Order selection on a single machine with high set-up costs

Dietrich, Brenda; Lee, Jon; Lee, Yew Sing

doi:10.1007/bf02024936

Cited by 7 publications

(19 citation statements)

References 9 publications

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“…These solutions then generate columns in their task grouping problem. They observed, as did Dietrich et al [7], that the linear programming relaxation of the problem is quite weak. As noted earlier, Dietrich et al improved the linear programming relaxation with the use of cuts.…”

Section: Introductionmentioning

confidence: 87%

“…A valid inequality y k 1 ϩ y k 2 Ն 1 is then generated so that whenever one of the variables is fixed to 0, the other will be fixed to 1. We note that Hirabayashi, Suzuki, and Tsuchiya [15] and Dietrich, Lee, and Lee [7] implemented preprocessing and cuts, respectively, on problems similar to (CSP). Our computational results show this type of simple cut to be very effective in fixing variables inside the branch-and-bound procedure.…”

Section: Branching Strategymentioning

confidence: 98%

“…They concluded that the latter relaxation is preferred. Dietrich, Lee, and Lee [7] developed a heuristic for (OMLP) which was shown to perform quite well. In addition, they developed several properties of relaxations of (OMLP) which led to effective cutting planes for the problem.…”

Section: Introductionmentioning

confidence: 97%

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Capacitated selection problem

Matta

Hsu

Lowe

1999

Naval Research Logistics

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Optimizing the selection of resources to accomplish a set of tasks involves evaluating the tradeoffs between the cost of maintaining the resources necessary to accomplish the tasks and the penalty cost associated with unfinished tasks. We consider the case where resources are categorized into types, and limits (capacity) are imposed on the number of each type that can be selected. The objective is to minimize the sum of penalty costs and resource costs. This problem has several practical applications including production planning, new product design, menu selection and inventory management. We develop a branch‐and‐bound algorithm to find exact solutions to the problem. To generate bounds, we utilize a dual ascent procedure which exploits the special structure of the problem. Information from the dual and recovered primal solutions are used to select branching variables. We generate strong valid inequalities and use them to fix other variables at each branching step. Results of tests performed on reasonably sized problems are presented. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 19–37, 1999

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Section: Introductionmentioning

confidence: 87%

Section: Branching Strategymentioning

confidence: 98%

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Capacitated selection problem

Matta

Hsu

Lowe

1999

Naval Research Logistics

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“…7. Marginal Gain [10]. Selection rule: Define the weight of a job to be the number of jobs that can be added without tool addition when this job is selected; select the job with maximum weight.…”

Section: Minimal Union (Mu)mentioning

confidence: 99%

Worst-case performance of approximation algorithms for tool management problems

Crama

Klundert

1999

Naval Research Logistics

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“…They investigate the polyhedral structure of the problem and focus on the special case in which all batches have the same revenue. For the same formulation, Dietrich, Lee, and Lee [8] define several sets of valid inequalities and observe that adding them to the formulation reduces the number of evaluated branch and bound subproblems. Nevertheless, as reported by several authors [7,8], the LP relaxation of BSP is rather weak, which explains the hardness of solving BSP from a practical viewpoint.…”

Section: Introductionmentioning

confidence: 99%

An implicit enumeration scheme for the batch selection problem

2004

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An important problem arising in the management of logistic networks is the following: given a set of activities to be performed, each requiring a set of resources, select the optimal set of resources compatible with the system capacity constraints. This problem is called Batch Selection Problem (BSP) from traditional applications to flexible manufacturing. BSP is known to be NPhard, and is also considered a difficult integer programming problem. In fact, polyhedral approaches to BSP suffer from the poor quality of the bound provided by the linear relaxation, even after strengthening. We devise an implicit enumeration scheme that attempts to overcome this difficulty. It is based on a formulation of BSP, which is equivalent to a stable set problem with one side constraint. This allows to exploit the upper bound, not only for pruning subproblems, but also for controlling the number and the quality of the subproblems generated. We show the effectiveness of the approach by an extensive computational experience on real-sized randomly generated instances.

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Order selection on a single machine with high set-up costs

Cited by 7 publications

References 9 publications

Capacitated selection problem

Capacitated selection problem

Worst-case performance of approximation algorithms for tool management problems

An implicit enumeration scheme for the batch selection problem

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