P-GWO and MOFA: two new algorithms for the MSRCPSP with the deterioration effect and financial constraints (case study of a gas treating company)

Abstract

This paper presents a bi-objective mathematical formulation for the multi-skill resource-constrained project scheduling problem (MSRCPSP) with the deterioration effect and financial constraints. The objectives are to optimize the makespan and cost of project, simultaneously. Due to the high NP-hardness of the proposed model, a Pareto-based Grey Wolf Optimizer (P-GWO) algorithm has been developed to solve the problem. A new procedure based on the Weighted Sum Method (WSM) has been designed for the P-GWO to rank the solutions of population in order to find the alpha, beta, delta, and omega wolves. The P-GWO also uses a new procedure based on the Data Envelopment Analysis (DEA) to keep the most efficient newly found solutions and update the archive of non-dominated solutions. Besides, a Multi-Objective Fibonacci-based Algorithm (MOFA) based on the characteristics of the Fibonacci sequence has been proposed to solve the problem. The MOFA utilizes a novel neighborhood operator to generate as many feasible solutions as required in each iteration. For the MOFA, new procedures for finding the best solution of each iteration, elitism and updating archive of non-dominated solutions have been developed as well. To evaluate the proposed algorithms, a series of numerical experiments have been conducted and the outputs of our proposed methods were compared with the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Imperialist Competitive Algorithm (MOICA), and Multi-Objective Fruit-Fly Optimization Algorithm (MOFFOA) in terms of several performance measures. Moreover, a real-life overhaul project in a gas treating company has been studied to demonstrate the practicality of the proposed model. The results of all numerical experiments demonstrate that the P-GWO outperforms other algorithms in terms of most of the metrics. The outputs imply that the MOFA can generate high quality solutions within a reasonable computation time.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Notes

  1. 1.

    Charnes, Cooper, and Rhodes (CCR)

References

  1. 1.

    Bibiks K, Hu YF, Li JP, Pillai P, Smith A (2018) Improved discrete cuckoo search for the resource-constrained project scheduling problem. Appl Soft Comput 69:493–503

    Article  Google Scholar 

  2. 2.

    Correia I, Saldanha-da-Gama F (2014) The impact of fixed and variable costs in a multi-skill project scheduling problem: an empirical study. Comput Ind Eng 72:230–238

    Article  Google Scholar 

  3. 3.

    Dai H, Cheng W, Guo P (2018) An improved Tabu search for multi-skill resource-constrained project scheduling problems under step-deterioration. Arab J Sci Eng 1:1–12

    Google Scholar 

  4. 4.

    Afshar-Nadjafi B, Basati M, Maghsoudlou H (2017) Project scheduling for minimizing temporary availability cost of rental resources and tardiness penalty of activities. Appl Soft Comput 61:536–548

    Article  Google Scholar 

  5. 5.

    Maghsoudlou H, Afshar-Nadjafi B, Niaki STA (2017) Multi-skilled project scheduling with level-dependent rework risk; three multi-objective mechanisms based on cuckoo search. Appl Soft Comput 54:46–61

    Article  Google Scholar 

  6. 6.

    Pei J, Liu X, Fan W, Pardalos PM, Lu S (2019) A hybrid BA-VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget, and resource constraint in multiple manufacturers. Omega 82:55–69

    Article  Google Scholar 

  7. 7.

    Leyman P, Driessche NV, Vanhoucke M, Causmaecker PD (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. Comput Oper Res 103:184–197

    MathSciNet  MATH  Article  Google Scholar 

  8. 8.

    Deb K, Pratap A, Agrawal S, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  9. 9.

    Rahmati SHA, Hajipour V, Niaki STA (2013) A soft-computing Pareto-based meta-heuristic algorithm for a multi-objective multi-server facility location problem. Appl Soft Comput 13:1728–1740

    Article  Google Scholar 

  10. 10.

    Zoraghi N, Shahsavar A, Niaki STA (2017) A hybrid project scheduling and material ordering problem: modeling and solution algorithms. Appl Soft Comput 58:700–713

    Article  Google Scholar 

  11. 11.

    Zandieh M, Khatami AR, Rahmati SHA (2017) Flexible job shop scheduling under condition-based maintenance: improved version of imperialist competitive algorithm. Appl Soft Comput 58:449–464

    Article  Google Scholar 

  12. 12.

    Fattahi P, Hajipour V, Nobari A (2015) A bi-objective continuous review inventory control model: Pareto-based meta-heuristic algorithms. Appl Soft Comput 32:211–223

    Article  Google Scholar 

  13. 13.

    Wang L, Zheng XL (2018) A knowledge-guided multi-objective fruit fly optimization algorithm for the multi-skill resource constrained project scheduling problem. Swarm Evol Comput 38:54–63

    Article  Google Scholar 

  14. 14.

    Gupta JND, Gupta SK (1988) Single facility scheduling with nonlinear processing times. Comput Ind Eng 14(4):387–393

    Article  Google Scholar 

  15. 15.

    Kunnathur AS, Gupta SK (1990) Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem. Eur J Oper Res 47(1):56–64

    MathSciNet  MATH  Article  Google Scholar 

  16. 16.

    Wu C-C, Lee WC, Shiau YR (2007) Minimizing the total weighted completion time on a single machine under linear deterioration. Int J Adv Manuf Technol 33(11):1237–1243

    Article  Google Scholar 

  17. 17.

    Wang D, Wang JB (2010) Single-machine scheduling with simple linear deterioration to minimize earliness penalties. Int J Adv Manuf Technol 46(1):285–290

    Article  Google Scholar 

  18. 18.

    Jafari A, Moslehi G (2012) Scheduling linear deteriorating jobs to minimize the number of tardy jobs. J Glob Optim 54(2):389–404

    MathSciNet  MATH  Article  Google Scholar 

  19. 19.

    Yin Y, Wu WH, Cheng TCE, Wu CC (2015) Single-machine scheduling with time-dependent and position-dependent deteriorating jobs. Int J Comput Integr Manuf 28(7):781–790

    Article  Google Scholar 

  20. 20.

    Pei J, Pardalos PM, Liu X, Fan W, Yang S (2015) Serial batching scheduling of deteriorating jobs in a two-stage supply chain to minimize the makespan. Eur J Oper Res 244(1):13–25

    MathSciNet  MATH  Article  Google Scholar 

  21. 21.

    Luo W, Ji M (2015) Scheduling a variable maintenance and linear deteriorating jobs on a single machine. Inf Process Lett 115(1):33–39

    MathSciNet  MATH  Article  Google Scholar 

  22. 22.

    Slowiński R (1984) Preemptive scheduling of independent jobs on parallel machines subject to financial constraints. Eur J Oper Res 15(3):366–373

    MathSciNet  MATH  Article  Google Scholar 

  23. 23.

    Guillén G, Badell M, Espuna A, Puigjaner L (2006) Simultaneous optimization of process operations and financial decisions to enhance the integrated planning/scheduling of chemical supply chains. Comput Chem Eng 30(3):421–436

    Article  Google Scholar 

  24. 24.

    Gafarov ER, Lazarev AA, Werner F (2011) Single machine scheduling problems with financial resource constraints: some complexity results and properties. Math Soc Sci 62(1):7–13

    MathSciNet  MATH  Article  Google Scholar 

  25. 25.

    Alghazi A, Elazouni A, Selim S (2012) Improved genetic algorithm for finance-based scheduling. J Comput Civ Eng 27(4):379–394

    Article  Google Scholar 

  26. 26.

    Györgyi P, Kis T (2014) Approximation schemes for single machine scheduling with non-renewable resource constraints. J Sched 17(2):135–144

    MathSciNet  MATH  Article  Google Scholar 

  27. 27.

    Wu L, Cheng CD (2016) On single machine scheduling with resource constraint. J Comb Optim 31(2):491–505

    MathSciNet  MATH  Article  Google Scholar 

  28. 28.

    Golari M, Fan N, Jin T (2017) Multistage stochastic optimization for production-inventory planning with intermittent renewable energy. Prod Oper Manag 26(3):409–425

    Article  Google Scholar 

  29. 29.

    Corominas A, Ojeda J, Pastor R (2005) Multi-objective allocation of multi-function workers with lower bounded capacity. J Oper Res Soc 56:738–743

    MATH  Article  Google Scholar 

  30. 30.

    Valls V, Perez A, Quintanilla S (2009) Skilled workforce scheduling in service centers. Eur J Oper Res 193(3):791–804

    MATH  Article  Google Scholar 

  31. 31.

    Kazemipoor H, Tavvakoli-Moghaddam R, Shahnazari-Shahrezaei P (2013) Solving a novel multi-skilled project scheduling model by scatter search. S Afr Jf Ind Eng 24:121–135

    MATH  Google Scholar 

  32. 32.

    Javanmard S, Afshar-Nadjafi B, Niaki STA (2016) Preemptive multi-skilled resource investment project scheduling problem; mathematical modelling and solution approaches. Comput Chem Eng 96:55–68

    Article  Google Scholar 

  33. 33.

    Maghsoudlou H, Afshar-Nadjafi B, Niaki STA (2016) A multi-objective invasive weeds optimization algorithm for solving multi-skill multi-mode resource constrained project scheduling problem. Comput Chem Eng 8:157–169

    Article  Google Scholar 

  34. 34.

    Chen R, Liang C, Gu D, Leung J (2017) A multi-objective model for multi-project scheduling and multi-skilled staff assignment for IT product development considering competency evolution. Int J Prod Res 55(21):6207–6234

    Article  Google Scholar 

  35. 35.

    Hosseinian AH, Baradaran V, Bashiri M (2019) Modeling of the time-dependent multi-skilled RCPSP considering learning effect: an evolutionary solution approach. J Model Manag 14(2):521–558. https://doi.org/10.1108/JM2-07-2018-0098

  36. 36.

    Correia I, Lourenco LL, Saldanha-da-Gama F (2012) Project scheduling with flexible resources: formulation and inequalities. OR Spectr 34(3):635–663

    MathSciNet  MATH  Article  Google Scholar 

  37. 37.

    Cordeau J, Laporte G, Pasin F, Ropke S (2010) Scheduling technicians and tasks in a telecommunications company. J Sched 13:393–409

    MathSciNet  MATH  Article  Google Scholar 

  38. 38.

    Tabrizi BH, Tavvakoli-Moghaddam R, Ghaderi SF (2014) A two-phase method for a multi-skilled project scheduling problem with discounted cash flows. Sci Iran 21:1083–1095

    Google Scholar 

  39. 39.

    Myszkowski PB, Skowronski M, Olech LP, Oslizlo K (2015) Hybrid ant colony optimization in solving multi-skill resource-constrained project scheduling problem. Soft Comput 19:3599–3619

    Article  Google Scholar 

  40. 40.

    Zheng H, Wang L, Zheng X (2015) Teaching–learning-based optimization algorithm for multi-skill resource constrained project scheduling problem. Soft Comput 21:1537–1548

    Article  Google Scholar 

  41. 41.

    Almeida BF, Correia I, Saldanha-da-Gama F (2016) Priority-based heuristics for the multi-skill resource constrained project scheduling problem. Expert Syst Appl 57:91–103

    Article  Google Scholar 

  42. 42.

    Myszkowski PB, Olech LP, Laszczyk M, Skowronski M (2018) Hybrid Differential Evolution and Greedy Algorithm (DEGR) for solving multi-skill resource-constrained project scheduling problem. Appl Soft Comput 63:1–14

    Article  Google Scholar 

  43. 43.

    Hosseinian AH, Baradaran V (2019) Detecting communities of workforces for the multi-skill resource-constrained project scheduling problem: a dandelion solution approach. Int J Ind Syst Eng 12:72–99

    Google Scholar 

  44. 44.

    Hosseinian AH, Baradaran V An evolutionary algorithm based on a hybrid multi-attribute decision making method for the multi-mode multi-skilled resource-constrained project scheduling problem. J Optimiz Ind Eng. https://doi.org/10.22094/JOIE.2018.556347.1531

  45. 45.

    Laszczyk M, Myszkowski PB (2019) Improved selection in evolutionary multi–objective optimization of multi–skill resource–constrained project scheduling problem. Inf Sci 481:412–431

    MathSciNet  Article  Google Scholar 

  46. 46.

    Zhu L, Lin J, Wang Z-J (2019) A discrete oppositional multi-verse optimization algorithm for multi-skill resource constrained project scheduling problem. Appl Soft Comput 85. https://doi.org/10.1016/j.asoc.2019.105805

  47. 47.

    Lin J, Zhu L, Gao K (2020) A genetic programming hyper-heuristic approach for the multi-skill resource constrained project scheduling problem. Expert Syst Appl 140. https://doi.org/10.1016/j.eswa.2019.112915

  48. 48.

    Dhiflaoui M, Nouri HE, Driss OB (2018) Dual-resource constraints in classical and flexible job shop problems: a state-of-the-art review. Procedia Comput Sci 126:1507–1515

    Article  Google Scholar 

  49. 49.

    Khodemani-Yazdi M, Tavvakoli-Moghaddam R, Bashiri M (2019) Solving a new bi-objective hierarchical hub location problem with an M/M/C queuing framework. Eng Appl Artif Intell 78:53–70

    Article  Google Scholar 

  50. 50.

    Mendes JJM, Gonçalves JF, Resende MGC (2009) A random key based genetic algorithm for the resource constrained project scheduling problem. Comput Oper Res 36(1):92–109

    MathSciNet  MATH  Article  Google Scholar 

  51. 51.

    Hartmann S (2013) Project scheduling with resource capacities and requests varying with time: a case study. Flex Serv Manuf J 25:74–93

    Article  Google Scholar 

  52. 52.

    Mirjalili S, Saremi S, Mirjalili SM, dos S. Coelho L (2016, 106) Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization. Expert Syst Appl 47:–119

  53. 53.

    Lu C, Gao L, Pan Q, Li X, Zheng J (2019) A multi-objective cellular grey wolf optimizer for hybrid flowshop scheduling problem considering noise pollution. Appl Soft Comput 75:728–749

    Article  Google Scholar 

  54. 54.

    Saremi S, Mirjalili SZ, Mirjalili SM (2015) Evolutionary population dynamics and grey wolf optimizer. Neural Comput & Applic 26(5):1257–1263

    Article  Google Scholar 

  55. 55.

    Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  56. 56.

    Marler RT, Arora JS (2010) The weighted sum method for multi-objective optimization: new insights. Struct Multidiscip Optim 41(6):853–862

    MathSciNet  MATH  Article  Google Scholar 

  57. 57.

    Charnes A, Cooper W, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2:429–444

    MathSciNet  MATH  Article  Google Scholar 

  58. 58.

    Hosseinzadeh Lotfi F, Jahanshahloo GR, Ebrahimnejad A, Soltanifar M, Mansourzadeh SM (2010) Target setting in the general combined-oriented CCR model using an interactive MOLP method. J Comput Appl Math 234(1):1–9

    MathSciNet  MATH  Article  Google Scholar 

  59. 59.

    Falcón S, Plaza A (2007) The k-Fibonacci sequence and the Pascal 2-triangle. Chaos Solitons Fract 33(1):38–49

    MathSciNet  MATH  Article  Google Scholar 

  60. 60.

    Zitzler E, Thiele L (1999) Multi-objective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271

    Article  Google Scholar 

  61. 61.

    Hajipour V, Mehdizadeh E, Tavakkoli-Moghaddam R (2014) A novel Pareto-based multi-objective vibration damping optimization algorithm to solve multi-objective optimization problems. Sci Iran 21(6):2368–2378

    Google Scholar 

  62. 62.

    Kayvanfar V, Zandieh M, Teymourian E (2017) An intelligent water drop algorithm to identical parallel machine scheduling with controllable processing times: a just-in-time approach. Comput Appl Math 36(1):159–184

    MathSciNet  MATH  Article  Google Scholar 

  63. 63.

    Baradaran V, Shafaei A, Hosseinian AH (2019) Stochastic vehicle routing problem with heterogeneous vehicles and multiple prioritized time windows: mathematical modeling and solution approach. Comput Ind Eng 131:187–199

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Vahid Baradaran.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hosseinian, A.H., Baradaran, V. P-GWO and MOFA: two new algorithms for the MSRCPSP with the deterioration effect and financial constraints (case study of a gas treating company). Appl Intell 50, 2151–2176 (2020). https://doi.org/10.1007/s10489-020-01663-x

Download citation

Keywords

  • Project scheduling
  • Deterioration effect
  • Financial constraints
  • Grey wolf optimizer
  • Fibonacci numbers