By Assistant Professor Vincent T’kindt Ph.D, Professor Jean-Charles Billaut (auth.)
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Extra info for Multicriteria Scheduling: Theory, Models and Algorithms
All jobs scheduled before are early or on time. Moore's algorithm puts Jk on time by removing the preceding job with the greatest processing time. The latter is scheduled late and is not considered anymore. This process is iterated until we have no late jobs in the schedule, except those which have been previously removed and voluntarily put late. The number of late jobs is equal to the number of removed jobs. 6. 24 1. Introduction to scheduling ALGORITHM EJM1 T is the set of jobs to schedule 1* We assume that dl :5 d2 :5 ...
The second is to propose an algorithm which calculates the optimal solution of the problem, but for which the maximal complexity is exponential. In this case, the challenge is to design an algorithm which can solve problems of the largest possible size. To calculate the complexity of scheduling problems, a certain amount of traditional results exist in the literat ure. They show the links between different single criterion scheduling problems. We can represent them under the form of trees of polynomial Thring reductions (see for example [Pinedo, 1995]) where the vertices characterise the problems and where there is an are between a vertex A and vertex B if A (XT B.
The encoding scheme used influences equally the efficiency of the proposable Thring machine. e. which does not pointlessly complicate the obtained grammar. For all reasonable encoding schemes, the proposable 30 2. Complexity of problems and algorithms Turing machines are judged equivalent ([Garey and Johnson, 1979]). Decision problem n Using an encoding seherne e we '''' CJ. I ::> provide a granunar which corresponds 10 the instances of Dn [ GrammarG J We refer 10 L(n,e) as the language associated 10 the chains produced by G aod which correspond 10 the instances of Yn ..
Multicriteria Scheduling: Theory, Models and Algorithms by Assistant Professor Vincent T’kindt Ph.D, Professor Jean-Charles Billaut (auth.)