A Float-Path Theory and Its Application to the Time-Cost Tradeoff Problem

Activity floats are vital for project scheduling, such as total floats which determine the maximum permissible delays of activities. Moreover, activity paths in activity networks present essences of many project scheduling problems; for example, the time-cost tradeoff is to shorten long paths at lower costs. We discovered relationships between activity floats and paths and established a float-path theory. The theory helps to compute path lengths using activity floats and analyze activity floats using paths, which helps to transmute a problem into the other simpler one. We discussed applications of the float-path theory and applied it to solve the time-cost tradeoff problem (TCTP), especially the nonlinear and discrete versions. We proposed a simplification from an angle of path as a preprocessing technique for the TCTP. The simplification is a difficult path problem, but we transformed it into a simple float problem using the float-path theory. We designed a polynomial algorithm for the simplification, and then the TCTP may be solved more efficiently.