Multi-Mode Resource Constrained Multi-Project Selecting and Scheduling Problem to Maximize Net Present Value

Document Type : Original Article


1 MSc. Student, Isfahan University.

2 Assistant Professor, Isfahan University.


In this article, with the aim of maximizing net present value and considering various ways of the payment, the problem of selecting and scheduling several projects using mathematical programming and constraint programming have been investigated, in a way that the project feasibility with regards to the level of available resources is guaranteed and all of the prerequisite relationships are observed. Activities with the different modes of resources can be done. They uses renewable (human resources, equipment) and non-renewable (raw materials, budgets) resources. In calculating the costs, the overtime cost of renewable resources, late penalties or rewards of delivery before the project due date is considered. Created Models are tested by a number of projects from the PSPLIB libraries.


1. Abdolshah, M. A (2014). Review of Resource-Constrained Project Scheduling Problems (RCPSP) Approaches and Solutions.International Transaction Journal of Engineering,Management, & Applied Sciences & Technologies, 50-84.
2. Alam-Tabriz A., Farrokh M. & Ahmadi E. A Comparison of the Neural Network Approach and the Earned Value Management in Predicting Final Cost and Duration of Projects. Journal of Industrial Management Perspective,13,51-65.
3. Bianco, L., Caramia, M., & Dell’Olmo, P. (1999). Solving a preemptive project scheduling problem with coloring techniques. Project Scheduling, 135-145.
4. Cavalcante, C., Souza, C. d., Savelsbergh, M. & Wang, L. W. Y. (2001). Scheduling projects with labor constraints. Discrete Applied Mathematics, 112, 27–52.
5. Chakrabortty, R. K., Sarker, R. A. & a. Essam, D. L. (2014). Event Based Approaches for Solving Multi-mode Resource Constraints Project Scheduling Problem.Computer Information Systems and Industrial Management, 375-386.
6. Chen, J. & Askin, R. G. (2009). Project selection, scheduling and resource allocation with time dependent returns.European Journal of Operational Research, 193, 23-34.
7. Czyzyk, J. M., Mesnier, P. & Moré,J. J. (1998). The NEOS Server.IEEE Journal on Computational Science and Engineering, 5(3), 68-75.
8. Farsijani H., Fattahi M. & Noroozi M. Project Portfolio Selection with Considering Interaction Between Projects using Particle Swarm Optimization (PSO) & Chaotic Dynamic. Journal of Industrial Management Perspective,13,51-65.
9. Focacci, F., Lodi A. & Milano, M. (2002). Mathematical Programming Techniques in Constraint Programming: A Short Overview.Journal of Heuristics, 8, 7–17.
10. Hartmann, S., & Briskorn, D. (2010). A survey of variants and extensions of the resource-constrained project scheduling problem. European Journal of Operational Research, 207, 1-14.
11. Keramati, A., Esmaeilian, M. & Rabieh, M. (2015). Developing a Model for Project Scheduling with Limited resources and Budget with Considering Discounted Cash Flows through Fixed Prioritization Method.Asian Journal of Research in Business Economics and Management, 5(1), 212-220.
12. Kone, O., Artigues, C., Lopez P. & Mongeau, M. (2011). Event-based MILP models for resource-constrained project scheduling problems.Computers & Operations Research, 38, 3-13.
13. Koné, O., Christian, A., Pierre, L. & Marcel , M. (2013). Comparison of mixed integer linear programming models for the resource-constrained project scheduling problem with consumption and production of resources.Flexible Services and Manufacturing Journal, 25, 25-47.
14. Liu, S.-S. & Wang, C.-J. (2011). Optimizing project selection and scheduling problems with time-dependent resource constraints.Automation in Construction,20, 1110–1119.
15. Mika, M., Waligóra, G. & Weglarz, J. (2008). Tabu search for multi-mode resourceconstrained project scheduling with schedule-dependent setup times. European Journal of Operational Research, 3(187), 1238–1250.
16. Pritsker, A. A. B. L., Waiters, J. & P. Wolfe, M. (1969). Multiproject scheduling with limited resources: A zero-one programming approach.Management science, 1(16), 93-108.
17. Project Management Institute, A guide to the project management body of knowledge (PMBOK guide), Newtown Square, Pa: Project Management Institute, 2008
18. Rabieh,M., Fadaie, A.(1394). Fuzzy Robust Mathematical Model for Project Portfolio Selection and its Solving through Multi Objective Differential Evolutionary Algorithm. Journal of Industrial Management Perspective,19,65-90.
16. Sabzehparvar, M. & Seyed-Hosseini, M. (2007). A mathematical model for the multi-mode resource-constrained project scheduling problem with mode dependent time lags.Journal of Supercomputing, 44(3), 257–273.
17. ski, R. S. (1981). Multiobjective network scheduling with efficient use of renewable and nonrenewable resources.European Journal of Operational Research,7, 265–273.
18. Trojet, M., H’Mida, F. & Lopez, P. (2011). Project scheduling under resource constraints: Application of the cumulative global constraint in a decision support framework.Computers & Industrial Engineering, 61, 357–363.