System feasible duration evaluation method for project management under budget and time constraints

A system feasible duration evaluation method for project management under budget and time constraints, using a computer containing an input unit, an operation unit and an output unit to execute a feasible duration evaluation software which provides a virtual network for simulating a project, the virtual network having a start node, a terminal node and plural arcs, wherein the unit of the arc is a duration and the arcs are located between the start node and the terminal node for constituting plural minimal paths, the method comprising the steps of:

• inputting a plurality of activities of the project, a budget constraint and a time constraint from the input unit by users of the feasible duration evaluation software;
• distributing orderly the activities in the virtual network;
• defining a time vector composed of the durations of the arcs, and the durations, wherein the value of the time vector is stochastic to correspond with a distribution of the feasible durations in the project;
• executing a time check by the operation unit to check if an activity duration of completing each activity is less than or equal to the time constraint, in order to find time vectors satisfying the activity duration;
• executing a budget check by the operation unit to check if a total cost of completing all the activities of the project is less than or equal to the budget constraint, in order to find time vectors satisfying the total cost;
• defining an upper boundary vector composed of the time vectors satisfying the conditions that all the activity durations equal to the time constraint and the total cost less than the budget constraint;
• defining a lower boundary vector composed of the time vectors satisfying the conditions that the total cost is equal to the budget constraint and the activity durations are less than the time constraint;
• and
• listing the time vector for one of the minimal paths in the virtual network less than or equal to the upper boundary vector and larger than or equal to the lower boundary vector, and defining the time vector as a system feasible duration of the project;
• and
• displaying the system feasible duration on the output unit.