Stochastic human fatigue modeling in production systems

Document Type : Research Paper


School of Engineering, Damghan University, Damghan, Iran


The performance of human resources is affected by various factors such as mental and physical fatigue, skill, and available time in the production systems. Generally, these mentioned factors have effects on human reliability and consequently change the reliability of production systems. Fatigue is a stochastic factor that changes according to other factors such as environmental conditions, work type, and work duration. Many models have been proposed to quantify fatigue in order to control its effect on reliability, but most of them considered the fatigue as a deterministic variable, while this factor is uncertain. In this paper, we propose a stochastic model for human fatigue with the aim of increasing the reliability. Considering the fatigue uncertainty, we use Chance Constraint (CC), and some methods are used to convert the model into the deterministic one. In the proposed model we consider the reliability of machines and the fatigue of human as two important factors in the production systems' reliability. The proposed model has been applied to a real case and the provided results show that production system reliability can be calculated more effectively using the proposed model.


Main Subjects

Al-Turki, U. M., Arifusalam, S., El-Seliaman, M., & Khand, M. (2011). Resource allocation,batching and dispatching in a stochastic flexible job shop. Advanced Materials Research, 264-265, 1758–1763
Albert, C. (1976). The Principles of Sociotechnical Design. Human Relations, 29(8), 783-792.
Allahverdi, A. (1995). Two-Stage Production Scheduling with Separated Set-up Times and Stochastic Breakdowns. Journal of the Operational Research Society, 46(7), 896-904.
Allahverdi, A., & Mittenthal, J. (1998). Dual criteria scheduling on a two-machine flowshop subject to random breakdowns. International Transactions in Operational Research, 5(4), 317-324.
Aloulou, M. A., & Della Croce, F. (2008). Complexity of single machine scheduling problems under scenario-based uncertainty. Operations Research Letters, 36(3), 338-342.
Altuger, G., & Chassapis, C. (2009). Multi criteria preventive maintenance scheduling through arena based simulation modeling. Paper presented at the IEEE Winter Simulation Conference, Austin,Tx.
Azizi, N., Liang, M., & Zolfaghari, S. (2013). Modelling human boredom at work: mathematical formulations and a probabilistic framework. Journal of Manufacturing Technology Management, 24(5), 711-746.
Battini, D., Persona, A., & Sgarbossa, F. (2014). Innovative real-time system to integrate ergonomic evaluations into warehouse design and management. Computers & Industrial Engineering, 77, 1-10.
Benbouzid-Sitayeb, F., Guebli, S. A., Bessadi, Y., Varnier, C., & Zerhouni, N. (2011). Joint scheduling of jobs and Preventive Maintenance operations in the flowshop sequencing problem: a resolution with sequential and integrated strategies. International Journal of Manufacturing Research, 6(1), 30-48.
Benmansour, R., Allaoui, H., Abdelhakim, A., Serguei, I., & Pellerin, R. (2011). Simulation‐based approach to joint production and preventive maintenance scheduling on a failure‐prone machine. Journal of Quality in Maintenance Engineering, 17(3), 254-267.
Bidanda, B., Ariyawongrat, P., Needy, K. L., Norman, B. A., & Tharmmaphornphilas, W. (2005). Human related issues in manufacturing cell design, implementation, and operation: a review and survey. Computers & Industrial Engineering, 48(3), 507-523.
Calafiore, G., & Campi, M. C. (2005). Uncertain convex programs: randomized solutions and confidence levels. Mathematical Programming, 102(1), 25-46.
Campi, M. C., & Garatti, S. (2011). A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality. Journal of Optimization Theory and Applications, 148(2), 257-280.
Cappadonna, F. A., Costa, A., & Fichera, S. (2013). Makespan Minimization of Unrelated Parallel Machines with Limited Human Resources. Procedia CIRP, 12, 450-455.
Charnes, A., Cooper, W. W., & Symonds, G. H. (1958). Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil. Management Science, 4(3), 235-263.
Clegg, C. W. (2000). Sociotechnical principles for system design. Applied Ergonomics, 31(5), 463-477.
Dumitru, V., & Luban, F. (1982). Membership functions, some mathematical programming models and production scheduling. Fuzzy Sets and Systems, 8(1), 19-33.
Dupačová, J., Gaivoronski, A., Kos, Z., & Szántai, T. (1991). Stochastic programming in water management: A case study and a comparison of solution techniques. European Journal of Operational Research, 52(1), 28-44.
El ahrache, K., Imbeau, D., & Farbos, B. (2006). Percentile values for determining maximum endurance times for static muscular work. International Journal of Industrial Ergonomics, 36(2), 99-108.
Elmaraghy, W. H., Nada, O. A., & Elmaraghy, H. A. (2008). Quality prediction for reconfigurable manufacturing systems via human error modelling. International Journal of Computer Integrated Manufacturing, 21(5), 584-598.
Gholami, M., Zandieh, M., & Alem-Tabriz, A. (2009). Scheduling hybrid flow shop with sequence-dependent setup times and machines with random breakdowns. The International Journal of Advanced Manufacturing Technology, 42(1), 189-201.
Griffith, C., & Mahadevan, S. (2011). Inclusion of fatigue effects in human reliability analysis.  . Reliabilty Engineering and System Safety, 96(11), 1437-1447
Henrion, R., Küchler, C., & Römisch, W. (2009). Scenario reduction in stochastic programming with respect to discrepancy distances. Computational Optimization and Applications, 43(1), 67-93.
Henrion, R., & Möller, A. (2003). Optimization of a continuous distillation process under random inflow rate. Computers & Mathematics with Applications, 45(1), 247-262.
Hollnagel, E. (1996). Reliability analysis and operator modelling. Reliability engineering and system safety, 52, 327-337.
Hunter, J. E. (1986). Cognitive ability, cognitive aptitudes, job knowledge, and job performance. Journal of Vocational Behavior, 29(3), 340-362.
Islam, R., Khan, F., Abbassi, R., & Garaniya, V. (2018). Human Error Probability Assessment During Maintenance Activities of Marine Systems. Safety and Health at Work, 9(1), 42-52.
Jamshidi, R., & Seyyed Esfahani, M. M. (2014). Human resources scheduling to improve the product quality according to exhaustion limit. TOP, 22(3), 1028-1041.
Jensen, P. L. (2002). Human factors and ergonomics in the planning of production. International Journal of Industrial Ergonomics, 29(3), 121-131.
Kasap, N., Aytug, H., & Paul, A. (2006). Minimizing makespan on a single machine subject to random breakdowns. Operations Research Letters, 34(1), 29-36.
Konz, S. (2000). Work/rest: Part II – The scientific basis (knowledge base) for the guide1 In A. Mital, Å. Kilbom, & S. Kumar (Eds.), Elsevier Ergonomics Book Series (Vol. 1, pp. 401-427): Elsevier.
Kulscar, G., & Kulscarine Forrai, M. (2009). Solving multi-objective production scheduling problems using a new approach. Production Systems and Information Engineering, 5, 81-94.
Li, W., & Cao, J. (1995). Stochastic scheduling on a single machine subject to multiple breakdowns according to different probabilities. Operations Research Letters, 18(2), 81-91.
Lodree, E. J., Geiger, C. D., & Jiang, X. (2009). Taxonomy for integrating scheduling theory and human factors: Review and research opportunities. International Journal of Industrial Ergonomics, 39(1), 39-51.
Ma, L., Chablat, D., Bennis, F., & Zhang, W. (2009). A new simple dynamic muscle fatigue model and its validation. International Journal of Industrial Ergonomics, 39(1), 211-220.
Mahdavi, I., Aalaei, A., Paydar, M. M., & Solimanpur, M. (2010). Designing a mathematical model for dynamic cellular manufacturing systems considering production planning and worker assignment. Computers & Mathematics with Applications, 60(4), 1014-1025.
Mahdavi, I., Shirazi, B., & Solimanpur, M. (2010). Development of a simulation-based decision support system for controlling stochastic flexible job shop manufacturing systems. Simulation Modelling Practice and Theory, 18(6), 768-786.
Martorell, S., Villamizar, M., Carlos, S., & Sánchez, A. (2010). Maintenance modeling and optimization integrating human and material resources. Reliability Engineering & System Safety, 95(12), 1293-1299.
Matamoros, M. E. V., & Dimitrakopoulos, R. (2016). Stochastic short-term mine production schedule accounting for fleet allocation, operational considerations and blending restrictions. European Journal of Operational Research, 255(3), 911-921.
Matsveichuk, N. M., Sotskov, Y. N., Egorova, N. G., & Lai, T. C. (2009). Schedule execution for two-machine flow-shop with interval processing times. Mathematical and Computer Modelling, 49(5), 991-1011.
Michalos, G., Makris, S., & Chryssolouris, G. (2013). The effect of job rotation during assembly on the quality of final product. CIRP Journal of Manufacturing Science and Technology, 6(3), 187-197.
Myszewski, J. M. (2010). Mathematical model of the occurrence of human error in manufacturing processes. Quality and Reliability Engineering International, 26(8), 845-851.
Neumann, W. P., & Dul, J. (2010). Human factors: spanning the gap between OM and HRM. International Journal of Operations & Production Management, 30(9), 923-950.
Neumann, W. P., & Medbo, P. (2009). Integrating human factors into discrete event simulations of parallel flow strategies. Production Planning & Control, 20(1), 3-16.
Neumann, W. P., & Village, J. (2012). Ergonomics action research II: a framework for integrating HF into work system design. Ergonomics, 55(10), 1140-1156.
Pagnoncelli, B. K., Ahmed, S., & Shapiro, A. (2009). Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications. Journal of Optimization Theory and Applications, 142(2), 399-416.
Paz Ochoa, M., Jiang, H., Gopalakrishnan, A., Lotero, I., & Grossmann, I. E. (2018). Optimal Production Scheduling of Industrial Gases under Uncertainty with Flexibility Constraints. In M. R. Eden, M. G. Ierapetritou, & G. P. Towler (Eds.), Computer Aided Chemical Engineering (Vol. 44, pp. 1513-1518): Elsevier.
Pereira, C. M. N. A., Lapa, C. M. F., Mol, A. C. A., & da Luz, A. F. (2010). A Particle Swarm Optimization (PSO) approach for non-periodic preventive maintenance scheduling programming. Progress in Nuclear Energy, 52(8), 710-714.
Ryan, B., Qu, R., Schock, A., & Parry, T. (2011). Integrating human factors and operational research in a multidisciplinary investigation of road maintenance. Ergonomics, 54(5), 436-452.
Sawik, T. (2005). Integer programming approach to production scheduling for make -to-order manufacturing. Mathematical and Computer Modelling, 41(1), 99-118.
Shakhlevich, N. V., & Strusevich, V. A. (2005). Pre-Emptive Scheduling Problems with Controllable Processing Times. Journal of Scheduling, 8(3), 233-253.
Taylor, J. C. (2000). The evolution and effectiveness of Maintenance Resource Management (MRM). International Journal of Industrial Ergonomics, 26(2), 201-215.
Touat, M., Tayeb, F. B.-S., & Benhamou, B. (2018). An effective heuristic for the single-machine scheduling problem with flexible maintenance under human resource constraints. Procedia Computer Science, 126, 1395-1404.
Wendt, M., Li, P., & Wozny, G. (2002). Nonlinear Chance-Constrained Process Optimization under Uncertainty. Industrial & Engineering Chemistry Research, 41(15), 3621-3629.
Yang, Z., Wang, J., Rochdi, M., & Belkacem, O. (2011). Bayesian modelling for human error probability analysis in CREAM. In:2011.Paper presented at the International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering, Xi'an, China.