many industries. The present study is developed a new mixed integer linear programming model for the problem. In addition, a new improved sooty tern optimization algorithm (STOA) is proposed to solve large-size problems as well as a new decoding method due to the NP-hardness of the problem. In order to evaluate the proposed optimization algorithm, 5 well-known algorithms in the literature including (Immunoglobulin-based artificial immune system (IAIS), Genetic algorithm (GA), Novel discrete artificial bee colony algorithm (DABC), Fruit fly optimization (IFFO), Effective modified migrating birds optimization (EMBO)) are adapted with the proposed problem and finally the performance of the proposed optimization algorithm is investigated against the adapted algorithms. All results and evaluations show the good performance of the new improved sooty tern optimization algorithm.