A neural network solution for forecasting labor demand of drop-in peer tutoring centers with long planning horizons

A Correction to this article is available

This article has been updated

Abstract

Like many other service organizations, drop-in peer tutoring centers often struggle to determine the required number of qualified tutors necessary to meet learner expectations. Service work is largely a response to probabilistic calls for staff action and therefore difficult to forecast with precision. Moreover, forecasting models under long planning horizons often lack the complexity or specificity necessary to accurately predict flexible labor demand due to sparse availability of influential model inputs. This study builds upon the flexible demand literature by exploring the use of neural networks for labor demand forecasting for a drop-in peer tutoring center of a large university. Specifically, this study employs a neural network solution that includes a genetic algorithm to search for optimal solutions using evolutional processes. The proposed forecasting model outperforms traditional smoothing and extrapolation forecasting methods.

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

Fig. 1
Fig. 2
Fig. 3

Change history

  • 11 July 2019

    The original version of this article unfortunately contained a mistake. The name of the last author was incorrectly spelled. The correct name of the last author is ���Brittaney Wheatley,��� which is now correctly spelled in this article.

References

  1. Agarwal, A., Colak, S., & Erenguc, S. (2011). A Neurogenetic approach for the resource-constrained project scheduling problem. Computers & Operations Research, 38(1), 44–50.

    MathSciNet  MATH  Article  Google Scholar 

  2. Albright, S. C., & Winston, W. L. (2017). Business analytics: Data analysis and decision making (6th ed.). Boston: Cengage Learning.

  3. Altay, A., Ozkant, O., & Kayakutlu, G. (2014). Prediction of aircraft failure times using artificial neural networks and genetic algorithms. Journal of Aircraft, 51(1), 47–53.

    Article  Google Scholar 

  4. Armstrong, J. S. (1984). Forecasting by extrapolation: Conclusions from 25 years of research. Interfaces, 14(6), 52–66.

    Article  Google Scholar 

  5. Armstrong, J. S. (1986). The ombudsman: Research on forecasting: A quarter-century review, 1960-1984. Interfaces, 16(1), 89–103.

    Article  Google Scholar 

  6. Backer, L., Van Keer, H., Moerkerke, B., & Valcke, M. (2016). Examining evolutions in the adoption of metacognitive regulation in reciprocal peer tutoring groups. Metacognition and Learning, 11(2), 187–213.

    Article  Google Scholar 

  7. Bard, J. F., Morton, D. P., & Yong Min, W. (2007). Workforce planning at USPS mail processing and distribution centers using stochastic optimization. Annals of Operations Research, 155(1), 51–78.

    MathSciNet  MATH  Article  Google Scholar 

  8. Billio, M., & Casarin, R. (2010). Identifying business cycle turning points with sequential Monte Carlo methods: An online and real-time application to the euro area. Journal of Forecasting, 29(1/2), 145–167.

    MathSciNet  MATH  Article  Google Scholar 

  9. Bolton, L. E. (2003). Stickier priors: The effects of nonanalytic versus analytic thinking in new product forecasting. Journal of Marketing Research (JMR), 40(1), 65–79.

    Article  Google Scholar 

  10. Brahnam, S., Chuang, C.-F., Sexton, R. S., & Shih, F. Y. (2007a). Machine assessment of neonatal facial expressions of acute pain. Decision Support Systems, 43(4), 1242–1254.

    Article  Google Scholar 

  11. Brahnam, S., Nanni, L., & Sexton, R. S. (2007b). Introduction to neonatal facial pain detection using common and advanced face classification techniques. In Yoshida H., Jain A., Ichalkaranje A., Jain L.C., Ichalkaranje N. (eds), Advanced computational intelligence paradigms in healthcare (pp. 225–239). Springer.

  12. Camm, J. D., Cochran, J. J., M.J., F., Ohlmann, J. W., Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2017). Essentials of Business Analytics (2 ed.). Boston: Cengage Learning. https://link.springer.com/chapter/10.1007%2F978-3-540-47527-9_9#citeas

  13. Chase Jr, C. W. (1997). Selecting the Appropriate Forecasting Method. Journal of Business Forecasting Methods & Systems, 16, (3) p. 2.

  14. Cooper, E. (2010). Tutoring center effectiveness: The effect of drop-in tutoring. Journal of College Reading and Learning, 40(2), 21–34.

    Article  Google Scholar 

  15. DeFeo, D. J., Bonin, D., & der-Gobeille, M. O. (2017). Waiting and help-seeking in math tutoring exchanges. Journal of Developmental Education, 40(3), 14–22.

    Google Scholar 

  16. Defraeye, M., & Van Nieuwenhuyse, I. (2016). A branch-and-bound algorithm for shift scheduling with stochastic nonstationary demand. Computers & Operations Research, 65, 149–162.

    MathSciNet  MATH  Article  Google Scholar 

  17. Delen, D. (2015). Real-World Data Mining. In Upper Saddle River. New Jersey: Pearson Education, Inc.

    Google Scholar 

  18. Dikmen, B., & Küçükkocaoğlu, G. (2010). The detection of earnings manipulation: The three-phase cutting plane algorithm using mathematical programming. Journal of Forecasting, 29(5), 442–466.

    MathSciNet  MATH  Google Scholar 

  19. Dorsey, R. E., & Johnson, J. D. (1997). Evolution of dynamic reconfigurable neural networks: Energy surface optimality using genetic algorithms. In D. Levine & W. Elsberry (Eds.), Optimality in Biological and Artificial Networks? (p. 185). Lawrence Erlbaum.

  20. Dorsey, R. E., & Mayer, W. J. (1995). Genetic algorithms for estimation problems with multiple optima, nondifferentiability, and other irregular features. Journal of Business & Economic Statistics, 13(1), 53–66.

    Google Scholar 

  21. Dorsey, R. E., Johnson, J. D., & Mayer, W. J. (1994a). A genetic algorithm for the training of feedforward neural networks. In J. D. Johnson & A. B. Whinston (Eds.), Advances in artificial intelligence in economics, finance, and management (Vol. 1, pp. 93–111). Greenwich: JAI Press Inc.

    Google Scholar 

  22. Dorsey, R. E., Johnson, J. D., & Van Boening, M. V. (1994b). The use of artificial neural networks for estimation of decision surfaces in first Price sealed bid auctions. In W. W. Cooper & A. B. Whinston (Eds.), New direction in computational economics (pp. 19–40). Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  23. Drago, A., Rheinheimer, D. C., & Detweiler, T. N. (2018). Effects of locus of control, academic self-efficacy, and tutoring on academic performance. Journal of College Student Retention: Research, Theory & Practice, 19(4), 433–451.

    Article  Google Scholar 

  24. Drwal, M. (2018). Robust scheduling to minimize the weighted number of late jobs with interval due-date uncertainty. Computers & Operations Research, 91, 13–20.

    MathSciNet  MATH  Article  Google Scholar 

  25. Ernst, A. T., Jiang, H., Krishnamoorthy, M., Owens, B., & Sier, D. (2004a). An annotated bibliography of personnel scheduling and rostering. Annals of Operations Research, 127(1–4), 21–144.

    MathSciNet  MATH  Article  Google Scholar 

  26. Ernst, A. T., Jiang, H., Krishnamoorthy, M., & Sier, D. (2004b). Staff scheduling and rostering: A review of applications, methods and models. European Journal of Operational Research, 153(1), 3–27.

    MathSciNet  MATH  Article  Google Scholar 

  27. Fullmer, P. (2012). Assessment of tutoring Laboratories in a Learning Assistance Center. Journal of College Reading and Learning, 42(2), 67–89.

    Article  Google Scholar 

  28. Gallard, A. J., Albritton, F., & Morgan, M. W. (2010). A comprehensive cost/benefit model: Developmental student success impact. Journal of Developmental Education, 34(1), 10–12.

    Google Scholar 

  29. Gerlaugh, K., Thompson, T., Boylan, H., & Davis, H. (2007). National Study of developmental education II: Baseline data for community colleges. Research in Developmental Education, 20(2), 1–4.

    Google Scholar 

  30. Gul, M., & Guneri, A. F. (2016). Planning the future of emergency departments: Forecasting Ed patient arrivals by using regression and neural network models. International Journal of Industrial Engineering, 23(2), 137–154.

    Google Scholar 

  31. Hao, G., Lai, K. K., & Tan, M. (2004). A neural network application in personnel scheduling. Annals of Operations Research, 128(1–4), 65–90.

    MATH  Article  Google Scholar 

  32. Jiang, S., Chin, K.-S., Wang, L., Qu, G., & Tsui, K. L. (2017). Modified genetic algorithm-based feature selection combined with pre-trained deep neural network for demand forecasting in outpatient department. Expert Systems with Applications, 82, 216–230.

    Article  Google Scholar 

  33. Kaboudan, M. A. (2003). Forecasting with computer-evolved model specifications: A genetic programming application. Computers & Operations Research, 30(11), 1661–1681.

    MATH  Article  Google Scholar 

  34. Lian, G., Zhang, Y., Desai, J., Xing, Z., & Luo, X. (2018). Predicting taxi-out time at congested airports with optimization-based support vector regression methods. Mathematical Problems in Engineering, 1–11.

  35. Liu, D., Li, H., Wang, W., & Zhou, C. (2015). Scenario forecast model of long term trends in rural labor transfer based on evolutionary games. Journal of Evolutionary Economics, 25(3), 649–670.

    Article  Google Scholar 

  36. Mozo, A., Ordozgoiti, B., & Gómez-Canaval, S. (2018). Forecasting short-term data center network traffic load with convolutional neural networks. PLoS One, 13(2), e0191939.

    Article  Google Scholar 

  37. Palma, W. (2016). Time Series Analysis. Hoboken. New Jersey: John Wiley & Sons, Inc.

    Google Scholar 

  38. Patuelli, R., Reggiani, A., Nijkamp, P., & Blien, U. (2006). New neural network methods for forecasting regional employment: An analysis of German labour markets. Spatial Economic Analysis, 1(1), 7–30.

    Article  Google Scholar 

  39. Pazgal, A. I., & Radas, S. (2008). Comparison of customer balking and reneging behavior to queueing theory predictions: An experimental study. Computers & Operations Research, 35(8), 2537–2548.

    MATH  Article  Google Scholar 

  40. Salcedo-Sanz, S., Xu, Y., & Yao, X. (2006). Hybrid meta-heuristics algorithms for task assignment in heterogeneous computing systems. Computers & Operations Research, 33(3), 820–835.

    MATH  Article  Google Scholar 

  41. Schnaars, S. P., & Joseph Bavuso, R. (1986). Extrapolation models on very short-term forecasts. Journal of Business Research, 14(1), 27–36.

    Article  Google Scholar 

  42. Sexton, R. S., Dorsey, R. E., & Johnson, J. D. (1998). Toward global optimization of neural networks: A comparison of the genetic algorithm and backpropagation. Decision Support Systems, 22(2), 171–185.

    Article  Google Scholar 

  43. Sexton, R. S., Sriram, R. S., & Etheridge, H. (2003). Improving decision effectiveness of artificial neural networks: A modified genetic algorithm approach. Decision Sciences, 34(3), 421–442.

    Article  Google Scholar 

  44. Sexton, R. S., Dorsey, R. E., & Sikander, N. A. (2004). Simultaneous optimization of neural network function and architecture algorithm. Decision Support Systems, 36(3), 283–296.

    Article  Google Scholar 

  45. Sexton, R. S., McMurtrey, S., Michalopoulos, J. O., & Smith, A. M. (2005). Employee turnover: A neural network solution. Computers & Operations Research, 32(10), 2635–2651.

    MATH  Article  Google Scholar 

  46. Sexton, R. S., McMurtrey, S., & Cleavenger, D. (2006). Knowledge discovery using a neural network simultaneous optimization algorithm on a real world classification problem. European Journal of Operational Research, 168(3), 1009–1018.

    MATH  Article  Google Scholar 

  47. Shmueli, G., Bruce, P. C., Yahav, I., Patel, N. R., & Lichtendahl, K. C., Jr. (2018). Data Mining for Business Analytics. Hoboken: John Wiley & Sons, Inc.

    Google Scholar 

  48. Stellwagen, E., & Tashman, L. E. N. (2013). ARIMA: The models of box and Jenkins. Foresight: The International Journal of Applied Forecasting, 30, 28–33.

    Google Scholar 

  49. Tabachnick, B. G., & Fidell, L. S. (1983). Using multivariate statistics. New York: Harper and Row.

    Google Scholar 

  50. Tang, Q., Wilson, G. R., & Perevalov, E. (2008). An approximation manpower planning model for after-sales field service support. Computers & Operations Research, 35(11), 3479–3488.

    MATH  Article  Google Scholar 

  51. Van den Bergh, J., Beliën, J., De Bruecker, P., Demeulemeester, E., & De Boeck, L. (2013). Personnel scheduling: A literature review. European Journal of Operational Research, 226(3), 367–385.

    MathSciNet  MATH  Article  Google Scholar 

  52. van den Oetelaar, W. F. J. M., van Stel, H. F., van Rhenen, W., Stellato, R. K., & Grolman, W. (2018). Mapping nurses’ activities in surgical hospital wards: A time study. PLoS One, 13(4), 1–18.

    Google Scholar 

  53. Wen-Ya, W., & Gupta, D. (2014). Nurse absenteeism and staffing strategies for hospital inpatient units. Manufacturing & Service Operations Management, 16(3), 439–454.

    Article  Google Scholar 

  54. Yi, Y., Yanhua, C., Jun, S., Mingfei, L., Caihong, L., & Lian, L. (2016). An improved Grey neural network forecasting method based on genetic algorithm for oil consumption of China. Journal of Renewable & Sustainable Energy, 8(2).

  55. Zeng, J. (2017). Forecasting aggregates with disaggregate variables: Does boosting help to select the Most relevant predictors? Journal of Forecasting, 36(1), 74–90.

    MathSciNet  Article  Google Scholar 

  56. Zhou, L., Zhao, P., Wu, D., Cheng, C., & Huang, H. (2018). Time Series Model for Forecasting the Number of New Admission Inpatients. BMC Medical Informatics & Decision Making, 18(1) N.PAG-N.PAG.

  57. Zolfaghari, S., El Bouri, A., Namiranian, B., & Quan, V. (2007). Heuristics for large scale labour scheduling problems in retail sector. INFOR, 45(3), 111–122.

    MathSciNet  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Rick Brattin.

Additional information

Publisher’s note

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

The original version of this article was revised: The original version of this article unfortunately contained a mistake. The name of the last author was incorrectly spelled. The correct name of the last author is “Brittaney Wheatley,” which is now correctly spelled in this article.

Appendix 1 – Technical overview of the NNSOA

Appendix 1 – Technical overview of the NNSOA

This section provides a technical overview of the Neural Network Simultaneous Optimization Algorithm (NNSOA) used in this study. The NNSOA first determines the appropriate number of hidden nodes for the neural network. Starting with two hidden nodes, the neural network is trained for 1000 generations and the best solution is saved. An additional hidden node is inserted into the best solution and trained for another 1000 generations. The best solution from the previous architecture is brought into the next architecture by setting the weights of the additional node to zero in order to preserve previous learning. The remaining solutions of the new neural network are reinitialized using a different random seed for drawing initial weights. The process of adding new hidden nodes and retraining continues until the new hidden node fails to improve overall performance. At this point the initial structure of the neural network is set.

It has been shown that a variety of neural network structures will reduce to the same equivalent structure (Dorsey et al. 1994a; Dorsey et al. 1994b). The NNSOA next follows the genetic algorithm logic as shown in Fig. 4 to determine the most parsimonious set of inputs for the model. It first builds a population of 12 solutions by modifying the input and output weights of the neural network. The input weights are randomly drawn from a uniform probability distribution [−1,1]. The output weights are determined by ordinary least squares, which prior research has found most effective and efficient (Dorsey et al. 1994a; Sexton et al. 1998; Sexton et al. 2003). These 12 solutions make up the first generation. The algorithm next creates a series of 10,000 successive populations, each a genetically modified version of the previous.

Fig. 4
figure4

NNSOA flowchart

At the beginning of each iteration all solutions of the current generation are individually evaluated by an objective function based on the sum of squares error (SSE). The function rewards parsimony by penalizing for each non-zero weight in the solution multiplied by the solution’s root mean square error (RMSE). The objective function is presented in eq. 3 below.

$$ E={\sum}_{i=1}^N{\left({O}_i-{\hat{O}}_i\right)}^2+C\sqrt{\frac{\sum_{i-1}^N{\left({O}_i-{\hat{O}}_i\right)}^2}{N}}. $$
(3)

where:

N:

the number of observations in the solution

O:

the observed value of the dependent variable

\( \hat{O} \) :

the estimated value of the dependent variable

C:

the number of non-zero weights in the solution

The probability of a solution being redrawn in the next generation is determined by eq. 4. A next generation of 12 solutions is then randomly drawn with replacement from the current generation (i.e. reproduction). Duplication is allowed. Probabilities assigned in the evaluation step ensure that better solutions are more likely than poor solutions to appear in the next generation. In this way, traits that favor the objective function will reproduce and thrive in future generations, while weaker traits will die out over time.

$$ P(survival)=\frac{E_{max}-E}{\sum_{i=1}^{12}\left({E}_{max}-{E}_i\right)} $$
(4)

where:

E:

objective value of a given solution

Emax:

maximum objective value of the current population

The 12 solutions of the next generation are then randomly organized into mating pairs. A random number is drawn from a uniform distribution [−1,1] for each pair. Each weight in the mating pair that is numerically less than the random number is switched for the weight in the same position of the mating solution. This crossover creates two new solutions, each with some parameters (weights) from each parent solution. Finally, each weight in each of the 12 solutions may receive additional adjustment (i.e. mutation). Each weight has a 5% chance for replacement by a randomly drawn value from the entire weight space. Searching the entire weight space enhances the algorithm’s ability to find global solutions. After 70% of specified generations are processed, convergence is enhanced by varying each mutation by a small random amount. The size of the random amount decreases with each subsequent generation. Once the specified number of generations have processed (10,000 for this study) the best solution is selected from the last generation according to the same objective function of the evaluation step.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Brattin, R., Sexton, R.S., Yin, W. et al. A neural network solution for forecasting labor demand of drop-in peer tutoring centers with long planning horizons. Educ Inf Technol 24, 3501–3522 (2019). https://doi.org/10.1007/s10639-019-09939-7

Download citation

Keywords

  • Neural network
  • Genetic algorithm
  • Labor demand modeling
  • Long planning horizon
  • Labor forecasting