Divisible Activities in Critical Path Analysis

Abstract

A critical path scheduling problem is investigated in which a single activity can have its completion time divided up and allocated to different “locations” in the project precedence network. An algorithm for determining the allocation that minimizes total project duration is given, together with an outline of an optimality proof, and an example. Although the algorithm is very similar to those used in network-flow type problems, and uses only integer-valued variables, the final results for the divisible-activity network are, in general, rational numbers.