Forecasting of Outbound Product Flow

Transcription

1 University of Twente Master s Thesis Extended Summary Forecasting of Outbound Product Flow Author: Catharina Elisabeth Lolkema Supervisory Committee: Dr. ir. L.L.M. van der Wegen Dr. M.C. van der Heijden J.J.T. Jaspers M.Sc. November 2, 2015

2 Author C.E. (Karin) Lolkema Education University of Twente M.Sc. Industrial Engineering and Management Specialization: Production and Logistic Management Graduation Date 6 November

3 Extended Summary This research study originates at the Supply Chain department of a global logistics service provider. Since 2005, logistical activities are employed for its only dedicated customer. One of these logistical processes, which we further refer to as the outbound process, is a highly intensive labor process directly subject to high fluctuating customer demand. Sharp standards are set by the customer to meet this fluctuating customer demand in time: received orders should be processed at the same day. To fulfill customer orders and manage peaks and falls in demand in the most effective manner against lowest possible cost, personnel should be scheduled efficiently one day in advance, what makes a reliable forecasting model as input for the personnel planning fundamental. In 2011, a forecasting model has been initiated for this outbound process by a graduation student, which currently retains a mean average absolute deviation of percent per day over the first 9 weeks of Besides its inaccuracy, forecasts generated by the model cannot be used as input for the personnel planning model due to the following reasons: the order structure in the forecasting model does not coincide with the order structure as required in the personnel scheduling model, and processes are differently measured in both models (items or lines), which cannot be directly rewritten into one another. Moreover, order types currently embedded in the model do not exist anymore, or new order types are not enclosed, leaving the model to retain a non up-to-date structure. Furthermore, nobody in the organization fully understands the model and has the ability to maintain it. Research Goal We identified the current forecasting model as quite inaccurate and costly, and specified the need for a forecasting model that can serve as an input for the personnel planning model. Since the planning of personnel occurs on a daily basis by the outbound (assistant) supervisor with an average educational background, our forecasting model should provide estimates on the same daily basis, and being easy to handle and maintain. Our research goal needs to satisfy these needs. In general terms, our main research goal is: Developing a practical forecasting model for the outbound process that is easy to understand and maintain, which serves as an input for the personnel planning model and provides forecasts on a daily level as accurate as possible. Note that our model aims to support the (assistant) supervisors in their scheduling proceedings, not to overrule their experiences. Since forecasting is only used for personnel scheduling purposes, the model 3

4 can be fully designed as input for the personnel planning model. To be clear, our new forecasting model will be newly developed, starting from scratch. Requirements Besides the persuasiveness to develop an easy-access forecasting model being an input for the personnel scheduling model, more requirements are defined. We adopt the outbound order structure from the personnel planning into our model, consisting of six outbound sub-processes with appropriate work load drive (WLD). The work load drive (lines or items) expresses the manner in which processes are measured. When work is embroiled per line, e.g. scanning of one box with 50 products (1 line with 50 items), the calculation of required employees is based on lines. When work is measured per item, the number of employees is calculated according to items. Forecasts should be finalized on a daily basis before the scheduling and recruitment process of personnel for the next day starts. As said earlier, received orders should be processed at the same day, meaning that today s volumes cannot be used for tomorrow s forecasts as they are not finalized yet at the time of scheduling. Accordingly, we propose to use yesterday s volumes for tomorrow s forecasts: a 2-day ahead forecast. To support this 2-day ahead forecast, we only opt for forecasting techniques useful for generating short-term forecasts. Ever changing order structures are faced by the customer due to marketing activities and changing customer preferences. As a result, the order structure should be adjustable in the sense that order types can easily be added and distracted, preferably by the people attaining such practical knowledge: the (assistant) supervisors. Last, to ease its maintenance and increase its sustainability within the organization, the forecasting model and inherent techniques should be easy to understand and maintain, requiring minimum data storage and running time. Selecting Forecasting Techniques To identify appropriate forecasting techniques, we initiated a literature research. Since our research is blessed with the availability of reliable historical data and we assume that patterns from the past will continue in the future, we narrow down our literature research to quantitative time series models. Type of Technique Technique Data pattern Naive Naive ST, T, S Averaging Moving averages ST Double moving averages ST, T Smoothing Simple exponential smoothing ST Trended exponential smoothing T Seasonal exponential smoothing T, S Table 1: A summary of the forecasting techniques and the data patterns they incorporate we use in our research, based on a framework provided by Hanke and Reitsch (1998), and Makridakis and Wheelwright (1978). Pattern of the data: ST, stationary; T, trended; S, seasonal; C, cyclical. 4

5 All quantitative time series models we identified during our literature research being appropriate for our situation are tabulated in Table 1. These models are ultimately suitable for short-term forecasts, easy to understand and maintain, easy to implement, and requiring minimum data storage and computational effort. With easy to understand and maintain we refer to forecasting models pertaining an easy initialization and update of parameters, that have a logical built-up of components to people without any statistical or mathematical background. According to Hanke and Reitsch (1998), the behavior of the data patterns mentioned in Table 1 can be defined as stated below. When making a forecast, the projection for each of these individual components is combined. Level (A): The level captures the scale of a time series, and shows a constant line if no trend is present. It indicates the initial height of a time series. Trend (T): The trend represents the growth or decline in the time series over a certain period of time. Seasonal component (S): The seasonal component is a pattern of change that repeats itself in a certain period of time (e.g. a week, month, or year). Techniques Although all techniques are relatively simple, some are simpler than others. We confine ourselves at this point to smoothing methods. Further details on the naive method and moving averages can be found in Hanke and Reitsch (1998) and Makridakis et al. (1978). Seasonal component Trend component N (none) A (additive) M (multiplicative) N (none) N-N N-A N-M A (additive) A-N A-A A-M DA (damped additive) DA-N DA-A DA-M M (multiplicative) M-N M-A M-M DM (damped multiplicative) DM-N DM-A DM-M Table 2: Exponential Smoothing Taxonomy Exponential Smoothing is very suitable in situations where managers need forecasts in a relatively short time. Taylor (2003) developed a taxonomy that describes various exponential smoothing techniques and their exploitation of different combinations of the trend and seasonal component, illustrated in Table 2. As can be seen, both the trend and seasonal component can be composed in an (damped) additive or (damped) multiplicative manner. For every combination of trend and seasonal component, an exponential smoothing method exists. Since an appropriate fit of a particular exponential smoothing technique with data gains surprisingly in accuracy, the detection of the best smoothing technique for our research is an important task. Based on the literature, we have chosen to incorporate the exponential smoothing methods listed in Table 3 in our research. These methods include Holt s, Brown s, and Winters models, which have been very popular with researchers and practitioners, and have proven their appropriateness and robustness in practice. Furthermore, we include the exponential trended models from Pegels (1969) and Taylor (2003), which are less commonly used, but have proven to be very accurate in a research study from Taylor as they tend to deal with the more common multiplicative data patterns (Hyndman et al., 2002; Taylor, 2003). 5

6 Trend Component N A DA M DM Seasonal Component N A M Simple Method At = α Yt + (1-α) Ŷt Ŷt+p = At Holt s Method At = αyt + (1-α)(At 1 + Tt 1) Tt = β(at - At 1) + (1-β)Tt 1 Ŷt+p = At + ptt Holt s Damped Method At = αyt + (1-α)(At 1 + ϕtt 1) Tt = β(at - At 1) + (1-β)ϕTt 1 Ŷt+p = At + p i=1 ϕ i Tt Pegels Method At = αyt + (1-α)(At 1Rt 1) Rt = β( A t At 1 + (1-β)Rt 1 Ŷt+p = AtR p t Pegels Damped Method At = αyt + (1-α)(At 1R ϕ t 1 ) Winters Additive Method At = α(yt St L) + (1-α)(At 1 + Tt 1) Tt = β(at - At 1) + (1-β)Tt 1 St = γ(yt At) + (1-γ)St L Ŷt+p = At + ptt + St L+p Winters Damped Additive Method At = αyt St L + (1-α)(At 1 + ϕtt 1) Tt = β(at - At 1) + (1-β)ϕTt 1 St = γ(yt At) + (1-γ)St L Ŷt+p = At + p i=1 ϕ i Tt + St L+p Winters Multiplicative Method At = α( Y t ) + (1-α)(At 1 + Tt 1) St L Tt = β(at - At 1) + (1-β)Tt 1 St = γ( Y t At ) + (1-γ)St L Ŷt+p = (At + ptt)st L+p Winters Damped Multiplicative Method At = α( Y t ) + (1-α)(At 1 + ϕtt 1) St L Tt = β(at - At 1) + (1-β)ϕTt 1 St = γ( Y t At Ŷt+p = (At + ) + (1-γ)St L p i=1 ϕ i Tt) St L+p Rt = β( A t A ϕ t 1 Ŷt+p = AtR + (1-β)Rt 1 p i=1 ϕi t Table 3: Exponential smoothing techniques and their equations used in our research. 6

7 Variable Y t Ŷ t+p α β γ ϕ A t T t R t S t L Description Observed value of the time series in period t Forecast for p periods ahead from period t Smoothing parameter for the level of a time series Smoothing parameter for the trend Smoothing parameter for the seasonal indices Autoregressive or damping parameter Smoothed level of a time series at the end of period t Smoothed additive trend of a time series at the end of period t Smoothed multiplicative trend of a time series at the end of period t Smoothed seasonal index of a time series at the end of period t Number of periods in the seasonal cycle Table 4: Explanation of variables used in the exponential smoothing taxonomy from Taylor (2003). Forecasting Forecasting involves the study of historical data to discover their underlying tendencies and patterns. This knowledge is used to project the data into future time periods as forecasts. (Hanke and Reitsch, 1998) To discover such tendencies and patterns, we first perform a data analysis. It helps us understanding if our chosen forecasting techniques form a good fit with our data and utilize existing data patterns to the fullest. Throughout this section, we use outbound process A as an illustrative example. Note that fictional data is used for process A: all facts and figures are made-up. Data analysis To involve timely data and follow Hyndman and Kostenko s (2007) suggestion that a minimum sample size of m+5 (where m stands for amount of seasons per year) observations is needed when data seems to own a yearly season, we opt for data from January 2012 till December 2014 for our data analysis. In respective order, per outbound sub-process we plot and analyze the data, perform autocorrelation analyses and use the Ljung-Box and t-statistic to strengthen our findings in estimating the existence of any (linear) trend or seasonality. Having put all these procedures into motion, we found that outbound process A possesses a negative linear trend and a weekly seasonality with a peaks in demand every Monday. Initial values To enable the forecasting process, initial values should be set for all parameters inherent in the forecasting techniques from Table 3: values for the data components A 0, T 0, S 0, and R 0, and values for the smoothing parameters α, β, γ and ϕ (only applicable for smoothing methods). We use the first 30 data points of 2012 to calculate the initial values for all data components, and use the (rest) data of 2012 and 2013 to set the initial values for the smoothing parameters, as our research has shown a higher forecast accuracy level can be achieved when more data is involved in setting these parameters. For both types of parameters (data component, smoothing parameter), different calculations are used. Data components are valued by the pragmatic and popular ratio to moving average technique. 7

8 Smoothing parameters are set by use of a grid search in Microsoft Excel s SOLVER. The SOLVER function minimizes the quadratic differences between observed values and forecasted values (error) in terms of the mean squared error (MSE). A minimization of the MSE measure is especially suitable for our setting, as it induces large penalties to large forecast errors by squaring all errors, which is useful in need of an accurate personnel planning every single day. We only allow values for the smoothing parameters between 0 and 1, as this range is often used in practice and more restricted parameters do not necessarily improve forecast accuracy (Gardner, 1985). Microsoft Excel s SOLVER is chosen because of its fast working and level of detail. Aggregation level, time horizon and outliers This section details some further requirements to include in the forecasting process. At first, we remark that forecasting can take place at two levels: (1) per outbound order type separately, with an addup of forecasts afterwards, or (2) directly at an aggregated level with an add-up of volumes per order type prior to forecasting. We decided to pursue the latter option, because analysis pointed out that on average a 1.12 percent gain in forecast accuracy can be reached. Furthermore, to make inclusion of marketing information and verification of volumes easier by our logistics service provider s customer, a weekly verification would be more appealing than a daily verification. Research showed that an increase of 4.11 percent in forecast accuracy can be reached when organizing a daily verification. As our research aims to achieve the highest possible accuracy level (and a daily verification is a reasonable prospect), we produce a 2-day ahead forecast on the aggregated level of an outbound sub-process. Last, as we do not want our forecasting techniques to keep track of non-repetitive events far into the future, we remove these events in the form of outliers from our data set. As its parameters used for outlier calculation are not affected by outliers, we use the Modified Z-Score technique for outlier detection (Moore and McCabe, 2002). Moreover, the technique is especially useful for our situation as it does not ask for any kind of prior knowledge or assumptions on outliers from the (assistant) supervisors, and does not acquire large storage capacity or incremental running time. Best forecasting technique Having set initial values and having applied the requirements from the previous section in our research, we can take the next step: detecting the best forecasting technique per outbound sub-process based on a proper fit with our data and delivered forecast accuracy. A decent fit of a forecasting technique with data is important to actually forecast and utilize existing patterns to the fullest. We identify a proper fit by plotting both the observed values and forecasts over 2014, and using an Autocorrelation Function (ACF) to discover any remaining pattern in the residuals (difference between the observed value and forecast). Furthermore, we use the property of smoothing parameters that they form a good fit if they are valued between 0.1 and 0.3 (Jacob and Chase, 2013; Schroeder et al., 2013; Gardner, 1985). Figure 1 visualizes the plots of both the observed values and forecasts, in which the simple exponential smoothing and Winters multiplicative exponential smoothing are exemplified. As can be seen, forecasts generated by Winters technique with additional seasonal parameter form a better fit with the data than the exponential smoothing technique with no trended nor seasonal parameter. 8

9 Figure 1: Behavior of forecasts generated by the simple smoothing and Winters multiplicative smoothing techniques in comparison to the observed values from Process A in If the Autocorrelation Function (ACF) of residuals appear not be random, a certain pattern still exists in the residuals, meaning that the forecasting technique does not properly utilize present data patterns (Hanke and Reitsch, 1998). Figure 2 proposes the ACF s of the residuals generated by all forecasting techniques. Only the autocorrelations for the naive method and damped Winters multiplicative appear to be randomly distributed, meaning they form a proper fit with the observed values as no pattern is left in the residuals. 9

10 Figure 2: Autocorrelation Functions (ACF) of the residuals produced by all forecasting techniques during the forecasting process for outbound Process A. Confining ourselves to the last step in identifying a proper fit, Table 5 tabulates the range of values the smoothing parameters have taken on during the forecast process. As smoothing values above 0.3 indicate an overcompensation of the parameter to keep up with patterns they are not built for, we conclude damped Holt s and damped Winters additive smoothing techniques to not form a proper fit with our observed values. Furthermore, techniques with smoothing values valued below 0.1 neither simulate a perfect fit, meaning that on these grounds, Brown s and Holt s are discarded too. 10

11 Parameters Forecasting Technique α β γ ϕ Simple Exponential Smoothing 0.25 Brown s Exponential Smoothing 0.03 Holt s Exponential Smoothing Holt s Damped Exponential Smoothing Winter s Mult. Exponential Smoothing Winter s Mult. Damped Exponential Smoothing Winter s Add. Exponential Smoothing Winter s Add. Damped Exponential Smoothing Pegel s Exponential Smoothing Pegel s Damped Exponential Smoothing NA NA NA NA Table 5: Parameter setting for the exponential smoothing techniques; used to generate forecasts for Process A. Excluding the forecasting techniques per outbound sub-process that do not form a good fit with its observed values, we submit remaining forecasting techniques to forecast accuracy measurements in terms of mean squared error (MSE), mean absolute deviation (MAD), and mean average percentage error (MAPE). From all techniques forming a good fit, the damped Winters multiplicative exponential smoothing technique appears to generate most accurate forecasts for outbound Process A. Table 6 tabulates the most appropriate forecasting technique per outbound sub-process, retrieving highest accuracy levels in all terms. We have opt for one generic forecasting technique for all outbound processes, but forecast accuracy would then be decreased by at least 8.7 percent (when generalizing Winters multiplicative method) on average for all processes, which is not consistent with our research goal to strive for the best possible result. Outbound sub-process Process A Process B Process C Process D Process E Process F Forecasting technique Damped Winters multiplicative exponential smoothing Damped Winters additive exponential Smoothing Damped Holt s exponential smoothing Winters additive exponential smoothing Winters multiplicative exponential smoothing Damped Winters additive exponential smoothing Table 6: An overview of the most appropriate forecasting technique per outbound sub-process. Further improvements To further improve forecast accuracy, we identified the influence of national holidays on its observed values just before or just after, and investigated the appropriate time at which to update the smoothing parameters (α, β, γ, ϕ) in smoothing methods. Adding prior knowledge on influences of national holidays in our data samples, we improved the forecast accuracy for Process A with 0.02 percent on average per day. By use of a tracking signal, which signals a drift in forecasts by means of a confidence interval, with an update at a 99 percent service level, we improved the forecast accuracy by 0.24 percent on average per day, in relation to no update at all. 11

12 Implementation Our forecasting model is built in Microsoft Excel, since this software programme is available on all computers within the organization, and general knowledge of the software is available in-house. Additionally, investment costs are saved. Our research has partially been initiated because of a lack of proper understanding of the current forecasting model and a non-defined responsibility. We therefore need to be aware of common failures of forecasting models, like a low credibility (Makridakis and Wheelwright, 1979), and low organizational support (Sanders and Manrodt, 1994). According to Silver et al. (1998), to improve credibility, one must be able to understand underlying choices and assumptions in the forecasting model, and the general idea of the statistical model. We therefore find it important to transfer knowledge about the model properly to the (assistant) supervisors, and make them responsible for the generation of accurate forecasts, merely because they attain most up-to-date information on operational proceedings. For additional proceedings, like the add-in of new processes, we suggest the Supply Chain department provides support, as they have knowledge of Microsoft Excel and logistical processes. To support a proper implementation, we recommend to train all involved people that need to work with the model: the (assistant) supervisors and the Supply Chain department. Clear manuals should be written, most preferable with an outline of the actions to take in case an error or other kind of scenario occurs. Besides a proper transfer of knowledge, any risk in implementation is located in IT capacity. Results Carrying out all our findings, we retain an average percentage deviation of actual volumes from forecasted volumes of percent per outbound sub-process per day. In contrast, the old forecasting model released an average percentage deviation of percent, which means we achieved an improvement of percent point on average per day. Conclusions and Recommendations We draw the following conclusions: We conclude that our research has delivered a forecasting model which satisfies our research goal. It not only improves the forecast accuracy by percent point on average per day, the model is also easy to understand and maintain by the (assistant) supervisor(s), as order types and its belonging historical data can easily be added and distracted from the total demand streams per process. Furthermore, the forecasting techniques used in the model can easily be interpreted by employees of the Supply Chain department to provide additional support (like the add-in of new processes). Besides, all techniques take on an easy update of parameters, without incremental running time. To increase its sustainability within the organization, the model is built in Microsoft Excel, which is accessible on all computers and of which general knowledge is available in-house. Furthermore, investment costs are saved. Most importantly, the model is customized towards the personnel planning, as it retains the same order structure and provides forecasts on a daily basis, to support the supervisors in their forecasting and planning process. 12

13 Of course, there is always room for improvement: Relating to the positive results, we recommend to use the new forecasting model as an input for the personnel planning. To finalize the bridge towards practice, the supervisors should own the model, as they now have the ability to properly work with the model. For additional proceedings, like the add-in of new order types, the Supply Chain department should be able to lend a hand. To sustain optimal results in case new order outbound processes are added, we propose further research on an automatic identification of the most appropriate forecasting technique per process. To include marketing information in forecasts and achieve even more accurate results, a verification process by the service provider s customer, who s attaining such knowledge in-house, should be introduced. Bibliography Gardner, E.S. (1985). Exponential Smoothing: The State of the Art. Journal of Forecasting, Vol. 4, Hanke, J.E., and Reitsch, A.G. (1998). Business Forecasting. 6th edition, Prentice Hall. Hyndman, R.J., Koehler, A.B., Snyder, R.D., Grose, S. (2002). A state space framework for automatic forecasting using exponential smoothing methods. International Journal of Forecasting 18, Hyndman, R.J., and Kostenko, A.V. (2007). Minimum sample size requirements for seasonal forecasting models. Foresight, Issue 6. Jacobs, F.R., and Chase, R.B. (2013). Operations and Supply Chain Management: The Core. 3rd Edition, McGraw-Hill Higher Education, Page 59, Chapter 3. Makridakis, S., and Wheelwright, S.C. (1978). Forecasting, methods and applications. 1st edition. USA: John Wiley and Sons Inc. Makridakis, S., and Wheelwright, S.C. (1979). Forecasting the Future and the Future of Forecasting. In S. Makridakis and S.C. Wheelwright (eds.), TIMS Studies in the Management Sciences, vol 12. Amsterdam: North-Holland, pp Moore, D.S., and McCabe, G.P. (2002). Introduction to the Practice of Statistics. 4th ed. New York: W. H. Freeman,. Pegels, C. (1969). Exponential forecasting: some new variations. Management Science, 15, Sanders, N., and K. Manrodt (1994). Forecasting Practices in US Corporations: Survey Results. Interfaces, 24(2), Schroeder, R., Rungtusanatham, M. J., and Goldstein, S. (2013). Operations Management in the Supply Chain: Decisions and Cases. 6th Edition, McGraw-Hill Higher Education, Page 261, Chapter 11. Silver, E.A., Pyke, D.F., Peterson, R., (1998), Inventory Management and Production Planning and 13

14 Scheduling. 3th edition, USA: John Wiley and Sons Inc. Taylor, J.W. (2003). Exponential smoothing with a damped multiplicative trend. International Journal of Forecasting, 19 (2003)