Download Advances in Project Scheduling by R. Slowinski and J. Weglarz (Eds.) PDF

By R. Slowinski and J. Weglarz (Eds.)

This multi-author quantity, containing contributions from foreign specialists within the box, provides fresh advancements in undertaking scheduling for either thought and perform. it really is equipped in 3 elements: I. uncomplicated deterministic types; II. distinct deterministic versions; III. Stochastic types. a number of methods is gifted facing multiple-category source constraints, various mathematical versions of actions, and numerous undertaking functionality measures in unmarried and multiobjective formula. unique and heuristic algorithms are awarded for either deterministic and stochastic venture description. the quantity could be of precise curiosity to scientists, scholars, selection makers, government managers, specialists and practitioners curious about structures administration or operations examine, particularly in enterprise, engineering, and finance, but additionally in different components of natural and technologies

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2 THEOREM: The piecewise linear and convex cost functions on closed intervals constitute the smallest class of cost functions that is both closed and contains the (affine) linear cost functions on closed intervals. This result uses linear programming techniques and could be derived completely within linear programming theory. 1, however, offers a rather elegant reduction of the proof to the case when all cost functions of 0 are linear. This is achieved by substituting a job with a piecewise-linear cost function by an appropriate chain of jobs with linear cost functions.

A. The function k. expresses the tradeoff between the cost of the resource allocation to a. and the thus achievable processing time x.. So I. denotes the set of achievable processing times for job a. and, for x. ) expresses the cost (= required resource allocation measured in money) for realizing the processing time x. for a.. , x ) of achievable processing times, 2. ) denotes the associated n' *& 3 3 3 cost. total 45 The main interest then concerns the following two problems: 1. Determination of the minimal cost function H(t): Given a fixed time limit t for the project duration, what is the least cost H(t) for achieving this task?

1) K Note that the infimum may not be attained and that the computation of H(t) may be a difficult problem. For instance, if the k. are piecewise linear but not convex, the usual solution approaches transform the problem into a mixed integer programming problem with 0-1 variables associated with the different slopes of the piecewise linear functions. The computational effort can be decreased by applying again the substitution decomposition [BR]. This holds even without any assumption on the cost function k..

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