An uncertain workforce planning problem with job satisfaction

  • Guoqing Yang
  • Wansheng TangEmail author
  • Ruiqing Zhao
Original Article


To investigate the effect of employees’ job satisfaction on the firm’s workforce planning, this paper builds a multi-period uncertain workforce planning model with job satisfaction level, where the labor demands and operation costs are characterized as uncertain variables. The job satisfaction level is defined as the employees’ psychological satisfaction about overtime through prospect theory. The proposed uncertain model can be transformed into an equivalent deterministic form, which contains complex nonlinear constraints and cannot be solved by conventional optimization methods. Thus, a hybrid joint operations algorithm (JOA) integrated with LINGO software is designed to solve the proposed workforce planning problem. Consequently, several numerical experiments are conducted to compare our proposed JOA with a hybrid particle swarm optimization algorithm to verify the effectiveness of the JOA algorithm. The results demonstrate that the firm’s total operation cost increases with the employees’ job satisfaction level, the loss averse degree and outside firms’ overtime level, respectively. Meanwhile, the firm would overpay in bounded rational cases with job satisfaction, and the overpayment can be seen as the value of bounded rationality, which ensures the firm’s normal operation.


Workforce planning Prospect theory Job satisfaction Uncertainty theory Joint operations algorithm 



This work is supported by the National Natural Science Foundation of China under Grant No. 71371133, and supported partially by Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20120032110071.


  1. 1.
    Ashfaq R, Wang X, Huang J, Abbas H, He Y (2016) Fuzziness based semi-supervised learning approach for Intrusion Detection System (IDS). Inform Sci. doi: 10.1016/j.ins.2016.04.019 (in press)
  2. 2.
    Anderson E Jr (2001) The nonstationary staff-planning problem with business cycle and learning effects. Manage Sci 47(6):817–832zbMATHCrossRefGoogle Scholar
  3. 3.
    Andrews B, Parsons H (1989) LL Bean chooses a telephone agent scheduling system. Interfaces 19(6):1–9CrossRefGoogle Scholar
  4. 4.
    Azizi N, Zolfaghari S, Liang M (2010) Modeling job rotation in manufacturing systems: The study of employee’s boredom and skill variations. Int J Product Econ 123(1):69–85CrossRefGoogle Scholar
  5. 5.
    Brusco M, Showalter M (1993) Constrained nurse staffing analysis. Omega: The. Int J Manage Sci 21(2):175–186Google Scholar
  6. 6.
    Brusco M, Jacobs L, Bongiorno R, Lyons D, Tang B (1995) Improving personnel scheduling at airline stations. Operat Res 43(5):741–751zbMATHCrossRefGoogle Scholar
  7. 7.
    Campbell G (2011) A two-stage stochastic program for scheduling and allocating cross-trained workers. J Operat Res Soc 62(6):1038–1047CrossRefGoogle Scholar
  8. 8.
    Cai X, Li K (2000) A genetic algorithm for scheduling staff of mixed skills under multi-criteria. Euro J Operat Res 125(2):359–369zbMATHCrossRefGoogle Scholar
  9. 9.
    Coomber B, Barriball K (2007) Impact of job satisfaction components on intent to leave and turnover for hospital-based nurses: A review of the research literature. Int J Nursing Stud 44(2):297–314CrossRefGoogle Scholar
  10. 10.
    Easton F (2014) Service completion estimates for cross-trained workforce schedules under uncertain attendance and demand. Prod Operat Manage 23(4):660–675CrossRefGoogle Scholar
  11. 11.
    Fowler J, Wirojanagud P, Gel E (2008) Heuristics for workforce planning with worker differences. Euro J Operat Res 190(3):724–740zbMATHCrossRefGoogle Scholar
  12. 12.
    Freeman N, Mittenthal J, Melouk S (2014) Parallel-machine scheduling to minimize overtime and waste costs. IIE Trans 46(6):601–618CrossRefGoogle Scholar
  13. 13.
    He Y, Wang X, Huang J (2016) Fuzzy nonlinear regression analysis using a random weight network. Inform Sci. doi: 10.1016/j.ins.2016.01.037 (in press)
  14. 14.
    Hewitt M, Chacosky A, Grasman S, Thomas B (2015) Integer programming techniques for solving non-linear workforce planning models with learning. Euro J Operat Res 242(3):942–950MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Hellman C (1997) Job satisfaction and intent to leave. J Soc Psychol 137(6):677–689CrossRefGoogle Scholar
  16. 16.
    Hertz A, Lahrichi N, Widmer M (2010) A flexible MILP model for multiple-shift workforce planning under annualized hours. Euro J Operat Res 200(3):860–873zbMATHCrossRefGoogle Scholar
  17. 17.
    Heinonen J, Pettersson F (2007) Hybrid ant colony optimization and visibility studies applied to a job-shop scheduling problem. Appl Math Comp 187(2):989–998MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Hu K, Zhang X, Gen M, Jo J (2015) A new model for single machine scheduling with uncertain processing time. J Intel Manufact. doi: 10.1007/s10845-015-1033-9
  19. 19.
    Kahneman D, Tversky A (1979) Prospect theory: An analysis of decision under risk. Econ J Econ Soc 47(2):263–291zbMATHGoogle Scholar
  20. 20.
    Kaluszka M, Krzeszowiec M (2012) Pricing insurance contracts under cumulative prospect theory. Insur Math Econ 50(1):159–166MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Kuo I, Horng S, Kao T, Lin T, Lee C, Terano T, Pan Y (2009) An efficient flow-shop scheduling algorithm based on a hybrid particle swarm optimization model. Expert Syst Appl 36(3):7027–7032CrossRefGoogle Scholar
  22. 22.
    Lee C, Vairaktarakis G (1997) Workforce planning in mixed model assembly systems. Oper Res 45(4):553–567zbMATHCrossRefGoogle Scholar
  23. 23.
    Li G, Jiang H, He T (2015) A genetic algorithm-based decomposition approach to solve an integrated equipment-workforce-service planning problem. Omega: The. Int J Manage Sci 50:1–17Google Scholar
  24. 24.
    Li R, Liu G (2014) An uncertain goal programming model for machine scheduling problem. JJ Intel Manufact. doi: 10.1007/s10845-014-0982-8
  25. 25.
    Liu B (2007) Uncertainty theory, 2nd edn. Springer-Verlag, BerlinzbMATHGoogle Scholar
  26. 26.
    Liu B, Wang L, Jin Y (2007) An effective PSO-based memetic algorithm for flow shop scheduling. IEEE Trans Syst Man Cyber Part B: Cybern 37(1):18–27CrossRefGoogle Scholar
  27. 27.
    Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer-Verlag, BerlinCrossRefGoogle Scholar
  28. 28.
    Liu Y (2013) Uncertain random variables: a mixture of uncertainty and randomness. Soft Comp 17(4):625–634zbMATHCrossRefGoogle Scholar
  29. 29.
    Lu S, Wang X, Zhang G, Zhou X (2015) Effective algorithms of the Moore-Penrose inverse matrices for extreme learning machine. Intel Data Anal 19(4):743–760CrossRefGoogle Scholar
  30. 30.
    Maenhout B, Vanhoucke M (2013) An integrated nurse staffing and scheduling analysis for longer-term nursing staff allocation problems. Omega: The. Int J Manage Sci 41(2):485–499Google Scholar
  31. 31.
    Moslehi G, Mahnam M (2011) A Pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search. Int J Product Econ 129(1):14–22CrossRefGoogle Scholar
  32. 32.
    Ning Y, Liu J, Yan L (2013) Uncertain aggregate production planning. Soft Comp 17(4):617–624CrossRefGoogle Scholar
  33. 33.
    Othman M, Bhuiyan N, Gouw G (2012) Integrating workers differences into workforce planning. Comp Indust Eng 63(4):1096–1106CrossRefGoogle Scholar
  34. 34.
    Pasquariello P (2014) Prospect theory and market quality. J Econ Theory 149:276–310MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Parisio A, Jones C (2015) A two-stage stochastic programming approach to employee scheduling in retail outlets with uncertain demand. Omega 53:97–103CrossRefGoogle Scholar
  36. 36.
    Ramos G, Daamen W, Hoogendoorn S (2014) A state of the art review: developments in utility theory, prospect theory and regret theory to investigate travellers’ behaviour in situations involving travel time uncertainty. Transp Rev 34(1):46–67CrossRefGoogle Scholar
  37. 37.
    Song H, Huang H (2008) A successive convex approximation method for multistage workforce capacity planning problem with turnover. Euro J Operat Res 188(1):29–48MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    Soukour A, Devendeville L, Lucet C, Moukrim A (2013) A Memetic algorithm for staff scheduling problem in airport security service. Expert Syst Appl 40(18):7504–7512CrossRefGoogle Scholar
  39. 39.
    Sun G, Zhao R, Lan Y (2016) Joint operations algorithm for large-scale global optimization. Appl Soft Comp 38:1025–1039CrossRefGoogle Scholar
  40. 40.
    Takahama T, Sakai S (2006) Constrained optimization by the constrained differential evolution with gradient-based mutation and feasible elites. IEEE Congress on In Evolutionary Computation, 2006. CEC 2006. (pp. 1–8). IEEEGoogle Scholar
  41. 41.
    Tseng C, Liao C (2008) A particle swarm optimization algorithm for hybrid flow-shop scheduling with multiprocessor tasks. Int J Prod Res 46(17):4655–4670zbMATHCrossRefGoogle Scholar
  42. 42.
    Wang X, Ashfaq R, Fu A (2015) Fuzziness based sample categorization for classifier performance improvement. J Intel Fuzzy Syst 29(3):1185–1196MathSciNetCrossRefGoogle Scholar
  43. 43.
    Wang X (2015) Uncertainty in Learning from Big Data-Editorial. J Intel Fuzzy Syst 28(5):2329–2330CrossRefGoogle Scholar
  44. 44.
    Wirojanagud P, Gel E, Fowler J, Cardy R (2007) Modelling inherent worker differences for workforce planning. Int J Prod Res 45(3):525–553CrossRefGoogle Scholar
  45. 45.
    Wright P, Mahar S (2013) Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction. Omega: The. Int J Manage Sci 41(6):1042–1052Google Scholar
  46. 46.
    Yang K, Lan Y, Zhao R (2014) Monitoring mechanisms in new product development with risk-averse project manager. J Intel Manufact. doi: 10.1007/s10845-014-0993-5
  47. 47.
    Yang G, Tang W, Zhao R (2015) An uncertain furniture production planning problem with cumulative service levels. Soft Comp. doi: 10.1007/s00500-015-1839-6
  48. 48.
    Yang G, Liu Y, Yang K (2015) Multi-objective biogeography-based optimization for supply chain network design under uncertainty. Comp Indust Eng 85:145–156CrossRefGoogle Scholar
  49. 49.
    Zhang X, Meng G (2013) Expected-variance-entropy model for uncertain parallel machine scheduling. Information 16(2):903–908Google Scholar
  50. 50.
    Zhou C, Tang W, Zhao R (2014) An uncertain search model for recruitment problem with enterprise performance. J Intel Manufact. doi: 10.1007/s10845-014-0997-1

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Systems EngineeringTianjin UniversityTianjinChina

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