Column generation for minimizing total completion time in a parallel-batching environment

This paper deals with the $$1|{p-\text {batch}, s_j\le b}|\sum C_j$$ 1 | p - batch , s j ≤ b | ∑ C j scheduling problem, where jobs are scheduled in batches on a single machine in order to minimize the total completion time. A size is given for each job, such that the total size of each batch cannot exceed a fixed capacity b. A graph-based model is proposed for computing a very effective lower bound based on linear programming; the model, with an exponential number of variables, is solved by column generation and embedded into both a heuristic price and branch algorithm and an exact branch and price algorithm. The same model is able to handle parallel-machine problems like $$Pm|{p-\text {batch}, s_j\le b}|\sum C_j$$ P m | p - batch , s j ≤ b | ∑ C j very efficiently. Computational results show that the new lower bound strongly dominates the bounds currently available in the literature, and the proposed heuristic algorithm is able to achieve high-quality solutions on large problems in a reasonable computation time. For the single-machine case, the exact branch and price algorithm is able to solve all the tested instances with 30 jobs and a good amount of 40-job examples.

Scheduling parallel-batching processing machines problem with learning and deterioration effect in fuzzy environment

In this paper, a problem of scheduling jobs with different sizes and fuzzy processing times (FPT) on non-identical parallel batch machines to minimize makespan is investigated. Moreover, the processing time (PT) of each batch is subject to the location-based learning and total-PT-based deterioration effect. Since this is an NP-hard combinatorial optimization problem, an improved intelligent algorithm based on fruit fly optimization algorithm (IFOA) is proposed. To verify the performance of the algorithm, the IFOA is compared with three state-of-the-art algorithms. The comparative results demonstrate that the proposed IFOA outperforms the other compared algorithms.