Minimizing the Project Cost with Generalized Precedence Relations

Minimizing the project cost is a task of project scheduling, and usually is a starting point in the optimization about cost, for example the time-cost tradeoff is to compress the project duration from the one with minimum cost. Project cost can be minimized by letting all activities choose their minimum cost durations only when strict precedence relations exist between activities. But if generalized precedence relations (GPRs) exist between activities, letting all activities choose their minimum cost durations may not satisfy the given precedence relationships and result in a unfeasible project. In minimizing the project cost with GPRs, we transformed the mathematical programming model into two equivalent special models: a minimum cost maximum flow model and a transportation model with balanced supply and demand. The two special models can be solved by using any current efficient algorithms.