Integration of multi-mode resource-constrained project scheduling under bonus-penalty policies with material ordering under quantity discount scheme for minimizing project cost

Document Type : Article

Author

Department of Industrial Engineering, Electronic Branch, Islamic Azad University, Tehran, Iran

Abstract

In this paper a mixed binary integer mathematical programming model is developed for integration of Multimode Resource-Constraint Project Scheduling Problem (MRCPSP) under bonus–penalty policies and Quantity Discount Problem in Material Ordering (QDPMO) with the objective of minimizing the total project cost. By proving a theorem, an important property of the optimum solution of the problem is found which reduces the search space significantly compared to previous studies. Since the RCPSP belongs to the class of problems that are NP-hard, four hybrid meta-heuristic algorithms called COA-GA, GWO-GA, PSO-GA and GA-GA is developed and tuned to solve the problem. Each of the proposed algorithms consists of outside and inside search components, which determine the best schedule, and materials procurement plan respectively. Finally a set of standard PROGEN test problems is solved by the proposed hybrid algorithms under fixed CPU time. The results show that the COA-GA algorithm outperforms others.

Keywords


References:
1. Elmaghraby, S.E., Activity Networks: Project Planning and Control by Network Models, John Wiley & Sons (1977).
2. S lowinski, R. "Two approaches to problems of resource allocation among project activities-a comparative study", Journal of the Operational Research Society, 31(8), pp. 711-723 (1980). 
3. Talbot, F.B. "Resource-constrained project scheduling with time-resource tradeoffs: The non-preemptive case", Management Science, 28(10), pp. 1197-1210 (1982).
4. Patterson, J.H., S lowinski, R., Talbot, F.B., and Weglarz, J. "An algorithm for a general class of precedence and resource constrained scheduling problems", Advances in Project Scheduling, Elsevier, Amsterdam, pp. 3-28 (1989).
5. Drexl, A. and Gruenewald, J. "Nonpreemptive multimode resource-constrained project scheduling", IIE Transactions, 25(5), pp. 74-81 (1993).
6. Speranza, M.G. and Vercellis, C. "Hierarchical models for multi-project planning and scheduling", European Journal of Operational Research, 64(2), pp. 312-325 (1993).
7. Hartmann, S. and Briskorn, D. "A survey of variants and extensions of the resource-constrained project scheduling problem", European Journal of Operational Research, 207, pp. 1-14 (2010).
8. Sprecher, A., Hartmann, S., and Drexl, A. "An exact algorithm for project scheduling with multiple modes", Operations-research-Spektrum, 19(3), pp. 195-203 (1997).
9. Demeulemeester, E.L. and Herroelen, W.S. "An efficient optimal solution procedure for the preemptive resource-constrained project scheduling problem", European Journal of Operational Research, 90(2), pp. 334-348 (1996).
10. Boctor, F.F. "Heuristics for scheduling projects with resource restrictions and several resource-duration modes", The International Journal of Production Research, 31(11), pp. 2547-2558 (1993).
11. Boctor F.F. "A new and efficient heuristic for scheduling projects with resource restrictions and multiple execution modes", European Journal of Operational Research, 90(2), pp. 349-361 (1996).
12. Kolisch, R. and Drexl, A. "Local search for nonpreemptive multi-mode resource-constrained project scheduling", IIE transactions, 29(11), pp. 987-999 (1997).
13. Sprecher, A. and Drexl, A. "Solving multi-mode resource-constrained project scheduling by a simple, general and powerful sequencing algorithm", European Journal of Operational Research, 107(2), pp. 431-450 (1998).
14. Bouleimen, K. and Lecocq, H.A. "new efficient simulated annealing algorithm for resource constrained scheduling problem", Technical Report, Service de Robotique et Automatisation, University de Liege, pp. 1-10 (1998).
15. Hartmann, S. "Project scheduling with multiple modes: a genetic algorithm", Annals of Operations Research, 102(1-4), pp. 111-135 (2001).
16. Jozefowska, J., Mika, M., Ro_zycki, R., Waligora, G., and Weglarz, J. "Simulated annealing for multi-mode resource-constrained project scheduling", Annals of Operations Research, 102(1-4), pp. 137-155 (2001).
17. Alcaraz, J., Maroto, C., and Ruiz, R. "Solving the multi-mode resource-constrained project scheduling problem with genetic algorithms", Journal of the Operational Research, 54(6), pp. 614-626 (2003).
18. Mika, M., Waligora, G., and Weglarz, 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, 164(3), pp. 639-668 (2005).
19. Zhang, H., Tam, C.M., and Li, H. "Multi-mode project scheduling based on particle swarm optimization", Computer-Aided Civil and Infrastructure Engineering, 21(2), pp. 93-103 (2006).
20. Jarboui, B., Damak, N., Siarry, P., and Rebai, A. "A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems", Applied Mathematics and Computation, 195(1), pp. 299-308 (2008).
21. Van Peteghem, V. and Vanhoucke, M. "An artificial immune system for the multi-mode resourceconstrained project scheduling problem", In European Conference on Evolutionary Computation in Combinatorial Optimization, Springer, Berlin, Heidelberg. pp. 85-96 (2009, April).
22. Van Peteghem, V. and Vanhoucke, M. "Genetic algorithm for the preemptive and non-preemptive multimode resource-constrained project scheduling problem", European Journal of Operational Research, 201(2), pp. 409-418 (2010).
23. Barrios, A., Ballestn, F., and Valls, V. "A double genetic algorithm for the MRCPSP/max", Computers & Operations Research, 38(1), pp. 33-43 (2011).
24. Khalilzadeh, M., Kianfar, F., Shirzadeh Chaleshtari, A., Shadrokh, S., and Ranjbar, M. "A modified PSO algorithm for minimizing the total costs of resources in MRCPSP", Mathematical Problems in Engineering, 2012, pp. 1-18 (2012). DOI: 10.1155/2012/365697.
25. Wang, L. and Fang, C. "An effective estimation of distribution algorithm for the multi-mode resourceconstrained project scheduling problem", Computers& Operations Research, 39(2), pp. 449-460 (2012). 
26. Li, H. and Zhang, H. "Ant colony optimizationbased multi-mode scheduling under renewable and nonrenewable resource constraints", Automation in Construction, 35, pp. 431-438 (2013).
27. Messelis, T. and De Causmaecker, P. "An automatic algorithm selection approach for the multi-mode resource-constrained project scheduling problem", European Journal of Operational Research, 233(3), pp. 511-528 (2014).
28. Aquilano, N.J. and Smith, D.E. "A formal set of algorithms for project scheduling with critical path method material requirements planning", Journal of Operations Management, 1(2), pp. 57-67 (1980).
29. Smith-Daniels, D.E. and Aquilano, N.J. "Constrained resource project scheduling subject to material constraints", Journal of Operations Management, 4(4), pp. 369-387 (1984).
30. Smith-Daniels, D.E. and Smith-Daniels, V.L. "Optimal project scheduling with materials ordering", IIE Transactions, 19(2), pp. 122-129 (1987).
31. Smith-Daniels, D.E. and Smith-Daniels, V. L. "Maximizing the net present value of a project subject to materials and capital constraints", Journal of Operations Management, 7(1-2), pp. 33-45 (1987).
32. Erbasi, A. and Sepil, C. "A modified heuristic procedure for materials management in project networks", International Journal of Industrial Engineering: Theory, Applications and Practice, 6(2), pp. 132-140 (1999).
33. Dodin, B. and Elimam, A.A. "Integrated project scheduling and material planning with variable activity duration and rewards", Iie Transactions, 33(11), pp. 1005-1018 (2001).
34. Sajadieh, M.S., Shadrokh, S., and Hassanzadeh, F. "Concurrent project scheduling and material planning: A genetic algorithm approach", Scientia Iranica, Transaction E, Industrial Engineering, 16(2), pp. 91- 99 (2009).
35. Tabrizi, B.H. and Ghaderi, S.F. "An integrated mixedinteger programming model to address concurrent project scheduling and material ordering", International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing engineering, 9, pp. 1960-1963 (2015).
36. Tabrizi, B.H. and Ghaderi, S.F. "A robust bi-objective model for concurrent planning of project scheduling and material procurement", Computers & Industrial Engineering, 98, pp. 11-29 (2016).
37. Zoraghi, N., Shahsavar, A., Abbasi, B., and Van Peteghem, V. "Multi-mode resource-constrained project scheduling problem with material ordering under bonus-penalty policies", Top, 25(1), pp. 49-79 (2017).
38. Shahsavar, A., Zoraghi, N., and Abbasi, B. "Integration of resource investment problem with quantity discount problem in material ordering for minimizing resource costs of projects", Operational Research, 18(2), pp. 315-342 (2018).
39. Zoraghi, N., Shahsavar, A., and Niaki, S.T.A. "A hybrid project scheduling and material ordering problem: Modeling and solution algorithms", Applied Soft Computing, 58, pp. 700-713 (2017).
40. Tabrizi, B.H. "Integrated planning of project scheduling and material procurement considering the environmental impacts", Computers & Industrial Engineering, 120, pp. 103-115 (2018).
41. Kolisch, R. "Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation", European Journal of Operational Research, 90(2), pp. 320-333 (1996).
42. Pierezan, J. and Coalho, L. "Coyote Optimization Algorithm: A new metaheuristic for global optimization problems", IEEE Congress on Evolutionary Computation (IEEE CEC), 2018 IEEE, pp. 2633-2640 (2018).
43. Mirjalili, S., Mirjalili, S.M., and Lewis, A. "Grey wolf optimizer", Advances in Engineering Software, 69, pp. 46-61 (2014).
44. Long, W. and Xu, S. "A novel grey wolf optimizer for global optimization problems", Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), pp. 1266- 1270 (2016).
45. Muro, C., Escobedo, R., Spector, L., and Coppinger, R.P. "Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations", Behavioural Processes, 88(3), pp. 192-197 (2011).
46. Eberhart, R. and Kennedy, J. "A new optimizer using particle swarm theory", In MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39-43 (1995).
47. Taguchi, G., Introduction to Quality Engineering,White Plains, Asian Productivity Organization, NewYork (1986).
48. Eberhart, R. and Kennedy, J. "A new optimizer using particle swarm theory", In Micro Machine and Human Science, MHS'95., Proceedings of the Sixth International Symposium on IEEE, pp. 39-43 (1995).