Project Scheduling with Simultaneous Optimization, Time, Net Present Value, and Project Flexibility for Multimode Activities with Constrained Renewable Resources


Faculty of Engineering, University of Kurdistan, Sanandaj, Iran


Project success is assessed based on various criteria, every one of which enjoys a different level of importance for the beneficiaries and decision makers. Time and cost are the most important objectives and criteria for the project success. On the other hand, reducing the risk of finishing activities until the predetermined deadlines should be taken into account. Having formulated the problem as a multi-objective planning problem, the present study aims at minimizing the project completion time as well as maximizing the net present value and project flexibility by taking into account the resource constraints and precedence relations. Here the flexibility of project is calculated by considering a free float for each activity and maximizing the sum of these flotation times. Although most of the researches considered the resources as non-renewable resources, here the resources are considered as renewable ones. Moreover, performing each activity may be possible in various states of using resources (mode) which can change the project completion time and cost. Owing to the complexity of the problem, the Multi Objective Simulated Annealing Meta-heuristic Algorithm is used to solve the proposed model. In doing so, first a feasible answers is proposed and then, using the aforementioned algorithm, it was attempted to find Pareto answers. For accrediting the algorithm, four benchmark problems have been considered. Since the algorithm performed well in finding the optimal answers to the benchmark problems, it was used to find the optimal answer of large scale problems.


1.     Węglarz, J., Józefowska, J., Mika, M. and Waligóra, G., "Project scheduling with finite or infinite number of activity processing modes–a survey", European Journal of Operational Research,  Vol. 208, No. 3, (2011), 177-205.
2.     Pritsker, A.A.B., Waiters, L.J. and Wolfe, P.M., "Multiproject scheduling with limited resources: A zero-one programming approach", Management Science,  Vol. 16, No. 1, (1969), 93-108.
3.     Talbot, F.B., "Resource-constrained project scheduling with time-resource tradeoffs: The nonpreemptive case", Management Science,  Vol. 28, No. 10, (1982), 1197-1210.
4.     Patterson, J., Słowiński, R., Talbot, F. and Węglarz, J., An algorithm for a general class of precedence and resource constrained scheduling problems, in Advances in project scheduling. 1989, Elsevier.3-28.
5.     Zhu, G., Bard, J.F. and Yu, G., "A branch-and-cut procedure for the multimode resource-constrained project-scheduling problem", INFORMS Journal on Computing,  Vol. 18, No. 3, (2006), 377-390.
6.     Hartmann, S. and Drexl, A., "Project scheduling with multiple modes: A comparison of exact algorithms", Networks: An International Journal,  Vol. 32, No. 4, (1998), 283-297.
7.     Hartmann, S., "Project scheduling with multiple modes: A genetic algorithm", Annals of Operations Research,  Vol. 102, No. 1-4, (2001), 111-135.
8.     Tseng, L.-Y. and Chen, S.-C., "Two-phase genetic local search algorithm for the multimode resource-constrained project scheduling problem", IEEE Transactions on Evolutionary Computation,  Vol. 13, No. 4, (2009), 848-857.
9.     Fahmy, A., Hassan, T.M. and Bassioni, H., "Improving rcpsp solutions quality with stacking justification–application with particle swarm optimization", Expert Systems with Applications,  Vol. 41, No. 13, (2014), 5870-5881.
10.   Xiao, J., Wu, Z., Hong, X.-X., Tang, J.-C. and Tang, Y., "Integration of electromagnetism with multi-objective evolutionary algorithms for rcpsp", European Journal of Operational Research,  Vol. 251, No. 1, (2016), 22-35.
11.   Zoraghia, N., Najafib, A. and Niaki, S., "Resource constrained project scheduling with material ordering: Two hybridized meta-heuristic approaches", International Journal of Engineering Transactions C: Aspects, Vol. 28, No. 6 (2015), 896-902..
12.   Ning, M., He, Z., Jia, T. and Wang, N., "Metaheuristics for multi-mode cash flow balancedproject scheduling with stochastic duration of activities", Automation in Construction,  Vol. 81, (2017), 224-233.
13.   Russell, A., "Cash flows in networks", Management Science,  Vol. 16, No. 5, (1970), 357-373.
14.   Sung, C. and Lim, S., "A project activity scheduling problem with net present value measure", International Journal of Production Economics,  Vol. 37, No. 2-3, (1994), 177-187.
15.   Mika, M., Waligóra, G. and Węglarz, J., "Simulated annealing and tabu search for multi-mode resource-constrained project scheduling with positive discounted cash flows and different payment models", European Journal of Operational Research,  Vol. 164, No. 3, (2005), 639-668.
16.   Najafi, A.A. and Niaki, S.T.A., "Resource investment problem with discounted cash flows",  International Journal of Engineering, Vol. 18, No. 1 (2005), 53-64.
17.   Seyfi, M. and Tavakoli, M.R., "A new bi-objective model for a multi-mode resource-constrained project scheduling problem with discounted cash flows and four payment models",  International Journal of Engineering Transactions A: Basics, Vol. 21, No. 4 (2008), 347-360.
18.   Leyman, P. and Vanhoucke,M., "Payment models and net present value optimization for resource-constrained project scheduling", Computers & Industrial Engineering,  Vol. 91, (2016), 139-153.
19.   Huang, X. and Zhao, T., "Project selection and scheduling with uncertain net income and investment cost", Applied Mathematics and Computation,  Vol. 247, (2014), 61-71.
20.   Kelley Jr, J.E., "Critical-path planning and scheduling: Mathematical basis", Operations research,  Vol. 9, No. 3, (1961), 296-320.
21.   Moder, J.J. and Phillips, C.R., " Project management with CPM, PERT and precedence diagramming”, (1983).
22.   Hindelang, T.J. and Muth, J.F., "A dynamic programming algorithm for decision cpm networks", Operations research,  Vol. 27, No. 2, (1979), 225-241.
23.   De, P., Dunne, E.J., Ghosh, J.B. and Wells, C.E., "Complexity of the discrete time-cost tradeoff problem for project networks", Operations Research,  Vol. 45, No. 2, (1997), 302-306.
24.   Erenguc, S.S., Tufekci, S. and Zappe, C.J., "Solving time/cost trade‐off problems with discountedcash flows using generalized benders decomposition", Naval Research Logistics (NRL),  Vol. 40, No. 1, (1993), 25-50.
25.   Icmeli, O. and Erenguc, S.S., "The resource constrained time/cost tradeoff project scheduling problem with discounted cash flows", Journal of Operations Management,  Vol. 14, No. 3, (1996), 255-275.
26.   Amiria, M.T., Haghighi, F., Eshtehardianc, E. and Abessib, O., "Optimization of time, cost and quality in critical chain method using simulated annealing",  International Journal of Engineering Transactions B: Applications , Vol. 30, No. 5 (2017), 627-635.
27.   Al-Fawzan, M.A. and Haouari, M., "A bi-objective model for robust resource-constrained project scheduling", International Journal of Production Economics,  Vol. 96, No. 2, (2005), 175-187.
28.   Ke, H., Wang, L. and Huang, H., "An uncertain model for rcpsp with solution robustness focusing on logistics project schedule", International Journal of e-Navigation and Maritime Economy,  Vol. 3, (2015), 71-83.
29.   Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P., "Optimization by simulated annealing", Science,  Vol. 220, No. 4598, (1983), 671-680.
30.   Černý, V., "Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm", Journal of Optimization Theory and Applications,  Vol. 45, No. 1, (1985), 41-51.
31.   Suppapitnarm, A. and Parks, G., "Simulated annealing: An alternative approach to true multiobjective optimization", in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 1999), Morgan Kaufmann Publishers., (1999), 406-407.