The Theory And Method Of The Super-large Type Network Simplification On Time-cost Tradeoff Problem

The research on time-cost tradeoff problem started from the early 1960s and the relative scope has expanded a lot in the following decades.However,no breakthrough has been made with regard to the solution of the problem.The main bottleneck is the high complexity and huge work load of computation involved in solving this kind of problem.In order to get rid of the bottleck,another way of thinking is introduced in this paper,namely,to simplify the target rather than to seek and improve the algorithm.By using Critical Path Method(abbreviated as CPM) of network planning technique as the tool,this paper studied the properties of float.Based on the above properties,the super-large type project network is simplified as an equivalent simple network,making the incomputable and complex problem a computable and easy one.What is particular is that the work load of computation of the simplified network is largely reduced whatever agrithorm is used.Therefore,the study made in this paper is not only of therotical significance but also of great practical value.The main study in this paper is detailed as follows:1.Based on the previous studies made by other researchers with regard to the relationship between the floats of identical activities and that of adjacent activities,with the help of new concepts of activity float,this paper studied that how an activity float used up influenced other activities,and then constructed the mathematical model in connection with the influence.By means of the above model,this paper presented the scope influenced,and given out the activities which keep invariable when other activities' float is used up.2.This paper studied the relationship between fore and back single float and length of path.Based on the study of the above properties of float,this paper designed the search method of the Kth sub-critical path.3.Based on the above theoretical system,the paper designed some methods of equivalent simplification of super-large type network in the problem of time-cost tradeoff,including:1) the method of seeking paths,i.e.constituting an equivalent sub-network through seeking the longer paths necessary to be considered in the original network;2) the method of deleting paths,i.e.constituting an equivalent sub-network through deleting the shorter paths uncessary to be considered in the original network.All these methods make use of the total float theorm,node float theorm,back single float theorm and fore single float theorm etc encompassed in the theorm of relationship between the float and the path.