Two-stage three-machine assembly scheduling problem with sum-of-processing-times-based learning effect

Researchers claim that the processing of most products can be formulated as a two-stage assembly scheduling model. The literature states that cumulative learning experience is neglected in solving two-stage assembly scheduling problems. The sum-of-processing-times-based learning effect means that the actual processing time of a job becomes shorter when it is scheduled later, which depends on the sum of processing time of the jobs already processed. Motivated by this observation, we investigate a novel two-stage assembly scheduling with three machines and sum-of-processing-times-based learning effect to minimize the makespan criterion, where two machines operate at the first stage and an assembly machine operates at the second stage. To solve this NP-hard problem, a branch-and-bound method incorporating with ten dominance properties and a lower bound procedure is first derived to obtain an optimal solution. Three heuristics based on Johnson’s rule with and without improvement are then applied separately to a genetic algorithm and a cloud theory-based simulated annealing algorithm, which are further modified with an interchange pairwise method for finding near-optimal solutions. Finally, the numerical results obtained using all proposed algorithms are reported and evaluated.