Page - 177 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 35 Mˆ (:, :,7)= 0.5105 0.1190 0.3705 0.3377 0.4472 0.2152 0.0493 0.8089 0.1418 Mˆ (:, :,8)= 0.1930 0.2289 0.5781 0.0701 0.8885 0.0414 0.3581 0.2238 0.4180 Mˆ (:, :,9)= 0.4487 0.2271 0.3242 0.2554 0.4309 0.3137 0.1151 0.7706 0.1143 Mˆ (:, :,10)= 0.6751 0.1230 0.2019 0.0287 0.3383 0.6330 0.0856 0.8210 0.0934 Omitting intermediate calculations, at Steps6and7, thealgorithmcomputesvaluesH(s) and REV(s) foreachcut s, aspresented inTable1. Table1.Computational results. S 0 1 2 3 4 5 6 H(s) 2.5693 1.2861 0.5972 0.1735 0.0953 0.0378 0.0235 REV(s) - 1 0.5368 0.3301 0.0609 0.0448 0.0111 Weobserve thatREV(6)value is less then ε=0.01, thereforewecanreduceourSCsizebytaking the truncatedmodelwith s=6. Theresultsofcomputationsaregraphicallypresented inFigure1. Figure1.Resultsofentropycomputations. 6.Conclusions Amain contributionof thispaper is the entropy-basedmethod for aquantitative assessment of the informationandknowledgerelevant to theanalysisof theSCsizeandcomplexity.Usingthe entropyapproach, thesuggestedmodelextractsasufficientamountofuseful informationfromthe 177