Modified Benders-DES algorithm for real-world flow shop and job shop scheduling problems

Real-world scheduling problems are often extremely challenging to solve, and DES is commonly used to find feasible production schedules without even considering optimization. However, DES can be integrated with MILP using Benders decomposition, which leads to an efficient Benders-DES algorithm (BDES). This work shows that BDES can be developed further to solve complex, real-world scheduling problems illustrated by 2 case studies. First, cut randomization, robustification, and re-optimization are proposed to enhance the solution speed and quality for a hybrid flow shop problem from agrochemical production involving lot-sizing decisions and secondary resources. BDES performs similarly well to a monolithic-sequential MILP-DES approach, a genetic algorithm, and an integer-linear programming approach, while offering practical advantages of solution robustness and re-optimization. Second, BDES is applied to a flexible paint production job shop with makespan and overproduction minimization objective. The performance of BDES is superior to that of the GA originally suggested, resulting in faster solution improvement with fewer DES model evaluations. This work concludes that BDES is a promising algorithmic approach for real-world scheduling problems and an alternative to established optimization methods.