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

A. Alfieri (), A. Druetto (), A. Grosso () and F. Salassa ()
Additional contact information
A. Alfieri: Politecnico di Torino
A. Druetto: Università di Torino
A. Grosso: Università di Torino
F. Salassa: Politecnico di Torino

Journal of Scheduling, 2021, vol. 24, issue 6, No 2, 569-588

Abstract: Abstract 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.

Keywords: Price and branch; Column generation; Parallel batching; Scheduling (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10951-021-00703-9

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