Abstract
(1) The author proposes in this paper a new, practical time-calculation method on network scheduling that is easy to understand in relation to understand in relation to time scaled chart, and that is efficient and speedy in contrast with the traditional hand work method. The procedure of this method is as follows : foward calculation of Earliest Start/Finish Time, Calculation of Free Float and backward calculation of Total (/Dependent) Float. In these calculation the backward is based on the following formulas, DF(J, END)=△T TF(I, J)=FF (I, J)+DF(I, J) [numerical formula] here, DF, TF : Dependent, Total Float to designated project duration (T_0), △T : float of foward-calculated project duration (T) to designated project duration (T_0), END : name of terminal node, I, J, K : name of intermediate nodes, N : set of jobs and nodes in a network. (2) The author extends here the meaning of Critical Path and defines the Longest Path from beginning node via node P or job A to terminal node. The Longest Path via P or A has following properties, (a) Slack of node P=Longest Path Float via P TF of job A=Longest Path Float via A here, Longest Path Float via P, A=T_0-Longest Path Duration via P, A, (b) Number of Longest Paths in a network≧1+number of jobs such as FF>0. By these properties, the meaning of negative TF or Slack can be explained elegantly and it is shown that paths except the Longest Path defined here has no meaning. (3) Besides, in this paper some properties of Floats or Slack and time scaled chart based on Latest Start/Finish Time are discussed.
