A column generation based decomposition algorithm for a parallel machine just-in-time scheduling problem

Chen, Zhi Long; Powell, Warren B.

doi:10.1016/s0377-2217(98)00136-2

Cited by 73 publications

(36 citation statements)

References 19 publications

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“…Due to this, few nodes need to be explored in the branch and bound tree, and many test problems are solved at the root node without any branching. This result is consistent with the results obtained by van den Akker, Hoogeveen, and van de Velde [26] and Chen and Powell [5][6][7] in solving other parallel-machine scheduling problems using the column generation approach. (2) When n and α are fixed, a problem with a larger m can usually be solved faster than a problem with a smaller m. This result is also consistent with those obtained in van den Akker, Hoogeveen, and van de Velde [26] and Chen and Powell [5][6][7].…”

Section: Computational Resultssupporting

confidence: 92%

“…The column generation method has been used in the literature to solve large-scale combinatorial optimization problems, including vehicle routing (Desrochers, Desrosievs, and Solomon [8]), cutting stock (Vance et al [27]), capacitated lot sizing (Cattrysse et al [3]), and air crew scheduling (Lavoie, Minoux, and Odier [12]). Recently, it has been successfully applied to solving large-scale scheduling problems; see, for example, van den Akker, Hoogeveen, and van de Velde [26] and Chen and Powell [5][6][7]. Chan et al [4] provide an error bound analysis of using column generation for solving parallel-machine scheduling problems.…”

Section: Branch and Bound Algorithms Formentioning

confidence: 99%

“…The constraint (11) means that exactly one partial schedule is selected for each machine. This constraint is different from (7). In (7), we do not distinguish different machines because the machines in the problem Pm|ind| w j C j are mutually independent and really identical and hence S 1 = S 2 = · · · = S m .…”

Section: Set Partitioning Type Formulationsmentioning

confidence: 99%

“…In [LIND], let the dual variable values be π j for index j in (6), and σ for (7). Similarly, in [LDEP], let the dual variable values be π j for index j in (10), σ k for index k in (11), and ρ k for index k in (12).…”

Section: Column Generation Approachmentioning

confidence: 99%

“…By a column generation approach, Chen and Powell [6] and van den Akker, Hoogeveen, and van de Velde [26] are able to solve this same problem with a much larger size (100 jobs and 20 machines). Chen and Powell [5,7] demonstrate that the column generation approach is also very effective for solving many other parallel-machine scheduling problems.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Scheduling jobs and maintenance activities on parallel machines

Lee

Chen

2000

Naval Research Logistics

Self Cite

182

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Section: Computational Resultssupporting

confidence: 92%

Section: Branch and Bound Algorithms Formentioning

confidence: 99%

Section: Set Partitioning Type Formulationsmentioning

confidence: 99%

Section: Column Generation Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Scheduling jobs and maintenance activities on parallel machines

Lee

Chen

2000

Naval Research Logistics

Self Cite

182

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Exact algorithms for scheduling multiple families of jobs on parallel machines

Chen

Powell

2003

Naval Research Logistics

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Abstract:In many practical manufacturing environments, jobs to be processed can be divided into different families such that a setup is required whenever there is a switch from processing a job of one family to another job of a different family. The time for setup could be sequence independent or sequence dependent. We consider two particular scheduling problems relevant to such situations. In both problems, we are given a set of jobs to be processed on a set of identical parallel machines. The objective of the first problem is to minimize total weighted completion time of jobs, and that of the second problem is to minimize weighted number of tardy jobs. We propose column generation based branch and bound exact solution algorithms for the problems. Computational experiments show that the algorithms are capable of solving both problems of medium size to optimality within reasonable computational time.

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Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs

Bülbül

Kaminsky

Yano

2004

Naval Research Logistics

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Abstract:We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding), and intermediate (work-in-process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two different, but closely related, Dantzig-Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig-Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two different lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near-optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with different types of strongly ᏺᏼ-hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near-optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs.

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A column generation based decomposition algorithm for a parallel machine just-in-time scheduling problem

Cited by 73 publications

References 19 publications

Scheduling jobs and maintenance activities on parallel machines

Scheduling jobs and maintenance activities on parallel machines

Exact algorithms for scheduling multiple families of jobs on parallel machines

Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs

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