Modified Trend and Seasonal Time Series Analysis for Operations: A Case Study of Soft Drink Production

Abstract:

Many Production and Business Time Series Are Non-Stationary Time Series that Contain Trend and Seasonal Variations. Seasonality Is a Periodic and Recurrent Pattern Caused by Factors such as Weather, Holidays, or Repeating Promotions. this Paper Presents a Trend and Seasonal Time Series Analysis of Soft Drink Production over the Period 2003–2010, it Is Necessary to Know the Trend in Soft Drink Production to Elicit the Reasons why Demand of Soft Drink Is Increased or Decreased at Specific Periods. the Objectives of this Paper Are (i) to Study the Trends in the Production and Productivity of a Soft Drink Bottling Company, and (ii) Analyze the Demand of the Firm with a View to Identifying Trend that Exists in the Company Using Time Series Analysis. A Software Program Was Developed Based on Applicable Methodology to Facilitate Accurate and Faster Analysis of Data. Characterization of Demand Data Using Decomposition Was Done, which Reveal the Nature of Seasonality, Cyclical Activity, Trend and Noise. on the Whole, the Results of the Decomposition Analysis Clearly Show that there Is a Remarkable Linear Trend in Demand Pattern. the Study of Seasonality Shows that the Highest Peak in Demand of the Product Occurred at 12th, 24th, 36th, 48th 60th, 72nd, 84th and 96th Months which Turn Out to Coincide with Yuletide. the Study Further Indicated a Positively Increasing Trend in the Demand Rate of Company’s Product.

• Periodical: International Journal of Engineering Research in Africa (Volume 7)
• Pages: 63-72
• DOI: https://doi.org/10.4028/www.scientific.net/JERA.7.63
• Online since: September 2012
• Authors: Harold C. Godwin, C.E. Okafor
• Keywords: Demand, Forecasting, Seasonality, Time Series, Trend

References

[1] A. B. Koehler, Forecasting models and prediction intervals for the multiplicative Holt-Winters method, International Journal of Forecasting 17 (2001) 269-286.

DOI: 10.1016/s0169-2070(01)00081-4

[2] R.I. Phelps, Optimal inventory rule for a linear trend in demand with a constant replenishment period, Journal of the Operational Research Society 31 (1980) 439-442.

DOI: 10.1057/jors.1980.78

[3] M.W. Watson, R.G. King, C. I. Plosser and J. H. Stock, Stochastic Trends and Economic Fluctuations, American Economic Review 81 (1991) 819-840.

DOI: 10.3386/w2229

[4] A. Mitra, J.F. Cox, and R.R. Jesse, A note on determining order quantities with a linear trend in demand, Journal of the Operational Research Society 35 (1984) 141-144.

DOI: 10.1057/jors.1984.21

[5] H. Arsham, Time-Critical Decision Making for Business Administration, Information on http: /home. ubalt. edu/ntsbarsh/stat-data/Forecast. htm. Retrieved December (2009).

[6] G. C Reinsel, G. E Box and G. M Jenkins, Time Series Analysis. Pearson Education (2003).

[7] Reddy Timma, Forecasting using Decomposition and Combination of Experts. Technical Report, Kanwal Rekhi School of Information Technology, IIT Bombay (2005).

[8] Seth Abhishek, On Using a Multitude of Time Series Forecasting Models, Master's Thesis, Kanwal Rekhi School of Information Technology, IIT Bombay (2005).

[9] Singh Rajveer, On Using Various Decomposition Methods in Time Series Forecasting, Master's Thesis, Kanwal Rekhi School of Information Technology, IIT Bombay (2005).

[10] Yang Yuhong and Hui Zou, Combining time series model for forecasting, International Journal of Forecasting (2004).

[11] W.M. Persons, Correlation of time series, Journal of American Statistical Association, 18 (1923) 5–107.

[12] C.C. Holt, Forecasting seasonal and trends by exponentially weighted moving averages, Office of Naval Research, Memorandum No. 52 (1957).

[13] P. R Winters, Forecasting Sales by Exponentially Weighted Moving Averages, Management Science 6 (1960) 324-342.

DOI: 10.1287/mnsc.6.3.324

[14] G.E.P. Box and G.M. Jenkins, Time Series Analysis: Forecasting and Control, Revised ed. San Fransisco: Holden-Day (1976).

[15] G. Zhang, B.E. Patuwo and M.Y. Hu, Forecasting with artificial neural networks: The state of the art, International Journal of Forecasting, 14 (1998) 35–62.

DOI: 10.1016/s0169-2070(97)00044-7

[16] M. Nelson, T. Hill, T. Remus and M. O'Connor, Time series forecasting using NNs: Should the data be deseasonalized first?, Journal of Forecasting, 18 (1999) 359–367.

DOI: 10.1002/(sici)1099-131x(199909)18:5<359::aid-for746>3.0.co;2-p

[17] J.V. Hansen and R.D. Nelson, Forecasting and recombining time-series components by using neural networks, Journal of the Operational Research Society, 54 (3) (2003) 307–317.

DOI: 10.1057/palgrave.jors.2601523

[18] P. Esmikol, Modeling Demand. Information on https: /www. student. gsu. edu/%7Esmikol. Retrieved December (2009).

[19] P. H Smith, Optimal production policies for items with decreasing demand, European Journal of Operational Research 1 (1977) 365-367.

DOI: 10.1016/0377-2217(77)90045-5

[20] B.L. Bowerman, and O'Connel, Forecasting and Time Series: An Applied Approach, 3rd ed, Belmont, California, Duxbury Press, (1993).

[21] George Box, Gwilym M. Jenkins and Gregory C. Reinsel. Time Series Analysis: Forecasting and Control, third edition. Prentice-Hall, (1994).

DOI: 10.1111/jtsa.12194

[22] G.E.P. Box, D.A. Pierce and P. Newbold, Estimating Trend and Growth Rates in Seasonal Time Series, Journal of the American Statistical Association 82 (1987) 276-282.

DOI: 10.1080/01621459.1987.10478430

[23] V. Assimakopoulos, and K. Nikolopoulos, The Theta Model: a Decomposition Approach to Forecasting, International Journal of Forecasting 16 (2000) 521-530.

DOI: 10.1016/s0169-2070(00)00066-2

[24] F. Busetti, and A.C. Harvey, Seasonality tests, Journal of Business and Economic Statistics 21, (2003) 420-436.

DOI: 10.1198/073500103288619061

[25] A. G. Bruce and S. R. Jurke, Non-Gaussian Seasonal Adjustment: X-12-ARIMA versus Robust Structural Models, Journal of Forecasting 15 (1996) 305-28.

DOI: 10.1002/(sici)1099-131x(199607)15:4<305::aid-for626>3.0.co;2-r