Research on the Optimization Decision-Making Two Row-Sequencing-Pairs of Activities with Slacks

421 As a matter of fact, they are from 5 different cognate ternary pairs as listed above. According to the definition cognate and the tardiness theory of the normalized ternary pair, cognate ternary pairs have the same normalization result. Therefore, any five of different cognate ternary pairs can represent total 15 different standard ternary pairs. We can select the first one from each monolog and call them as basic ternary pair. From the theory of standard ternary pair and that of the normalized ternary pair, it could be deduced that the best pair must be a standard and normalized one. So, if the basic ternary pairs are not normalized, it will be normalized first. Then, if the result is not standard any more, a standardization process will ensued, which will change its monolog. As there are only 5 monologs, so if the normalized basic ternary pair is not a standard one, it will be eliminated. The step 2 is right. From theory of standard and normalized ternary pair, it could be deduced that the best pair must be a standard and normalized one. Therefore, the standard normalized ternary pair with minimum tardiness value must be the best solution. Based on the property of the CPM network, this paper developed the preceding main chain theory and the succeeding main chain theory. With these theories, the tardiness theories for duality pair and ternary pair are proved. Then, the standard ternary pair theory, the barycentre theory and the standardized ternary pair theory are developed. Further, a scientific demonstration is give to the above problem for the first time. Finally, an optimization method is designed for the 3 activity pair on the basis of the theories above. The method is simple and can be applied in any circumstance. A branch and bound algorithm for the robust shortest path problem with interval data. The sequential optimal decision of three parallel procedure chains. Abstract. In Operation research, how to schedule parallel activities to sequential ones is typical project scheduling problem with restrained resources, and it is also complicated optimization problem. In this paper, on the basis of characteristic of CPM (Critical Path Method) network, theories of Deficient Values of sequencing-pair and standard row-sequencing-pair are deduced. Based on these theories, an optimization method on selecting 4 activities from N parallel activities to constitute 2 row-sequencing-pairs of activities is designed. By proof, using the method could get optimal …