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Resolution branch and bound and an application: The maximum weighted stable set problem

OPERATIONS RESEARCH 2007年第5期55卷 932-948页

作者： Avenali, Alessandro Univ Roma La Sapienza Dipartimento Informat & Sistemist I-00185 Rome Italy

We propose a new resolution algorithm, called resolution branch and bound (RBB), where a branch-and-bound scheme is empowered by exploiting the information contained in a family of closed subproblems, collected by a full resolution phase. In particular, we use this information to define a new branching rule that seems able to reduce the risk of incurring inappropriate branchings. We apply RBB and the proposed branching rule to the maximum weighted stable set problem, as its features allow us to speed up a time-consuming step in the full resolution phase. To compute upper bounds, we generalize to the weighted case the polynomial time procedure provided by Mannino and Sassano [Mannino, C., A. Sassano. 1994. An exact algorithm for the maximum stable set problem. Computational Optim. Appl. 3 243-258] for the unweighted case. Computational results validate the effectiveness of the provided branching rule and the good performance of RBB on many DIMACS benchmarks.

关键词： algorithms: branch and bound mathematics: combinatorics networks/graphs programming: integer

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A branch AND bound APPROACH FOR MACHINE LOAD BALANCING IN FLEXIBLE MANUFACTURING SYSTEMS

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MANAGEMENT SCIENCE 1986年第10期32卷 1316-1335页

作者： BERRADA, M STECKE, KE UNIV MICHIGAN GRAD SCH BUSINESS ADMANN ARBORMI 48109

A flexible manufacturing system (FMS) is an integrated system of computer numerically controlled machine tools connected with automated material handling. A set of production planning problems for FMSs has been defined (Stecke [Stecke, Kathryn E. 1983. Formulation and solution of nonlinear integer production planning problems for flexible manufacturing systems. Management Sci. 29 (3, March) 273–288.]), and this paper considers one called the loading problem. This problem involves assigning to the machine tools, operations and associated cutting tools required for part types that have been selected to be produced simultaneously. The part types will be machined during the upcoming production period (say, of one to three weeks duration on average) and according to a prespecified part mix. This assignment is constrained by the capacity of each machine's tool magazine as well as by the production capacities of both the system, and each machine type. There are several loading objectives that are applicable in a flexible manufacturing situation. This paper considers the most commonly applied one, that of balancing the workload on all machines.

关键词： production/scheduling: flexible manufacturing production/scheduling: line balancing programming: integer algorithms: branch and bound

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