Effective algorithms for single-machine learning-effect scheduling to minimize completion-time-based criteria with release dates

Abstract Multi-variety and small-batch productions are usually undertaken by skilled workers instead of an automatic assembly line because of economic cost consideration. In the production process, a worker's familiarity to an operation influences the length of task execution time. An interesting phenomenon called learning effect has become a trending research topic. This study investigates a learning effect scheduling model on a single machine system, in which the learning effect is position-dependent and each task is released at different dates. Two optimal criteria are individually discussed: one is total k-power completion time, and the other is maximum lateness. Both problems are NP-hard, therefore, effective algorithms are provided to handle different scale problems within an appropriate CPU time. The heuristic algorithms, namely, shortest processing time available and earliest due date available, are introduced to achieve feasible schedules for large-scale instances, and their asymptotic optimality is proven given that the problem scale tends to infinity. The two heuristics can thus serve as optimal algorithms in mass production. For small-scale instances, a branch and bound algorithm is presented to achieve the optimal solution, where a release-date-based branching rule and preemption-based lower bounds eliminate as many invalid nodes as possible. For medium-scale instances, an evolutionary-based metaheuristic algorithm, namely, discrete differential evolution, is utilized to seek high-quality solutions, in which the initial population and crossover operator are well-designed to enhance its performance. A number of random experiments demonstrate the superiority of the proposed algorithms.