Application of activities with monotone increasing cost function in MPM/PDM least cost scheduling ‘time–cost trade off’ problem

Least cost scheduling techniques on CPM network (shortly CPM/cost problem) originate from Kelly and Walker and was developed in 1959. First algorithm based on network flows was published by Fulkerson in 1961. In classical model every activity has a monotone decreasing cost function. In this paper monotone increasing cost function is also allowed and a new project scheduling model is presented as an application of the mathematical model. An algorithm is presented that follows the main steps of algorithm of CPM/cost method published by Klafszky in 1969. Starting from an optimal initial solution, project duration time is decreased step by step until minimum project duration time is attained. In each step only a maximum flow problem must be solved. An example is presented in order to show the new developments.