Multi-objective Optimization of Multi-mode Resource-constrained Project Selection and Scheduling Problem Considering Resource Leveling and Time-varying Resource Usage

Document Type : Research Paper

Authors

1 Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

2 Department of Industrial Engineering and Management, Shahrood University of Technology, Shahrood, Iran

Abstract

In this paper, a multi-objective mixed-integer programming model is developed to cope with the multi-mode resource-constrained project selection and scheduling problem, aiming to minimize the makespan, maximize the net present value of project cash flows, and minimize the fluctuation of renewable resource consumption between consecutive time periods. Moreover, activities are considered to be subject to generalized finish-to-start precedence relations, and time-varying resource usage between consecutive time periods. To assess the performance of the proposed model, 30 different-sized numerical examples are solved using goal programming, epsilon constraint, and augmented epsilon constraint methods. Afterward, Tukey test is used to statistically compare the solution methods. Moreover, VIKOR method is used to make an overall assessment of the solution methods. Statistical comparisons show that there is a significant difference between the mean of the resource leveling objective functions for all the solution methods. In other words, goal programming statistically outperforms other solution methods in terms of the resource leveling objective function. This is not the case for the other objective functions and CPU times. In addition, results of the VIKOR method indicate that the goal programming method outperforms the other solution methods. Hence, goal programming method is used to perform some sensitivity analyses with respect to the main parameters of the problem. Results show that by improving any of the parameters at least one objective function improves. However, due to the conflicting nature and the impact of weights of objective functions, in most cases, the trend are not constant to describe a general pattern.

Keywords

References

Afshar-Nadjafi, B. (2014). Multi-mode resource availability cost problem with recruitment and release dates for resources. Applied Mathematical Modelling, Vol. 38(21), pp. 5347–5355.
Afshar-Nadjafi, B. (2018). A solution procedure for preemptive multi-mode project scheduling problem with mode changeability to resumption. Applied Computing and Informatics, Vol. 14(2), pp. 192-201.
Atan, T., and Eren, E. (2018). Optimal project duration for resource leveling. European Journal of Operational Research, Vol. 266(2), pp. 508-520.
Babaee Tirkolaee, E., and Goli, A., & Hematian, M., & Sangaiah, A.K., & Han, T. (2019). Multi-objective multi-mode resource constrained project scheduling problem using Pareto-based algorithms. Computing, Vol. 101, pp.  547-570.
Balouka, N, Cohen, I, and Shtub, A. (2016). Extending the Multimode Resource-Constrained Project Scheduling Problem by Including Value Consideration. IEEE Transaction on Engineering Management, Vol. 63(1), pp. 4-15.
Beşikci, U., Bilge, Ü., and Ulusoy, G. (2014). Multi-mode resource constrained multiproject scheduling and resource portfolio problem. European Journal of Operational Research, Vol. 240(1), pp. 22-31.
Chakrabortty, R.K., Abbasi, A., and Ryan, M.J. (2020). Multi-mode resource-constrained project scheduling using modified variable neighborhood search heuristic. International Transactions in Operational Research, Vol. 27(1), pp. 138-167.

Chakrabortty, R.K., Sarker, R.A., and Essam, D.L. (2016). Multi-mode resource constrained project scheduling under resource disruptions. Computers & Chemical Engineering, Vol. 88, pp. 13-29.

Coughlan, E. T., Lübbecke, M. E., and Schulz, J. (2015). A branch-price-and-cut algorithm for multi-mode resource leveling. European Journal of Operational Research, Vol. 245(1), pp. 70-80.
Delgoshaei, A., Ali, A., Parvin, M., and Ghoreishi, M. (2018). An Applicable Heuristic for Scheduling Multi-mode Resource Constraint Projects Using PERT Technique in the Presence of Uncertain Duration of Activities. International Journal of Supply and Operations Management, Vol.  5(4), pp. 338-360.
Elloumi, S., Fortemps, P., and Loukil, T. (2017). Multi-objective algorithms to multi-mode resource constrained projects under mode change disruption. Computers & Industrial Engineering, Vol. 106, pp. 161-173.
Elmaghraby, S. E. (1977). Activity networks: Project planning and control by networkModels. 1st Edition.New York: Wiley.
García -Nieves, J. D., Ponz-Tienda, J. L., Salcedo-Bernal, A., and Pellicer, E. (2018). The Multimode Resource-Constrained Project Scheduling Problem for Repetitive Activities in Construction Projects. Computer-Aided Civil and Infrastructure Engineering, Vol. 33(8), pp. 655-671.
García-Nieves, J. D., Ponz-Tienda, J. L., Ospina-Alvarado, A., and Bonilla-Palacios, M. (2019). Multipurpose linear programming optimization model for repetitive activities scheduling in construction projects. Automation in Construction, Vol. 105, pp. 102799.
Gnägi, M., Rihm, T., Zimmermann, A., and Trautmann, N. (2019). Two continuous-time assignment-based models for the multi-mode resource-constrained project scheduling problem. Computers & Industrial Engineering, Vol. 129, pp. 346-353.
Gutjahr, W.J., Katzensteiner, S., and Reiter, P. (2010). Christian Stummer, Michaela Denk, Multi-objective decision analysis for competence-oriented project portfolio selection. European Journal of Operational Research, Vol. 205(3), pp. 670-679.
Hafezalkotob, A., Hosseinpour, E., Moradi, M., and Khalili-Damghani, K. (2017). Multi-resource trade-off problem of the project contractors in a cooperative environment: highway construction case study. International Journal of Management Science and Engineering Management, Vol. 13(2), pp. 129-138.
Hartmann, S., and Briskorn, D. (2010). A survey of variants and extensions of the resource-constrained project scheduling problem. European Journal of Operational Research, Vol. 207(1), pp. 1-14.
Hartmann, S., and Briskorn, D. (2021). An updated survey of variants and extensions of the resource-constrained project scheduling problem. European Journal of Operational Research, 2021, In press.
He, Z., He, H., Liu, R., and Wang, N. (2016). Variable neighbourhood search and tabu search for a discrete time/cost trade-off problem to minimize the maximal cash flow gap. Computers & Operations Research, Vol. 78, pp. 564-577.
Heidari-Fathian, H., and Davari-Ardakani, H. (2019). Bi-objective optimization of a project selection and adjustment problem under risk controls. Journal of Modelling in Management, Vol. 15(1), pp. 89-111.
Hochbaum, D.S. (2016). A polynomial time repeated cuts algorithm for the time – cost tradeoff problem: The linear and convex crashing cost deadline problem. Computers & Industrial Engineering, Vol. 95, pp. 64-71.
Hosseinian, A., Baradaran, V., and Bashiri, M. (2019). Modeling of the time-dependent multi-skilled RCPSP considering learning effect: An evolutionary solution approach. Journal of Modelling in Management, Vol. 14(2), pp. 521-558
Kazemi, S., and Davari-Ardakani, H. (2020). Integrated resource leveling and material procurement with variable execution intensities. Computers & Industrial Engineering, Vol. 148, pp. 1-24.
Khalili-Damghani, K., Tavana, M., Abtahi, A. R., and Arteaga, F. J. S. (2016). Solving multi-mode time–cost–quality trade-off problems under generalized precedence relations. Optimization Methods and Software, Vol. 30(5), pp. 965-1001.
Kumar, M., Mittal, M.L., Soni, G., and Joshi, D. (2018). A hybrid TLBO-TS algorithm for integrated selection and scheduling of projects. Computers & Industrial Engineering, Vol. 119, pp. 121-130.
Leyman, P., Van Driessche, N., Vanhoucke, M., and De Causmaecker, P. (2019). The impact of solution representations on heuristic net present value optimization in discrete time/cost trade-off project scheduling with multiple cash flow and payment models. Computers & Operations Research, Vol. 103, pp. 184-197.
Leyman, P., and Vanhoucke, M. (2016). Payment model and net present value optimazation for resource-constrained project scheduling. Computers & Industrial Engineering, Vol. 91, pp. 139-153.
Li, H., and Dong, X. (2018). Multi-mode resource leveling in projects with mode-dependent generalized precedence relations. Expert Systems with Applications, Vol. 97, pp. 193–204.
Li, H., Xiong, L., Liu, Y., and Li, H. (2018). An effective genetic algorithm for the resource levelling problem with generalized precedence relations. International Journal of Production Research, Vol. 56(5), pp. 2054-2075.
Mavrotas, G. (2009). Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems. Applied Mathematics and Computation, Vol. 213(2), pp. 455-465.
Moomivand, S., Davari-Ardakani, H., Abouei Ardakan, M., and Mosadegh, H. (2019). Multi-mode resource constrained project section and scheduling considering reinvestment strategy and flexible time horizon (In Persian). Computational Methods in Engineering, Accepted for publication.
Nemati-Lafmejani, R., Davari-Ardakani, H., and Najafzad, H. (2019). Multi-mode resource constrained project scheduling and contractor selection: mathematical formulation and metaheuristic algorithms. Applied Soft Computing, Vol. 81, pp. 105533.
Nemati-Lafmejani, R., and Davari-Ardakani, H. (2020). Multi-mode resource constrained project scheduling problem along with contractor selection. INFOR: Information Systems and Operational Research, Accepted for publication.
Opricovic, S., and Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, Vol. 156, pp. 445-455.
Qiao, J., and Li, Y. (2018). Resource leveling using normalized entropy and relative entropy. Automation in Construction, Vol. 87, pp. 263-272.
RezaHoseini, A., Ghannadpour, S. F., and Hemmati, M. (2020). A comprehensive mathematical model for resource-constrained multi-objective project portfolio selection and scheduling considering sustainability and projects splitting. Journal of Cleaner Production, Vol. 269, pp. 1-20.
Schnell, A., and Hartl, R.F. (2016). On the efficient modeling and solution of the multi-mode resource-constrained project scheduling problem with generalized precedence relations. OR Spectrum, Vol. 38(2), pp. 283-303.
Shariatmadari, M., Nahavandi, N., Zegordi, S.H., and Sobhiyah, M.H. (2017). Integrated
resource management for simultaneous project selection and scheduling. Computers & Industrial Engineering, Vol. 109, pp. 39-47.
Toffolo, T. A. M., Santos, H. G., Carvalho, M. A. M., and Soares, J. A. (2015). An integer programming approach to the multimode resource-constrained multiproject scheduling problem. Journal of Scheduling, Vol. 19(3), pp. 295-307.
Toffolo, T.A.M., Santos, H.G., Carvalho, M.A.M. and Soares, J.A. (2016). An integer programming approach to the multimode resource-constrained multiproject scheduling problem. Journal of Scheduling, Vol. 19, pp. 295-307.
Tofighian, A. A., and Naderi, B. (2015). Modeling and solving the project selection and scheduling. Computers & Industrial Engineering, Vol. 83, pp. 30-38.
Turkgenci, A., Guden, H., and Gülşen, M. (2021). Decomposition based extended project scheduling for make-to-order production. Operational Research, Vol. 21, pp. 801-825.
Zimmermann, A., and Trautmann, N. (2018). A list-scheduling heuristic for the short-term planning of assessment centers. Journal of Scheduling, Vol. 21, pp. 131-142
Zoraghi, N., Shahsavar, A., and Niaki, S.T.A. (2017). A hybrid project scheduling and material ordering problem: Modeling and solution algorithms. Applied Soft Computing, Vol. 58, pp. 700-713.
International Journal of Supply and Operations Management
Volume 9, Issue 1
February 2022
Pages 34-55

Files

Share

How to cite

Statistics