An interval programming based approach for fully uncertain resource-constrained project scheduling problem considering project manager’s attitude toward risk

Abstract

In recent years, there has been a growing attention to model and solve resource-constrained project scheduling problem (RCPSP) under uncertain environments. In most of the real-life cases, project managers may face with many uncertainties in activity durations, resource availabilities, resource requirements of the activities, the earliest and latest finishing times of the activities etc. In addition to these input parameters, project schedule which represents the starting and/or completion times of the activities should also be considered as uncertain variables in such a fully uncertain environments where all of the project data are imprecise. Based on this motivation, this paper presents an interval programming based transformation approach to overcome fully uncertain nature of the problem. In detail, classical discrete-time binary integer programming model of the deterministic problem was extended by incorporating interval-valued parameters and decision variables. Then, fully uncertain RCPSP was transformed into the crisp equivalent form by making use of interval programming, interval ranking and interval arithmetic operations. In the proposed approach, interval arithmetic operations are performed by using supplementary information obtained from the project manager. Thus, the proposed approach is also able to take into account the project managers’ attitude toward risk and produces more acceptable and risk-free solutions. Finally, a real-life liquefied natural gas (LNG) storage tank construction project in a petroleum refinery is presented for testing its validity and practicality. The computational results have shown that more applicable and information efficient project schedules can be derived via the proposed approach according to the project manager’s attitude toward risk.

Keywords

• Resource-Constrained project scheduling,Interval programming,Risk attitude

Tamamen belirsiz kaynak kısıtlı proje çizelgeleme problemi için proje yöneticisinin riske karşı tutumunu dikkate alan aralık programlama tabanlı bir yaklaşım

Abstract

Son yıllarda, belirsizlik altında kaynak kısıtlı proje çizelgeleme problemlerinin modellenmesi ve çözümüne, giderek artan bir ilgi olduğu görülmektedir. Gerçek hayat uygulamalarının birçoğunda, proje yöneticileri, aktivite süreleri, kaynak kapasiteleri, aktivitelerin kaynak gereksinimleri ve en erken/en geç bitiş zamanlarının kesin ve net bir şekilde belirlenememesinden ötürü, birçok belirsizlik ile karşı karşıya kalmaktadır. Tüm bu parametrelerin belirsizlik içerdiği ortamlarda, aktivitelerin başlangıç veya bitiş zamanları olarak tanımlanan karar değişkenleri de kesin ve net bir şekilde belirlenememekte olup belirsizlik içerecektir. Bu araştırma motivasyonu ile bu çalışmada, aralık programlama tabanlı bir yaklaşım önerilerek, tamamen belirsiz ortamlarda problemin çözümü gerçekleştirilmiştir. Daha ayrıntılı olarak, probleme ait klasik kesikli zamanlı ikili tamsayılı programlama modeli, aralık sayılar ile ifade edilen parametre ve karar değişkenleri kullanılarak genişletilmiştir. Daha sonra, tamamen belirsiz kaynak kısıtlı proje çizelgeleme problemine ait matematiksel formülasyon, aralık programlama, aralık sıralama ve aralık aritmetik operasyonlar yardımıyla, belirlilik altındaki klasik eşdeğer forma dönüştürülmüştür. Önerilen yaklaşımda, aralık aritmetik operasyonlar, proje yöneticisinden elde edilen ek bilgiler yardımıyla gerçekleştirilmiştir. Bu sayede, proje yöneticilerinin riske karşı tutumları dikkate alınabilmekte ve riskten bağımsız, kabul edilebilir çözümler elde edilebilmektedir. Son olarak, önerilen yaklaşımın geçerliliğinin ve uygulanabilirliğinin test edilebilmesi için, bir petrol rafinerisindeki sıvılaştırılmış doğal gaz tankına ait inşaat projesine yer verilmiştir. Elde edilen sonuçlar göstermektedir ki, önerilen yaklaşım ile proje yöneticisinin riske karşı tutumu doğrultusunda, uygulanabilir ve bilgi etkin çözümler üretilebilmektedir.

Keywords

• Kaynak kısıtlı proje çizelgeleme,Aralık programlama,Riske karşı tutum

References

1. Chen Z, Demeulemeester E, Bai S, Guo Y. “Efficient priority rules for the stochastic resource-constrained project scheduling problem”. European Journal of Operational Research, 270(3), 957-967, 2018.
2. Rostami S, Creemers S, Leus R. “New strategies for stochastic resource-constrained project scheduling”. Journal of Scheduling, 21(3), 349-365, 2018.
3. Atli O, Kahraman C. “Fuzzy resource-constrained project scheduling using taboo search algorithm”. International Journal of Intelligent Systems, 27(10), 873-907, 2012.
4. Atli O, Kahraman C. “Resource-constrained project scheduling problem with multiple execution modes and fuzzy/crisp activity durations”. Journal of Intelligent & Fuzzy Systems, 26(4), 2001-2020, 2014.
5. Kahraman C, Kerre EE, Bozbura FT. Uncertainty modelling and in knowledge engineering and decision making. Proceedings of the 10th International FLINS Conference, Istanbul, Turkey, 26-29 August 2012.
6. Subulan K. “Fully uncertain resource constrained project scheduling problem via interval programming: a real-life application in a LNG storage tank construction”. 2nd International Conference on Economics Business Management and Social Sciences, Belgrade, Serbia, 10-14 May 2017.
7. Baykasoğlu A, Subulan K. “Constrained fuzzy arithmetic approach to fuzzy transportation problems with fuzzy decision variables”. Expert Systems with Applications, 81, 193-222, 2017.
8. Baykasoğlu A, Subulan K. “A direct solution approach based on constrained fuzzy arithmetic and metaheuristic for fuzzy transportation problems”. Soft Computing, https://doi.org/10.1007/s00500-017-2890-2.

9. Malcolm DG, Rosenbloom JM, Clark CE, Fazar W. “Application of a technique for research and development program evaluation”. Operations Research, 7, 646-669, 1959.
10. Jørgensen T. Project Scheduling as a Stochastic Dynamic Decision Problem. PhD Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 1999.
11. Artigues C, Leus R, Nobibon FT. “Robust optimization for resource-constrained project scheduling with uncertain activity durations”. Flexible Services and Manufacturing Journal, 25, 175-205, 2013.
12. Li H, Womer NK. “Solving stochastic resource-constrained project scheduling problems by closed-loop approximate dynamic programming”. European Journal of Operational Research, 246, 20-33, 2015.
13. Perez M. A simulation based optimization approach for stochastic resource constrained project management with milestones. MSc Thesis, Rochester Institute of Technology, New York, USA, 2015.
14. Ashtiani B, Leus R, Aryanezhad MB. “New competitive results for the stochastic resource-constrained project scheduling problem: exploring the benefits of pre-processing”. Journal of Scheduling, 14(2), 157-171, 2011.
15. Wang L, Huang H, Ke H. “Chance-Constrained model for RCPSP with uncertain durations”. Journal of Uncertainty Analysis and Applications, 12(3), 1-10, 2015.
16. Tseng CC, Ko PW. “Measuring schedule uncertainty for a stochastic resource-constrained project using scenario-based approach with utility-entropy decision model”. Journal of Industrial and Production Engineering, 33(8), 558-567, 2016.
17. Creemers S. “The preemptive stochastic resource-constrained project scheduling problem: an efficient globally optimal solution procedure”. Working paper KBI_1626. KU Leuven, Faculty of Economics and Business, Department of Decision Sciences and Information Management, 2016.
18. Chakrabortty RK, Sarker RA, Essam DL. “Resource constrained project scheduling with uncertain activity durations”. Computers & Industrial Engineering, 112, 537-550, 2017.
19. Bruni ME, Pugliese LDP, Beraldi P, Guerriero F. “An adjustable robust optimization model for the resource-constrained project scheduling problem with uncertain activity durations”. Omega, 71, 66-84, 2017.
20. Bruni ME, Pugliese LDP, Beraldi P, Guerriero F. “A computational study of exact approaches for the adjustable robust resource-constrained project scheduling problem”. Computers & Operations Research, 99, 178-190, 2018.
21. Chand S, Singh HK, Ray T. “Finding robust solutions for resource constrained project scheduling problems involving uncertainties”. 2016 IEEE Congress on Evolutionary Computation (CEC), Vancouver, Canada, 24-29 July 2016.
22. Uysal F, Işleyen SK, Çetinkaya C. “Resource constrained project scheduling with stochastic resources”. Journal of Applied Research on Industrial Engineering, 5(1), 39-49, 2018.
23. Hapke M, Jaszkiewicz A, Slowinski R. “Fuzzy project scheduling system for software development”. Fuzzy Sets Systems, 21, 101-117, 1994.
24. Hapke M, Slowinski R. “Fuzzy priority heuristics for project scheduling”. Fuzzy Sets Systems, 83, 291-299, 1996.
25. Ozdamar L, Alanya E. “Uncertainty modelling in software development projects (with case study)”. Annals of Operations Research, 102(1-4), 157-178, 2001.
26. Pan, H, Willis, RJ, Yeh CH. Resource constrained project scheduling with fuzziness”. Advances in Fuzzy Systems and Evolutionary Computation, WSEAS Press, 173-179, 2001.
27. Pan H, Yeh CH. “Fuzzy project scheduling”. The 12th IEEE International Conference on Fuzzy Systems, St Louis, USA, 25-28 May 2003.
28. Liu S, Yung KL, Ip WH. “Genetic local search for resource-constrained project scheduling under uncertainty”. Information and Management Sciences, 18(4), 347-363, 2007.
29. Long LD, Ohsato A. “Fuzzy critical chain method for project scheduling under resource constraints and uncertainty”. International Journal of Project Management, 26(6), 688-698, 2008.
30. Bhaskar T, Pal MN, Pal AK. “A heuristic method for RCPSP with fuzzy activity times”. European Journal of Operational Research, 208, 57-66, 2011.
31. Wang X, Huang W. “Fuzzy resource-constrained project scheduling problem for software development”. Wuhan University Journal of Natural Sciences, 15(1), 25-30, 2010.
32. Kaveh A, Khanzadi M, Alipour M. “Fuzzy resource constraint project scheduling problem using cbo and css algorithms”. International Journal of Civil Engineering, 14(5), 325-337, 2016.
33. Sajadi SM, Azimi P, Ghamginzadeh A, Rahimzadeh A. “A new fuzzy multi-objective multi-mode resource-constrained project scheduling model”. International Journal of Mathematics in Operational Research, 11(1), 45-66, 2017.
34. Wang J. “A fuzzy project scheduling approach to minimize schedule risk for product development”. Fuzzy Sets and Systems, 127(2), 99-116, 2002.
35. Wang J. “A fuzzy robust scheduling approach for product development projects”. European Journal of Operational Research, 152, 180-194, 2004.
36. Masmoudi M, Hait A. “Project scheduling under uncertainty using fuzzy modelling and solving techniques”. Engineering Applications of Artificial Intelligence, 26, 135-149, 2013.
37. Zha H, Zhang L. “Fuzzy flexible resource constrained project scheduling based on genetic algorithm”. Transactions of Tianjin University, 20(6), 469-474, 2014.
38. Knyazeva M, Bozhenyuk A, Rozenberg I. “Resource-constrained project scheduling approach under fuzzy conditions”. Procedia Computer Science, 77, 56-64, 2015.
39. Yousefli A. “A fuzzy ant colony approach to fully fuzzy resource constrained project scheduling problem”. Industrial Engineering & Management Systems, 16(3), 307-315, 2017.
40. Nematian J, Eshghi K, Eshragh-Jahromi A. “A resource-constrained project scheduling problem with fuzzy random duration”. Journal of Uncertain Systems, 4(2), 123-132, 2010.
41. Bellman R, Zadeh LA. “Decision-making in a fuzzy environment”. Management Science, 17, 141-164, 1970.
42. Artykov D, Atymtayeva L. “A fuzzy linear programming approach for resource-constrained project scheduling”. Advanced Engineering Technology and Application, 4(3), 47-52, 2015.
43. Xu Z, Zhang Z. “A fuzzy random resource-constrained scheduling model with multiple projects and its application to a working procedure in a large-scale water conservancy and hydropower construction project”. Journal of Scheduling, 15, 253-272, 2012.
44. Gang J, Xu J, Xu Y. “Multiproject resources allocation model under fuzzy random environment and its application to industrial equipment installation engineering”. Journal of Applied Mathematics, Article ID 818731, 1-19, 2013.
45. Zhang Z. “A MODM bi-level model with fuzzy random coefficients for resource-constrained project scheduling problems”. Seventh International Joint Conference on Computational Sciences and Optimization (CSO), Beijing, China, 4-6 July 2014.
46. Xu J, Feng C. “Multimode resource-constrained multiple project scheduling problem under fuzzy random environment and its application to a large scale hydropower construction project”. The Scientific World Journal, Article ID 463692, 1-20, 2014.
47. Chen L, Zhang Z. “Preemption resource-constrained project scheduling problems with fuzzy random duration and resource availabilities”. Journal of Industrial and Production Engineering, 33(6), 373-382, 2016.
48. Xu ZS. “On multi-period multi-attribute decision making”. Knowledge-Based Systems, 21, 164-171, 2008.
49. Yue Z. “An extended TOPSIS for determining weights of decision makers with interval numbers”. Knowledge-Based Systems, 24(1), 146-153, 2011.
50. Li M, Fu Q, Singh VP, Liu D. “An interval multi-objective programming model for irrigation water allocation under uncertainty”. Agricultural Water Management, 196, 24-36, 2018.
51. Dawood H. Theories of Interval Arithmetic: Mathematical Foundations and Applications. Saarbrücken, Germany, LAP Lambert Academic Publishing, 2011.
52. Li D, Zeng W, Yin Q. “Novel ranking method of interval numbers based on the Boolean matrix”. Soft Computing, 22, 4113-4122, 2018.
53. Zuras D, Hayes NT. “Midpoint and unbounded intervals”. http://grouper.ieee.org/groups/1788/email/pdf26UeyTcNEW.pdf (30.07.2018).
54. Sengupta A, Pal TK. “On comparing interval numbers”. European Journal of Operational Research, 127, 28-43, 2000.
55. Sengupta A, Pal TK, Chakraborty D. “Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming”. Fuzzy Sets and Systems, 119, 129-138, 2001.
56. Gani AN, Assarudeen SNM. “A new operation on triangular fuzzy number for solving fuzzy linear programming problem”. Applied Mathematical Sciences, 6, 525-532, 2012.
57. Klir GJ, Cooper JA. “On constrained fuzzy arithmetic”. Proceedings of 5th international IEEE conference on fuzzy systems, New Orleans, USA, 11 September 1996.
58. Klir GJ, Pan Y. “Constrained fuzzy arithmetic: basic questions and some answers”. Soft Computing, 2, 100-108, 1998.
59. Klir GJ. “Fuzzy arithmetic with requisite constraints”. Fuzzy Sets Systems, 91, 165-175, 1997.
60. Lodwick WA. “Constrained interval arithmetic”. Department of Mathematics, Colorado University, Denver, USA, CCM Report, 138, 1999.
61. Lodwick WA, Untiedt EA. “A comparison of interval analysis using constraint interval arithmetic and fuzzy interval analysis using gradual numbers”. NAFIPS 2008- Annual Meeting of the North American Fuzzy Information Processing Society, New York, USA, 19-22 May 2008.
62. Pritsker A, Watters L, Wolfe P. “Multi-project scheduling with limited resources: a zero−one programming approach”. Management Science, 16, 93-108, 1969.
63. Uysal MP. “An empirical study in software engineering: the effects of project-based and project-supported methods on product and academic achievements”. Pamukkale University Journal of Engineering Sciences, 24(2), 226-237, 2018.
64. Gür Ş, Hamurcu M, Eren T. “Selecting of Monorail projects with analytic hierarchy process and 0-1 goal programming methods in Ankara”. Pamukkale University Journal of Engineering Sciences, 23(4), 437-443, 2017.
65. Subulan K, Saltabas A, Tasan AS, Girgin SC. “Modeling and analyzing of a construction project considering resource allocation through a hybrid methodology: petri nets and fuzzy rule based systems”. Proceedings of the 41st International Conference on Computers & Industrial Engineering, California, USA, 23-25 October 2011.
66. Akboga O, Percin SS, Baradan S, Girgin SC. “A comparative study on the influence of cultural differences on project duration in international construction projects”. 9th International Congress on Advances in Civil Engineering, Trabzon, Turkey, 27-30 September 2010.
67. The Observer. “Hot Topic News”. https://www.gladstoneobserver.com.au/videos/roof-raised-huge-lng-tank/17461/ (06.08.2018).
68. Nippon Steel & Sumitomo Metal Corporation. “Press Release”. http://www.nssmc.com/en/news/20140619_100.html (06.08.2018).