October  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. CoxeS. West and 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. EfronT. HastieI. Johnstone and 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. HastieR. Tibshirani and 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. KimesR. B. ChaseS. ChoiP. Y. Lee and 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. LasekN. Cercone and 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 and 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. ReynoldsI. Rahman and W. Balinbin, Econometric modeling of the U.S. restaurant industry International, J. Hospitality Manage, 34 (2013), 317-323. 

[9]

K. Ryu and 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 JrK. P. SinghF. FamoyeT. N. Thomas and G. McGwin, Regression analysis of count data, J. Ind. Soc. Ag. Statistics, 55 (2002), 220-230. 

show all references

References:
[1]

S. CoxeS. West and 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. EfronT. HastieI. Johnstone and 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. HastieR. Tibshirani and 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. KimesR. B. ChaseS. ChoiP. Y. Lee and 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. LasekN. Cercone and 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 and 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. ReynoldsI. Rahman and W. Balinbin, Econometric modeling of the U.S. restaurant industry International, J. Hospitality Manage, 34 (2013), 317-323. 

[9]

K. Ryu and 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 JrK. P. SinghF. FamoyeT. N. Thomas and 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
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