Finding Pareto Optimal Front For The Multi- Mode Time, Cost Quality Trade-Off In Project Scheduling

Project managers are the ultimate responsible for theoverall characteristics of a project, i.e. they should deliver the projecton time with minimum cost and with maximum quality. It is vital forany manager to decide a trade-off between these conflictingobjectives and they will be benefited of any scientific decisionsupport tool. Our work will try to determine optimal solutions (ratherthan a single optimal solution) from which the project manager willselect his desirable choice to run the project. In this paper, theproblem in project scheduling notated as(1,T|cpm,disc,mu|curve:quality,time,cost) will be studied. Theproblem is multi-objective and the purpose is finding the Paretooptimal front of time, cost and quality of a project(curve:quality,time,cost), whose activities belong to a start to finishactivity relationship network (cpm) and they can be done in differentpossible modes (mu) which are non-continuous or discrete (disc), andeach mode has a different cost, time and quality . The project isconstrained to a non-renewable resource i.e. money (1,T). Becausethe problem is NP-Hard, to solve the problem, a meta-heuristic isdeveloped based on a version of genetic algorithm specially adaptedto solve multi-objective problems namely FastPGA. A sample projectwith 30 activities is generated and then solved by the proposedmethod.