Document Type : Article

**Authors**

^{1}
Department of Logistics Management, School of Business Administration, Guangdong University of Finance, Guangzhou, 510521, China.

^{2}
Department of Management Science, School of Business, Sun Yat-Sen University, Guangzhou, 510275, China.

^{3}
Department of Industrial Engineering, Chung Yuan Christian University, No. 200, Chung Pei Road, Chung li District, Taoyuan City, 32023, Taiwan.

**Abstract**

Behavioral economic has received much attention recently. Learning and fatigue are two typical behavioral phenomena in industrial production operation processes. The existence of learning and fatigue result in a dynamic change in productivity. In this paper, a classical economic production quantity model is extended to consider the behavioral economic value of learning and fatigue. Based on a real case study, each production cycle is divided into five phases, i.e, the learning phase, stable phase, fatigue phase, fatigue recovery (rest) phase, and the relearning phase. The new production inventory decision model is incorporated with dynamic productivity and learning-stable-fatigue-recovery effect. Numerical simulation and sensitivity analysis show that appropriate rest alleviates employees fatigue and increases productivity, resulting in a lower average production cost. On the other hand, when the rest time is too high, exceeding a certain value, it leads to the decline of the actual labor productivity, resulting in an increase in the average cost of the system.

**Keywords**

- Behavioral economics
- productivity
- human factor
- learning effect
- fatigue effect
- production inventory decision

**Main Subjects**

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25. Barker, L.M. and Nussbaum, M.A. "Fatigue, performance and the work environment: a survey of registered nurses", Journal of Advanced Nursing, 67(6), pp. 1370-1382 (2011).

26. Jaber, M.Y. and Glock, C.H. "A learning curve for tasks with cognitive and motor elements", Computers and Industrial Engineering, 64(3), pp. 866-871 (2013).

27. Givi, Z.S., Jaber, M.Y., and Neumann, W.P. "Modelling worker reliability with learning and fatigue", Applied Mathematical Modelling, 39(17), pp. 5186- 5199 (2015).

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31. Lindstrom, L., Kadefors, R., and Petersen, I. "An electromyographic index for localized muscle fatigue", Journal of Applied Physiology: Respiratory, Environmental and Exercise Physiology, 43(4), pp. 750-754 (1977).

32. Battini, D., Glock, C.H., Grosse, E.H., Persona, A., and Sgarbossa, F. "Ergo-lot-sizing: an approach to integrate ergonomic and economic objectives in manual materials handling", International Journal of Production Economics, 185, pp. 230-239 (2017).

33. Kang, C.W., Ullah, M., and Sarkar, B. "Human errors incorporation in work-in-process group manufacturing system", Scientia Iranica, 24(4), pp. 2050-2061 (2017).

34. Cheng, Y.L., Wang, W.T., Wei, C.C., and Lee, K.L. "An integrated lot-sizing model for imperfect production with multiple disposals of defective items",Scientia Iranica, 25(2), pp. 852-867 (2018).

35. Besheli, S.F., Keshteli, R.N., Emami, S., and Rasouli, S.M. "A fuzzy dynamic multi-objective, multi-item model by considering customer satisfaction in supply chain", Scientia Iranica, 24(5), pp. 2623-2639 (2017).

36. Chen, T.H. and Tsao, Y.C. "Optimal lot-sizing integration policy under learning and rework effects in a manufacturer-retailer chain", International Journal of Production Economics, 155(5), pp. 239-248 (2014).

37. Manna, A.K., Das, B., Dey, J.K., and Mondal, S.K. "Multi-item EPQ model with learning effect on imperfect production over fuzzy-random planning horizon", Journal of Management Analytics, 4(1), pp. 80-110 (2016).

38. Mahata, G.C. "A production-inventory model with imperfect production process and partial backlogging under learning considerations in fuzzy random environments", Journal of Intelligent Manufacturing, 28(4), pp. 883-897 (2017).

39. Grosse, E.H. and Glock, C.H. "Production economics and the learning curve: a meta-analysis", International Journal of Production Economics, 170, pp. 401-412 (2015).

40. Glock, C.H. and Jaber, M.Y. "A multi-stage production-inventory model with learning and forgetting effects, rework and scrap", Computers and Industrial Engineering, 64(2), pp. 708-720 (2013).

41. Kumar, R.S. and Goswami, A. "EPQ model with learning consideration, imperfect production and partial backlogging in fuzzy random environment", International Journal of Systems Science, 46(8), pp. 1486- 1497 (2015).

42. Sturm, J.C., Gronet, C.M., and Gibbons, J.F. "A production-inventory model with imperfect production process and partial backlogging under learning considerations in fuzzy random environments", Journal of Intelligent Manufacturing, 28(4), pp. 1-15 (2017).

43. Okogbaa, O.G. An Empirical Model for Mental Work Output and Fatigue, University of Cincinnati, University Microfilms (1983).

44. Bechtold, S.E. and Sumners, D.W.L. "Optimal workrest scheduling with exponential work-rate decay", Management Science, 34(4), pp. 547-552 (1988).

45. Lindstrom, L., Kadefors, R., Petersen, I. "An electromyographic index for localized muscle fatigue", Journal of Applied Physiology: Respiratory, Environmental and Exercise Physiology, 43(4), pp.750-754 (1977).

2. Zhao, X., Zhao, X., and Wu, Y. "Opportunities for research in behavioral operations management", International Journal of Production Economics, 142(1), pp. 1-2 (2013).

3. Wright, T.P. "Factors affecting the cost of airplanes", Journal of Aeronautical Sciences, 3(4), pp. 122-128 (1936).

4. Jaber, M.Y., Givi, Z.S., and Neumann, W.P. "Incorporating human fatigue and recovery into the learningforgetting process", Applied Mathematical Modelling, 37(12-13), pp. 7287-7299 (2013).

5. Jaber, M.Y. and Guiffrida, A.L. "Observations on the economic manufacture quantity model with learning and forgetting", International Transactions in Operational Research, 14(2), pp. 91-104 (2007).

6. Jaber, M.Y. and Bonney, M. "The lot sizing problem and the learning curve: A review", In M.Y. Jaber (Ed.), Learning Curves: Theory, Models, and Applications, FL, Boca Raton: CRC Press-Taylor and Francis Group, pp. 265-291 (2011).

7. Salameh, M.K., Abdul-Malak, M.A.U., and Jaber, M.Y. "Mathematical modelling of the effect of human learning in the finite production inventory model", Applied Mathematical Modelling, 17(11), pp. 613-615 (1993).

8. Jaber, M.Y. and Guiffrida, A.L. "Observations on the economic manufacture quantity model with learning and forgetting", International Transactions in Operational Research, 14(2), pp. 91-104 (2007).

9. Jaber, M.Y. and Bonney, M. "The lot sizing problem and the learning curve: A review", In M.Y. Jaber (Ed.), Learning Curves: Theory, Models, and Applications, FL, Boca Raton: CRC Press-Taylor and Francis Group. pp. 265-291 (2011).

10. Salameh, M.K., Abdul-Malak, M.A.U., and Jaber, M.Y. "Mathematical modelling of the effect of human learning in the finite production inventory model", Applied Mathematical Modelling, 17(11), pp. 613-615 (1993).

11. Jaber, M.Y. and Salameh, M.K. "Optimal lot sizing under learning considerations: shortages allowed and backordered", Applied Mathematical Modelling, 19(5), pp. 307-310 (1995).

12. Balkhi, Z.T. "The effects of learning on the optimal production lot size for deteriorating and partially backordered items with time varying demand and deterioration rates", Applied Mathematical Modelling, 27(10), pp. 763-779 (2003).

13. Boer, A.V.D. and Zwart, B. "Dynamic pricing and learning with finite inventories", Operations Research, 63(4), pp. 965-978 (2015).

14. Teng, J.T., Lou, K.R., and Wang, L. "Optimal trade credit and lot size policies in economic production quantity models with learning curve production costs", International Journal of Production Economics, 155(5), pp. 318-323 (2014).

15. Khan, M., Jaber, M.Y., and Ahmad, A.R. "An integrated supply chain model with errors in quality inspection and learning in production", Omega, 42(1), pp. 16-24 (2014).

16. Mahata, G.C., "A production-inventory model with imperfect production process and partial backlogging under learning considerations in fuzzy random environments", Journal of Intelligent Manufacturing, 28(4), pp. 883-897 (2017).

17. Khan, M., Hussain, M., and Cardenasbarron, L.E. "Learning and screening errors in an EPQ inventory model for supply chains with stochastic lead time demands", International Journal of Production Research, 135, pp.1-17 (2017).

18. Jaber, M.Y. and Bonney, M. "Production breaks and the learning curve: the forgetting phenomenon", Applied Mathematical Modelling, 20(2), pp. 162-169 (1996).

19. Chiu, H.N. and Chen, H.M. "An optimal algorithm for solving the dynamic lot-sizing model with learning and forgetting in setups and production", International Journal of Production Economics, 95(2), pp. 179-193 (2005).

20. Alamri, A.A. and Balkhi, Z.T. "The effects of learning and forgetting on the optimal production lot size for deteriorating items with time varying demand and deterioration rates", International Journal of Production Economics, 107(1), pp. 125-138 (2007).

21. Teyarachakul, S., Chand, S., and Ward, J. "Effect of learning and forgetting on the batch size", Production and Operations Management, 20(1), pp. 116-128 (2011).

22. Zanoni, S., Jaber, M.Y., and Zavanella, L.E. "Vendor managed inventory (vmi) with consignment considering learning and forgetting effects", International Journal of Production Economics, 140(2), pp. 721-730 (2012).

23. Glock, C.H. and Jaber, M.Y. "A multi-stage production-inventory model with learning and forgetting effects, rework and scrap", Computers and Industrial Engineering, 64(2), pp. 708-720 (2013).

24. Teyarachakul, S., C omez, D., and Tarakci, H. "Steadystate skill levels of workers in learning and forgetting environments: a dynamical system analysis", European Journal of Operational Research, 232(1), pp. 9-21 (2014).

25. Barker, L.M. and Nussbaum, M.A. "Fatigue, performance and the work environment: a survey of registered nurses", Journal of Advanced Nursing, 67(6), pp. 1370-1382 (2011).

26. Jaber, M.Y. and Glock, C.H. "A learning curve for tasks with cognitive and motor elements", Computers and Industrial Engineering, 64(3), pp. 866-871 (2013).

27. Givi, Z.S., Jaber, M.Y., and Neumann, W.P. "Modelling worker reliability with learning and fatigue", Applied Mathematical Modelling, 39(17), pp. 5186- 5199 (2015).

28. Asfaw, A., Pana-Cryan, R., and Rosa, R. "The business cycle and the incidence of workplace injuries: evidence from the USA", Journal of Safety Research, 42(1), pp. 1-8 (2011).

29. Bevilacqua, M., Ciarapica, F.E., and Mazzuto, G. "Analysis of injury events with fuzzy cognitive maps", Journal of Loss Prevention in the Process Industries, 25(4), pp. 677-685 (2012).

30. Frank, A.L. "Injuries related to shiftwork", American Journal of Preventive Medicine, 18(4), pp. 33-36 (2000).

31. Lindstrom, L., Kadefors, R., and Petersen, I. "An electromyographic index for localized muscle fatigue", Journal of Applied Physiology: Respiratory, Environmental and Exercise Physiology, 43(4), pp. 750-754 (1977).

32. Battini, D., Glock, C.H., Grosse, E.H., Persona, A., and Sgarbossa, F. "Ergo-lot-sizing: an approach to integrate ergonomic and economic objectives in manual materials handling", International Journal of Production Economics, 185, pp. 230-239 (2017).

33. Kang, C.W., Ullah, M., and Sarkar, B. "Human errors incorporation in work-in-process group manufacturing system", Scientia Iranica, 24(4), pp. 2050-2061 (2017).

34. Cheng, Y.L., Wang, W.T., Wei, C.C., and Lee, K.L. "An integrated lot-sizing model for imperfect production with multiple disposals of defective items",Scientia Iranica, 25(2), pp. 852-867 (2018).

35. Besheli, S.F., Keshteli, R.N., Emami, S., and Rasouli, S.M. "A fuzzy dynamic multi-objective, multi-item model by considering customer satisfaction in supply chain", Scientia Iranica, 24(5), pp. 2623-2639 (2017).

36. Chen, T.H. and Tsao, Y.C. "Optimal lot-sizing integration policy under learning and rework effects in a manufacturer-retailer chain", International Journal of Production Economics, 155(5), pp. 239-248 (2014).

37. Manna, A.K., Das, B., Dey, J.K., and Mondal, S.K. "Multi-item EPQ model with learning effect on imperfect production over fuzzy-random planning horizon", Journal of Management Analytics, 4(1), pp. 80-110 (2016).

38. Mahata, G.C. "A production-inventory model with imperfect production process and partial backlogging under learning considerations in fuzzy random environments", Journal of Intelligent Manufacturing, 28(4), pp. 883-897 (2017).

39. Grosse, E.H. and Glock, C.H. "Production economics and the learning curve: a meta-analysis", International Journal of Production Economics, 170, pp. 401-412 (2015).

40. Glock, C.H. and Jaber, M.Y. "A multi-stage production-inventory model with learning and forgetting effects, rework and scrap", Computers and Industrial Engineering, 64(2), pp. 708-720 (2013).

41. Kumar, R.S. and Goswami, A. "EPQ model with learning consideration, imperfect production and partial backlogging in fuzzy random environment", International Journal of Systems Science, 46(8), pp. 1486- 1497 (2015).

42. Sturm, J.C., Gronet, C.M., and Gibbons, J.F. "A production-inventory model with imperfect production process and partial backlogging under learning considerations in fuzzy random environments", Journal of Intelligent Manufacturing, 28(4), pp. 1-15 (2017).

43. Okogbaa, O.G. An Empirical Model for Mental Work Output and Fatigue, University of Cincinnati, University Microfilms (1983).

44. Bechtold, S.E. and Sumners, D.W.L. "Optimal workrest scheduling with exponential work-rate decay", Management Science, 34(4), pp. 547-552 (1988).

45. Lindstrom, L., Kadefors, R., Petersen, I. "An electromyographic index for localized muscle fatigue", Journal of Applied Physiology: Respiratory, Environmental and Exercise Physiology, 43(4), pp.750-754 (1977).

Transactions on Industrial Engineering (E)

March and April 2020Pages 918-934