A novel MIP model and a hybrid genetic algorithm for operation outsourcing in production scheduling with carbon tax policy

Abstract

In the defense industry, outsourcing has become crucial during production stages, primarily because certain tasks involve complex operations that may exceed the capabilities of in-house machinery. This is often influenced by factors such as technical competencies and high production costs. On the other side, recent shifts in climate patterns and growing environmental concerns have led to a significant impact on scheduling decisions, especially influenced by the carbon footprint of production factories. Therefore, it is important for manufacturing factories to evaluate both economic and environmental costs. A Mixed Integer Programming (MIP) model is formulated to solve the real -life production scheduling problem including machine costs, operation outsourcing and carbon footprint of the schedule with minimizing total costs. Since the mathematical model has difficulty in finding solutions as the problem size increases, a Hybrid Genetic Algorithm (HGA) which combines Genetic Algorithm (GA) with Iterated Local Search (ILS) procedure is proposed to solve especially medium-sized and large -sized problems. The efficiency of the proposed algorithm is demonstrated through randomly generated test problems. Obtained results indicate the superiority of the proposed HGA over GA, showcasing its ability to generate high -quality solutions and reduce overall costs in a reasonable solution times.