×

Retail store scheduling for profit. (English) Zbl 1339.90129

Summary: In spite of its tremendous economic significance, the problem of sales staff schedule optimization for retail stores has received relatively scant attention. Current approaches typically attempt to minimize payroll costs by closely fitting a staffing curve derived from exogenous sales forecasts, oblivious to the ability of additional staff to (sometimes) positively impact sales. In contrast, this paper frames the retail scheduling problem in terms of operating profit maximization, explicitly recognizing the dual role of sales employees as sources of revenues as well as generators of operating costs. We introduce a flexible stochastic model of retail store sales, estimated from store-specific historical data, that can account for the impact of all known sales drivers, including the number of scheduled staff, and provide an accurate sales forecast at a high intra-day resolution. We also present solution techniques based on mixed-integer (MIP) and constraint programming (CP) to efficiently solve the complex mixed integer non-linear scheduling (MINLP) problem with a profit-maximization objective. The proposed approach allows solving full weekly schedules to optimality, or near-optimality with a very small gap. On a case-study with a medium-sized retail chain, this integrated forecasting-scheduling methodology yields significant projected net profit increases on the order of 2–3% compared to baseline schedules.

MSC:

90B35 Deterministic scheduling theory in operations research
90C11 Mixed integer programming
62P30 Applications of statistics in engineering and industry; control charts
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aitchison, J.; Brown, J. A.C., The lognormal distribution, with special reference to its uses in econometrics (1957), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 0081.14303
[2] Avramidis, A. N.; Chan, W.; Gendreau, M.; L’Ecuyer, P.; Pisacane, O., Optimizing daily agent scheduling in a multiskill call centers, European Journal of Operational Research, 200, 3, 822-832 (2010) · Zbl 1177.90262
[3] Aykin, T., Optimal shift scheduling with multiple break windows, Management Science, 42, 591-602 (1996) · Zbl 0880.90065
[4] Bechtolds, S.; Jacobs, L., Implicit optimal modeling of flexible break assignments, Management Science, 36, 1339-1351 (1990)
[6] Box, G. E.P.; Jenkins, G. M.; Reinsel, G. C., Time series analysis: Forecasting and control (2008), John Wiley & Sons · Zbl 1154.62062
[7] Brockwell, P. J.; Davis, R. A., Time series: Theory and methods (1991), Springer · Zbl 0709.62080
[8] Chapados, N.; Joliveau, M.; Rousseau, L.-M., Retail store workforce scheduling by expected operating income maximization, (Achterberg, T.; Beck, J., Integration of AI and OR techniques in constraint programming for combinatorial optimization problems. Integration of AI and OR techniques in constraint programming for combinatorial optimization problems, Lecture notes in computer science, Vol. 6697 (2011), Springer: Springer Berlin/Heidelberg), 53-58 · Zbl 1302.90075
[9] Côté, M.-C.; Gendron, B.; Quimper, C.-G.; Rousseau, L.-M., Formal languages for integer programming modeling of shift scheduling problem, Constraints, 16, 1, 54-76 (2011) · Zbl 1215.90026
[10] Côté, M.-C.; Gendron, B.; Rousseau, L.-M., Grammar-based integer programming models for multi-activity shift scheduling, Management Science, 57, 1, 151-163 (2011) · Zbl 1214.90077
[11] Dantzig, G., A comment on Edie’s traffic delay at toll booths, Journal of Operation Research Society of America, 2, 339-341 (1954)
[12] Demassey, S.; Pesant, G.; Rousseau, L.-M., A cost-regular based hybrid column generation approach, Constraints, 11, 4, 315-333 (2006) · Zbl 1117.90066
[13] Diebold, F. X.; Mariano, R. S., Comparing predictive accuracy, Journal of Business & Economic Statistics, 13, 3, 253-263 (1995)
[14] Edie, L., Traffic delays at toll booths, Operations Research, 2, 2, 107-138 (1954)
[15] Ernst, A.; Jiang, H.; Krishnamoorthy, M.; Owens, B.; Sier, D., An annotated bibliography of personnel scheduling and rostering, Annals of Operations Research, 127, 21-144 (2004) · Zbl 1090.90078
[16] Ernst, A.; Jiang, H.; Krishnamoorthy, M.; Sier, D., Staff scheduling and rostering: A review of applications, methods and models, European Journal of Operational Research, 153, 3-27 (2004) · Zbl 1053.90034
[17] Hastie, T.; Tibshirani, R.; Friedman, J., Elements of statistical learning (2009), Springer
[18] Hilbe, J. M., Negative binomial regression (2011), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 1269.62063
[20] Hyndman, R. J.; Koehler, A. B.; Ord, J. K.; Snyder, R. D., Forecasting with exponential smoothing: The state space approach (2008), Springer: Springer Berlin and Heidelberg · Zbl 1211.62165
[21] Kabak, Ö.; Ülengin, F.; Aktaş, E.; Önsel, Ş.; Topcu, Y. I., Efficient shift scheduling in the retail sector through two-stage optimization, European Journal of Operational Research, 184, 1, 76-90 (2008) · Zbl 1175.90170
[22] Koole, G.; Pot, A., A note on profit maximization and monotonicity for inbound call centers, Operations Research, 59, 5, 1304-1308 (2011) · Zbl 1235.90201
[23] Lam, S. Y.; Vandenbosch, M.; Hulland, J.; Pearce, M., Evaluating promotions in shopping environments: Decomposing sales response into attraction, conversion, and spending effects, Marketing Science, 20, 2, 194-215 (2001)
[24] Lam, S. Y.; Vandenbosch, M.; Pearce, M., Retail sales force scheduling based on store traffic forecasting, Journal of Retailing, 74, 1, 61-88 (1998)
[25] Lehmann, E. L.; Casella, G., Theory of point estimation (1998), Springer · Zbl 0916.62017
[26] Makridakis, S. G.; Wheelwright, S. C.; Hyndman, R. J., Forecasting: Methods and applications (1997), Wiley
[28] McCullagh, P., Regression models for ordinal data (with discussion), Journal of the Royal Statistical Society B, 42, 2, 109-142 (1980) · Zbl 0483.62056
[29] McCullagh, P.; Nelder, J. A., Generalized linear models (1989), Chapman & Hall: Chapman & Hall London · Zbl 0744.62098
[30] McCulloch, C. E.; Searle, S. R.; Neuhaus, J. M., Generalized, linear, and mixed models. Generalized, linear, and mixed models, Wiley Series in Probability and Statistics (2008), John Wiley & Sons: John Wiley & Sons Hoboken, NJ · Zbl 1165.62050
[31] Mehrotra, A.; Murthy, K.; Trick, M., Optimal shift scheduling: A branch-and-price approach, Naval Research Logistics, 47, 185-200 (2000) · Zbl 0972.90032
[33] Perdikaki, O.; Kesavan, S.; Swaminathan, J. M., Effect of traffic on sales and conversion rates of retail stores, Manufacturing and Service Operations Management, 14, 1, 145-162 (2012)
[35] Pinheiro, J. C.; Bates, D. M., Mixed effects models in S and S-Plus (2000), Springer-Verlag: Springer-Verlag New York, NY · Zbl 0953.62065
[36] Rekik, M.; Cordeau, J.-F.; Soumis, F., Using benders decomposition to implicitly model tour scheduling, Annals of Operations Research, 128, 111-133 (2004) · Zbl 1056.90073
[37] Rekik, M.; Cordeau, J.-F.; Soumis, F., Implicit shift scheduling with multiple breaks and work stretch duration restrictions, Journal of Scheduling, 13, 1, 49-75 (2010) · Zbl 1185.90091
[38] Thompson, G. M., Labor scheduling using NPV estimates of the marginal benefit of additional labor capacity, Journal of Operations Management, 13, 1, 67-86 (1995)
[41] Van den Bergh, J.; Beliën, J.; De Bruecker, P.; Demeulemeester, E.; De Boeck, L., Personnel scheduling: A literature review, European Journal Of Operational Research, 226, 367-385 (2013) · Zbl 1292.90001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.