A branch-and-bound algorithm for discrete multi-factor - download pdf or read online

By Niu Shu-fen, Wang Guo-xin, Sun Xiao-ling

During this paper, a brand new branch-and-bound set of rules in keeping with the Lagrangian twin leisure and non-stop rest is proposed for discrete multi-factor portfolio choice version with roundlot limit in monetary optimization. This discrete portfolio version is of integer quadratic programming difficulties. The separable constitution of the version is investigated by utilizing Lagrangian rest and twin seek. Computational effects express that the set of rules is able to fixing real-world portfolio issues of information from US inventory industry and randomly generated try issues of as much as one hundred twenty securities.

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18 2 Deterministic Models: Preliminaries Tj Lj dj Cj dj Cj Uj 1 dj Cj Fig. 1 Due date related penalty functions The objective to be minimized is always a function of the completion times of the jobs, which, of course, depend on the schedule. The completion time of the operation of job j on machine i is denoted by Cij . The time job j exits the system (that is, its completion time on the last machine on which it requires processing) is denoted by Cj . The objective may also be a function of the due dates.

After completion on one machine a job joins the queue at the next machine. Usually, all queues are assumed to operate under the First In First Out (FIFO) discipline, that is, a job cannot ”pass” another while waiting in a queue. If the FIFO discipline is in effect the flow shop is referred to as a permutation flow shop and the β field includes the entry prmu. Flexible flow shop (F F c) A flexible flow shop is a generalization of the flow shop and the parallel machine environments. Instead of m machines in series there are c stages in series with at each stage a number of identical machines in parallel.

For a survey of scheduling problems with job families and scheduling problems with batch processing, see Potts and Kovalyov (2000). Comments and References 33 The definitions of non-delay, active, and semi-active schedules have been around for a long time; see, for example, Giffler and Thompson (1960) and French (1982) for a comprehensive overview of classes of schedules. 2, which illustrates some of the anomalies of non-delay schedules, is due to Graham (1966). The complexity hierarchy of scheduling problems is motivated primarily by the work of Rinnooy Kan (1976), Lenstra (1977), Lageweg, Lawler, Lenstra and Rinnooy Kan (1981, 1982) and Lawler, Lenstra, Rinnooy Kan and Shmoys (1993).

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A branch-and-bound algorithm for discrete multi-factor portfolio optimization model by Niu Shu-fen, Wang Guo-xin, Sun Xiao-ling

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