2016, 1(4): 299-308. doi: 10.3934/bdia.2016012

Modeling daily guest count prediction

Department of Computer Science and Engineering York University 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada

* Corresponding author: Ricky Fok

Published  April 2017

We present a novel method for analyzing data with temporal variations. In particular, the problem of modeling daily guest count forecast for a restaurant with more than 60 chain stores is presented. We study the transaction data collected from each store, perform data preprocessing and feature constructions for the data. We then discuss different forecasting techniques based on data mining and machine learning techniques. A new modeling algorithm SW-LAR-LASSO is proposed. We compare multiple regression model, poisson regression model, and the proposed SW-LAR-LASSO model for prediction. Experimental results show that the approach of combining sliding windows and LAR-LASSO produces the best results with the highest precision. This approach can also be applied to other areas where temporal variations exist in the data.

Citation: Fok Ricky, Lasek Agnieszka, Li Jiye, An Aijun. Modeling daily guest count prediction. Big Data & Information Analytics, 2016, 1 (4) : 299-308. doi: 10.3934/bdia.2016012
References:
[1]

S. Coxe, S. West, L. S. Aiken, The analysis of count data: A gentle introduction to poisson regression and its alternatives, J. Pers. Assess, 91 (2009), 121-136. doi: 10.1080/00223890802634175.

[2]

B. Efron, T. Hastie, I. Johnstone, R. Tibshirani, Tibshirani, Least angle regression, The Annals of Statistics, 32 (2004), 407-499. doi: 10.1214/009053604000000067.

[3]

F. G. Forst, Forecasting restaurant sales using multiple regression and box-jenkins analysis, J. Appl. Bus. Res, 382 (1992), 2157-8834. doi: 10.19030/jabr.v8i2.6157.

[4]

T. Hastie, R. Tibshirani, J. Friedman, The Elements of Statistical Learning, Data Mining, Inference, and Prediction, Springer Series in Statistics, Springer, New York, (2009). doi: 10.1007/978-0-387-84858-7.

[5]

S. E. Kimes, R. B. Chase, S. Choi, P. Y. Lee, E. N. Ngonzi, Restaurant revenue management applying yield management to the restaurant industry, Cornell Hospitality Q, 39 (1998), 32-39. doi: 10.1177/001088049803900308.

[6]

A. Lasek, N. Cercone, J. Saunders, Restaurant sales and customer demand forecasting: Literature survey and categorization of methods, Smart City 360, 166 (2016), 479-491. doi: 10.1007/978-3-319-33681-7_40.

[7]

M. S. Morgan, P. K. Chintagunta, Forecasting restaurant sales using self-selectivity models, J. Retail. Consum. Serv, 4 (1997), 117-128. doi: 10.1016/S0969-6989(96)00035-5.

[8]

D. Reynolds, I. Rahman, W. Balinbin, Econometric modeling of the U.S. restaurant industry International, J. Hospitality Manage, 34 (2013), 317-323.

[9]

K. Ryu, A. Sanchez, The evaluation of forecasting methods at an institutional foodservice dining facility, J. Hospitality Financ. Manage, (2013), 27-45. doi: 10.1080/10913211.2003.10653769.

[10]

K. F. Sellers and G. Shmueli, Predicting censored count data with COM-Poisson regression, Working Paper, Indian School of Business, Hyderabad, 2010.

[11]

J. T. Wulu Jr, K. P. Singh, F. Famoye, T. N. Thomas, G. McGwin, Regression analysis of count data, J. Ind. Soc. Ag. Statistics, 55 (2002), 220-230.

show all references

References:
[1]

S. Coxe, S. West, L. S. Aiken, The analysis of count data: A gentle introduction to poisson regression and its alternatives, J. Pers. Assess, 91 (2009), 121-136. doi: 10.1080/00223890802634175.

[2]

B. Efron, T. Hastie, I. Johnstone, R. Tibshirani, Tibshirani, Least angle regression, The Annals of Statistics, 32 (2004), 407-499. doi: 10.1214/009053604000000067.

[3]

F. G. Forst, Forecasting restaurant sales using multiple regression and box-jenkins analysis, J. Appl. Bus. Res, 382 (1992), 2157-8834. doi: 10.19030/jabr.v8i2.6157.

[4]

T. Hastie, R. Tibshirani, J. Friedman, The Elements of Statistical Learning, Data Mining, Inference, and Prediction, Springer Series in Statistics, Springer, New York, (2009). doi: 10.1007/978-0-387-84858-7.

[5]

S. E. Kimes, R. B. Chase, S. Choi, P. Y. Lee, E. N. Ngonzi, Restaurant revenue management applying yield management to the restaurant industry, Cornell Hospitality Q, 39 (1998), 32-39. doi: 10.1177/001088049803900308.

[6]

A. Lasek, N. Cercone, J. Saunders, Restaurant sales and customer demand forecasting: Literature survey and categorization of methods, Smart City 360, 166 (2016), 479-491. doi: 10.1007/978-3-319-33681-7_40.

[7]

M. S. Morgan, P. K. Chintagunta, Forecasting restaurant sales using self-selectivity models, J. Retail. Consum. Serv, 4 (1997), 117-128. doi: 10.1016/S0969-6989(96)00035-5.

[8]

D. Reynolds, I. Rahman, W. Balinbin, Econometric modeling of the U.S. restaurant industry International, J. Hospitality Manage, 34 (2013), 317-323.

[9]

K. Ryu, A. Sanchez, The evaluation of forecasting methods at an institutional foodservice dining facility, J. Hospitality Financ. Manage, (2013), 27-45. doi: 10.1080/10913211.2003.10653769.

[10]

K. F. Sellers and G. Shmueli, Predicting censored count data with COM-Poisson regression, Working Paper, Indian School of Business, Hyderabad, 2010.

[11]

J. T. Wulu Jr, K. P. Singh, F. Famoye, T. N. Thomas, G. McGwin, Regression analysis of count data, J. Ind. Soc. Ag. Statistics, 55 (2002), 220-230.

Figure 1.  Examples of boxplots for some of the stores from the chain of restaurants
Figure 2.  Three iterations of the sliding window are shown. Each line interval denotes a week. The shaded boxes denote the sliding windows for the training data over eight weeks and the empty boxes denote the weeks where the guest counts are predicted
Figure 3.  Experimental process for guest count predictions
Table 1.  Table of results from chosen stores. The bolded results denote the lowest predictive error among the three algorithms tested
Benchmark StoresMultiple regressionPoisson regressionSW-LAR-LASSOlocalization
Store_1 7.888.288.40Canada stores
Store_215.5616.71 15.00
Store_3 10.2010.8610.25
Store_413.1514.51 12.86
Store_510.5011.44 10.25
Store_616.0417.66 14.19US Stores
Store_718.6224.37 15.60
Store_816.0215.69 12.89
Store_9----22.57
Store_10----14.68
Benchmark StoresMultiple regressionPoisson regressionSW-LAR-LASSOlocalization
Store_1 7.888.288.40Canada stores
Store_215.5616.71 15.00
Store_3 10.2010.8610.25
Store_413.1514.51 12.86
Store_510.5011.44 10.25
Store_616.0417.66 14.19US Stores
Store_718.6224.37 15.60
Store_816.0215.69 12.89
Store_9----22.57
Store_10----14.68
[1]

Shaoyong Lai, Qichang Xie. A selection problem for a constrained linear regression model. Journal of Industrial & Management Optimization, 2008, 4 (4) : 757-766. doi: 10.3934/jimo.2008.4.757

[2]

Lianjun Zhang, Lingchen Kong, Yan Li, Shenglong Zhou. A smoothing iterative method for quantile regression with nonconvex $ \ell_p $ penalty. Journal of Industrial & Management Optimization, 2017, 13 (1) : 93-112. doi: 10.3934/jimo.2016006

[3]

Song Wang, Quanxi Shao, Xian Zhou. Knot-optimizing spline networks (KOSNETS) for nonparametric regression. Journal of Industrial & Management Optimization, 2008, 4 (1) : 33-52. doi: 10.3934/jimo.2008.4.33

[4]

Jiang Xie, Junfu Xu, Celine Nie, Qing Nie. Machine learning of swimming data via wisdom of crowd and regression analysis. Mathematical Biosciences & Engineering, 2017, 14 (2) : 511-527. doi: 10.3934/mbe.2017031

[5]

Andrew J. Majda, Yuan Yuan. Fundamental limitations of Ad hoc linear and quadratic multi-level regression models for physical systems. Discrete & Continuous Dynamical Systems - B, 2012, 17 (4) : 1333-1363. doi: 10.3934/dcdsb.2012.17.1333

[6]

Wei Xue, Wensheng Zhang, Gaohang Yu. Least absolute deviations learning of multiple tasks. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1-11. doi: 10.3934/jimo.2017071

[7]

Xiang-Sheng Wang, Luoyi Zhong. Ebola outbreak in West Africa: real-time estimation and multiple-wave prediction. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1055-1063. doi: 10.3934/mbe.2015.12.1055

[8]

Urszula Ledzewicz, Eugene Kashdan, Heinz Schättler, Nir Sochen. From the guest editors. Mathematical Biosciences & Engineering, 2011, 8 (2) : i-ii. doi: 10.3934/mbe.2011.8.2i

[9]

Alberto d’Onofrio, Paola Cerrai, Alberto Gandolfi. From the Guest Editors. Mathematical Biosciences & Engineering, 2013, 10 (1) : i-ii. doi: 10.3934/mbe.2013.10.1i

[10]

Abba Gumel, James Watmough. From the guest editors. Mathematical Biosciences & Engineering, 2006, 3 (3) : i-ii. doi: 10.3934/mbe.2006.3.3i

[11]

Gerardo Chowell, Zhilan Feng, Baojun Song. From the guest editors. Mathematical Biosciences & Engineering, 2013, 10 (5/6) : i-xxiv. doi: 10.3934/mbe.2013.10.5i

[12]

David Logan. From the Guest Editor. Mathematical Biosciences & Engineering, 2007, 4 (1) : i-ii. doi: 10.3934/mbe.2007.4.1i

[13]

Urszula Ledzewicz, Avner Friedman, Jacek Banasiak, Heinz Schättler, Edward M. Lungu. From the guest editors. Mathematical Biosciences & Engineering, 2013, 10 (3) : i-ii. doi: 10.3934/mbe.2013.10.3i

[14]

Urszula Ledzewicz, Andrzej Swierniak. From the Guest Editors. Mathematical Biosciences & Engineering, 2005, 2 (3) : i-ii. doi: 10.3934/mbe.2005.2.3i

[15]

Carlos Castillo-Chávez, Christopher Kribs Zaleta, Yang Kuang, Baojun Song. From the Guest Editors. Mathematical Biosciences & Engineering, 2009, 6 (2) : i-ii. doi: 10.3934/mbe.2009.6.2i

[16]

Fred Brauer, Carlos Castillo-Chavez, Thomas G. Hallam, Jia Li, Jianhong Wu, Yicang Zhou. From the Guest Editors. Mathematical Biosciences & Engineering, 2006, 3 (1) : i-ix. doi: 10.3934/mbe.2006.3.1i

[17]

Manisha Pujari, Rushed Kanawati. Link prediction in multiplex networks. Networks & Heterogeneous Media, 2015, 10 (1) : 17-35. doi: 10.3934/nhm.2015.10.17

[18]

Margherita Nolasco. Breathing modes for the Schrödinger-Poisson system with a multiple--well external potential. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1411-1419. doi: 10.3934/cpaa.2010.9.1411

[19]

Antonio DeSimone, Natalie Grunewald, Felix Otto. A new model for contact angle hysteresis. Networks & Heterogeneous Media, 2007, 2 (2) : 211-225. doi: 10.3934/nhm.2007.2.211

[20]

Miao-Miao Li, Chun-Lei Tang. Multiple positive solutions for Schrödinger-Poisson system in $\mathbb{R}^{3}$ involving concave-convex nonlinearities with critical exponent. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1587-1602. doi: 10.3934/cpaa.2017076

 Impact Factor: 

Article outline

Figures and Tables

[Back to Top]