INPUT DEMAND FORECASTING

Sudiyanti Sudiyanti

1 Introduction

We believe that there is a greater impact of UW-Whitewater population's input demand or consumption on number of generated carbon footprint within the campus area. In our case, the population refers to UW-Whitewater students and enrollments.

Moved by above ideas, we then adopted the principle of Bill of Material approach and employed Forecasting method. What, why and how we utilized these techniques are explained in the next sections.

2 What

2.1 Bill of Material

Bill of Material is an approach that listing the items, ingredients, or materials needed to produce a parent item, end item, or product (Tersine, 1994). The Bill of Material can be structured (1) as simple parts list, (2) to specify how product is generated, or (3) to simplify forecasting and master scheduling. This approach is also called as the product structure when it indicates how a product will be produced. The specific format for the Bill of Material depends upon its intended use. Some of its important uses are to (1) define the product and distinguish it from other products; (2) facilitate the forecasting of optional product features; (3) permit the master schedule to be stated in terms of the fewest possible end items; (4) allow easy order entry from customers; (5) provide the basis for product costing; (6) facilitate material procurement; (7) aid manufacturing planning and final assembly scheduling; and (8) permit efficient file storage and maintenance. Bill of Material can be structured to provide information by either tracing down (exploding) or tracing up (imploding) a product structure. Explosion begins with the parent and breaks it into its lower level components; implosion begins with the component and builds into the parent or higher-level items. The explosion of end item requirements or master scheduled items into component requirements is vital for MRP to establish all lower level component scheduling (Tersine, 1994). Hence, the usability of Bill of Material is important for MRP. MRP approach and its application in Greening Whitewater project are explained in the separate report.

2.2 Forecasting Methods

Forecasting is a method used for translating precedent experience into estimates of the future. A comprehensive definition describes that forecasting is the prediction of values of a variable based on known past values of that variable or other related variables, expert judgments, which in turn based on historical data and experience (Makridakis, Wheelwright, & McGee, Forecasting: Methods and Applications, 1983).

There are several methods in forecasting, which can be categorized into:

1. Qualitative Approaches
   1. Delphi method
   2. Market research
   3. Product life-cycle analogy
   4. Expert judgments by management
2. Quantitative Approaches
   1. Causal Methods
   2. Time-series Methods

For this project we come up with (1) Moving Average; (2) Single Exponential and Double Exponential; and (3) Lagged Regression, which are parts of Time-series and Causal methods in quantitative system.

3 Why

3.1 Bill of Material

Most organizations either make to stock, so that all planning is based on forecasts, or use customer orders in the short range and forecasts to fill out the remainder of the planning horizon. Some specific Bill of Material is needed to link the master schedule to its dependent components that have to be obtained prior to receiving the customer orders. Thus, planning bills perform this function and substantially reduce the number of items to be forecasted and master scheduled (Tersine, 1994).

3.2 Forecasting

Supply chain management decisions are based on forecasts that define which products will be required, what amount of these products will be called for, and when they will be needed. The demand forecast becomes the basis for companies to plan their internal operations and cooperate among each other to meet market demand. By forecasting, it can help the UWW to predict when the demand of, for instance papers will increase? How much papers are needed in a right time?

Achieving effective procurement is begun with an understanding of how much of what categories of products are being bought across the entire organization as well as by each operating unit. This refers to the consideration of how much of what kinds of products are bought from whom and at what prices (Hugos, 2003). Thus, the need of forecasting is important in these matters. The use of forecasting in this project is aimed to identify and predict the unit consumption (input) of UW-Whitewater students and enrollments in order to estimate the carbon footprint. Another purpose is to get better understanding of the usefulness of forecasting methods in supply chain management and business knowledge.

3.2.1 Moving Average Method.

Moving Average is also known as Weighted Moving Average. Some of its characteristics are (1) very simple method for time series forecasting, (2) before any forecast can be prepared, we must have as many historical observations as are needed for the moving average, (3) the greater number of observations included in the moving average, the greater smoothing effect on the forecast (Makridakis & Wheelwright, 1989). Moreover, there are two types of moving average can be applied: 1) the three-month and the five-month moving average. Which moving average would be more appropriate, the three-month or the five-month? In the next section, we will find the detail explanation for this.

Inherent in the collection of data taken over time is some form of random variation. There exist methods for reducing of canceling the effect due to random variation. An often-used technique in industry is ``smoothing''. This technique, when properly applied, reveals more clearly the underlying trend, seasonal and cyclic components. Equation 1 shows the formula of Moving Average, where the multiplier $(\frac{1}{n})$ is called the weight and they sum to 1.

$$\overline{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\biggl(\frac{1}{... ...(\frac{1}{n}\biggr)x_{2}+\ldots+\biggl(\frac{1}{n}\biggr)x_{n}$$ (1)

The major strength of Moving Average is that this method is well suited to situations for products with fairly stable purchasing data. Unfortunately, it does have some of drawbacks; such as the requirement of a large amount of historical data and it assign equal weight to each period.

3.2.2 Exponential.

Exponential smoothing methods overcome both of drawbacks of Moving Average models. This is a very popular scheme to produce a smoothed Time Series. Whereas in Single Moving Averages the past observations are weighted equally, Exponential Smoothing assigns exponentially decreasing weights as the observation get older. In the case of moving averages, the weights assigned to the observations are the same and are equal to 1/N. In exponential smoothing, however, there are one or more smoothing parameters to be determined (or estimated) and these choices determine the weights assigned to the observations.

The basic premise of exponential smoothing is that the data values for more recent periods have more impact on the forecast and therefore should be given more weight. The goal is to distinguish between the random fluctuations and the basic underlying pattern by ``smoothing'' the historical values. The selection of the technique depends on the forecaster. If it is desired to portray the growth process in a more aggressive manner, then one selects double smoothing.

Single Exponential Smoothing

The smoothing scheme begins by setting S₂ to y₁, where ... stands for smoothed observation, and y stands for the original observation. The subscripts refer to the time periods, 1, 2, ..., n. For the third period: S₃ = αy₂ + (1 - α)S₂; and so on. There is no S₁; the smoothed series starts with the smoothed version of the second observation. For any time period t, the smoothed value S_t is found by computing:

$$S_{t}=\alpha y_{t-1}+(1-\alpha)S_{t-1}\quad0<\alpha\leq1\quad t\geq3$$ (2)

This is the basic equation of single exponential smoothing and the constant or parameter α, is called the smoothing constant. The speed at which the older responses are dampened (smoothed) is a function of the value of α. When α is close to 1, dampening is quick and when α is close to 0, dampening is slow. The lower α is the smoother result. We use trial-and-error method to select the α value from 0.1 to 0.9. The LGR LGRa value was selected based on the lowest MSE value. In the case, we take an α value of 0.65.

Double Exponential Smoothing

Single Smoothing does not excel in following the data when there is a trend. This situation can be improved by the introduction of a second equation with a second constant, γ, which must be chosen in conjunction with α. Here are the two equations associated with Double Exponential Smoothing:

$$S_{t}=\alpha y_{t}+(1-\alpha)(S_{t-1}+b_{t-1}\quad0\leq\alpha\leq1$$ (3)

$$b_{t}=\gamma(S_{t}-S_{t-1})+(1-\gamma)b_{t-1}\quad0\leq\gamma\leq1$$ (4)

Initial values

As in the case for single smoothing, there are a variety of schemes to set initial values for S_t and b_t in double smoothing. S_t is in general set to y₁. The b₁ is calculating by the following technique:

$$b_{1}=[(y_{2}-y_{1})+(y_{3}-y_{2})+(y_{4}-y_{3})]/3$$ (5)

The first smoothing equation adjusts S_t directly for the trend of the previous period, b_t-1, by adding it to the last smoothed value, S_t-1. This helps to eliminate the lag and brings S_t to the appropriate base of the current value. The second smoothing equation then updates the trend, which is expressed as the difference between the last two values. The equation is similar to the basic form of single smoothing, but here applied to the updating of the trend. We have also used trial-and-error method to determine the α and γ values. The one-period-ahead forecast is given by:

$$F_{t+1}=S_{t}+b_{t}$$ (6)

3.2.3 Simple and Lagged Regression.

Simple regression is a statistical technique for measuring the relationship between a dependent variable and one independent variable (Kress, 1985). In this method, only a straight line (linear) is used as a regression line in describing the shape of the average relationship between two variables. The straight line can be expressed by the linear equation:

$$Y_{e}=a+bX$$ (7)

The best way to obtain the linear equation from a series of data is to use the method of least squares regression analysis. The equation derived by this method will have a regression line, which will give the best fit to the data (observed data). The least squares method for calculating the a and b values can be drawn as follows:

$$a=\frac{{\displaystyle \sum X^{2}\cdot\sum Y-\sum X\cdot\sum(XY)}}{{\displaystyle n\sum X^{2}-(\sum X)^{2}}}$$ (8)

$$b=\frac{{\displaystyle n\sum(XY)-\sum X\cdot\sum Y}}{{\displaystyle n\sum X^{2}-(\sum X)^{2}}}$$ (9)

The strengths of simple regression method are that it is available in most software and inexpensive. Moreover, it provides accurate short and medium-term forecasts, as well as statistical test and confidence interval. In spite of these, some of drawbacks may be found such as the accuracy depends on a consistent relationship between independent and dependent variables, and also user needs to understand all the tests of significance to prevent an inappropriate model from being used (Makridakis & Wheelwright, 1989). We do not encourage do the lagged regression forecasting manually, unless one rests on a certain software to support in calculating. Please go to the illustration of Lagged Regression in Greening Whitewater Forecasting Demand to see the detail processes of its calculation.

4 How

4.1 Sampling

In this project, we applied the convenience sampling method to select the respondents. This technique is the simplest one that involves selecting sample elements that are most readily available to participate in the study and who can provide the information required (Hair, et al, 2003). The sample of this project consists of 5 categories:

1. Student. Students are the largest population in UW-Whitewater. We argue that the number of population of this category has the largest impact on the carbon footprint or other outputs. For major reasons, we divided this category into two different groups: a) local student, and b) commuter student.
2. Faculty members. The major reason of taking faculty members as the sample is because they have authority to purchase the office supplies. The same reason goes for department and administrative office.
3. Staffs. The second largest population in the building is the staffs. We also argue that their consumptions have a significant contribution on produced output.
4. Department employees. As mentioned above, this category has the authority to order particular necessities of department such as paper, toner, and cartridge. Therefore, we argue that this category can be taken as source of required data.
5. Administrative Office. The administrative office plays an important role in ordering office supplies and other utensils.

The aim of this categorization is to obtain the simplest illustration in determining which category has the largest impact on the output. Please note that for time efficiency reason, we did not consider UW-Whitewater visitors and any other parties who only stop by to UW-Whitewater by chance.

4.2 Data Aggregation Level

Data aggregation level is constituted on semester basis. The using of this approach is aimed as we suspect that there may be difference between the spring and autumn semester in term of number of students.

4.3 Bill of Material

We applied the concept of the traditional Bill of Material to trace the output structure down.

Figure 1: Breakdown of output structure

Figure 1 illustrates how we break the output down. Suppose one building, in our figure is depicted by Carlson building, may have population category of consumers such as students, departments, staffs, administrative officers, and faculty enrollments. Obviously, each category is the main contributor of outputs. In Carlson building, a local student for instance, consumes A, B, and C products. Here, we call A, B, and C as the mother products. Subsequently, each product will be broken down into pieces of compositions of α, β, γ, and δ. The information we generate in this stage will facilitate the MRP system to determine the carbon footprint generated by its mother product.

4.4 Assumptions

We realize that there must be some limitations of using above approaches. Therefore, we rest on the following assumptions:

• Each individual has the same pattern of consumption within her/his category. On other words, one local student consumption pattern represents others' consumption pattern in local student category. The same assumption goes to other categories.
• One semester consist of 4 months or 4 × 4 weeks or 4 × 4 × 5 workdays. Please note that for campus works, we do not consider Saturday and Sunday.

4.5 Data Collecting

We used questionnaire in collecting primary data from the students. This tool was designed to find out what are the students' daily consumptions in terms of food and beverage packages, papers, transportation, and other related stuffs, which they used and consumed in the particular building. In our research, we focus on Carlson building only. It is also helpful on identifying the difference of commuter and local students' consumption pattern. For this purposes, we involved 38 students as the respondents, which are composed of 12 commuter and 26 local students. We asked the students to trace their consumption on a daily basis during 1 week.

By assuming that if a student's 1-week consumption is repetitive pattern and 1 semester has 16 weeks (4 weeks multiply by 4 months), subsequently we can calculate his or her consumption on semester basis. It is acquired by applying this following formula:

$$C_{i,s}=C_{i,w}\times16$$ (10)

Equation (10), C denotes student consumption on item ``i'', while ``s'' is for semester and ``w is for weekly basis. For instance, suppose that averagely a student consumes 12 sheets in a week (C_i,w). We can compute that she or he consumes 192 sheets in 1 semester (12 sheets × 16 = 192 sheets). Moreover, the similar method goes for other items.

Meanwhile, we also interviewed staffs and faculty members, consumption data from department and administrative office were acquired by investigating the purchase files. These secondary data provide purchasing records of each office, which helped us in determining the consumption of office supplies. The good thing from this secondary data is that they have a very good record on each item purchased in the monthly and semester basis. Equation (11) demonstrates the formula we used to computing the consumption of enrollments.

$$C_{i,s}=C_{i,m}\times4$$ (11)

The enrollment consumption on item ``i'' is denoted by C, while ``s'' is for semester and ``m'' is for monthly basis. For instance, suppose that averagely an enrollment purchases 2 reams of copy papers in a month (C_i,m). We can compute that she or he purchases 8 reams in 1 semester (2 reams × 4 = 8 reams), this method similarly goes for other items.

Figure 2: The illustration of local student's Food and Beverage consumption output breakdown

Figure 2 exemplifies the breakdown of local student's consumption output on food and beverage (B&F). On the specific words, a local student for instance, consumes foods and beverages, which then they will be broken down into pieces of compositions of paper box, can, plastic bottle, and plastic bag. The information we generate in this phase will aid the MRP system to determine the carbon footprint generated by paper box, can, plastic bottle, and plastic bag. Please visit the Bill of Material link for its detail computations.

Suppose in one semester, one person has the number of generated output for item ``i'' as , thus, we can calculate the total number of each category's generated output ($\Pi_{i}$) by multiplying the number of generated output ($\varphi_{i}$) per semester by the number of population within each category (n). Equation (12) shows the formula for computing the total number of each category's generated output.

$$\Pi_{i}=\varphi_{i}\times n$$ (12)

For example, in average, a local student consumes 112 plastic bottle of soda (item ``i'') per semester and we have 3,000 local students in Carlson, subsequently this category will have 3,000 × 112 = 336,000 plastic bottles output within one semester.

4.6 Forecasting

4.6.1 Moving Average and Exponential

We provide the illustration of forecasting methods implementation for this project. Please refer to the Greening Whitewater Forecasting Demand link to see the calculation approaches were used. For overall of Moving Average and Exponential, the accuracy of the forecasting methods indicates a good or bad estimation. The accuracy will depend on the error. The thumb of rules for these indications of error explain that the smaller value of error, the better result of forecasting.

Figure 3: The comparison of paper consumption per commuter student based on 3-Semester and 5-Semester Moving Average Forecasting

Figure 3 shows the illustration of paper consumption forecast per commuter student on 3-semester basis compared to the 5-semester moving average. If compare the error of using 3-semester that gives us total error of 5 and mean of error = 1, and 5-semester moving average forecasting method that provides total error of -1.4 and mean of error = -0.175, thus, we can conclude that the 5-semester moving average forecasting method shows the more accuracy result than the 3-semester basis. Therefore, we recommend that this project should apply the 5-semester moving average forecasting for further research.

The major strength of Moving Average is that this method is well suited to situations for products with fairly stable observed data such as monthly purchasing or monthly consumptions. Consequently, it requires a large amount of historical data.

Figure 4: The comparison of paper consumption per commuter student based on Single and Double Exponential Forecasting Methods

The similar approach goes to both single and double exponential forecasting methods. Figure 4 shows the implication of using single and double exponential for predicting commuter student's paper consumption based on semester data observation. Single exponential gives us 52 total error, while the double exponential the lower number of error -94. If we go back to the thumb of rules that rest on the deviation between observed data and forecast data we got (or error), we can say that error in using Single Exponential is larger than what we have in Double Exponential. Other words, the better result is shown by Double Exponential forecasting. For this reason, we subsequently recommend to use Double Exponential forecasting in for further research.

The exponential method is used to overcome some of drawbacks in Moving Average systems. Accordingly, the more benefits and advantages can be obtained by using exponential than the moving overage in term of implementation and data availability.

4.6.2 Simple Regression

The basic premise of a causal model like Simple Regression is that changes in the value of a certain variable (number of student, for instance) are closely associated with changes in the other one variable (in our case it is number of paper consumption).

Figure 5: The computation of paper consumption forecast based on Semester Basis Using Simple Regression Method

Figure 5 illustrates how we can obtain a (a = 121.8) and b (b = 1.8) in order to develop regression model for paper consumption forecast. Given a and b, we can predict how much paper had been consumed per semester (Forecast or Y_e) if the number of students (X) changes. Please refer to the Greening Whitewater Forecasting Demand link to see the relevant and comprehensive computations of this technique.

5 Conclusions

This report deserves comments due to its limitations. Prior to conduct the sampling process, it is essential to define how we determine the sample size. Roscoe (Sekaran, 2003) proposes the following rules of thumb for determining sample size:

1. Sample sizes larger than 30 and less than 500 are appropriate for most research.
2. Where samples are to be broken into subsample; (males/females, juniors/seniors, etc.), a minimum sample size of 30 for each category is necessary.
3. In multivariate research (including multivariate regression analyses), the sample size should be several times (preferably 10 times or more) as large as the number of variables in the study.
4. For simple experimental research with tight experimental controls (matched pairs, etc.), successful research is possible with samples as small as 10 to 20 in size.

Based on above rules, the numbers of respondents in our research should be greater than 30 respondents for each category. However, the assumptions that we mentioned in the previous section are strong enough to prop up our findings. We also realize that the data collected are not properly consistent among the categories. For instance, food consumptions were not gathered from all categories. Another example is we counted the transportation miles used by the students, faculty, and staffs, but not in department and administrative office categories. Moreover, the major difficulty we faced during data collecting was the inconsistency of respondents in answering the questionnaires. Additionally, what we found regarding paper printing system in Carlson is that most students go to other buildings in where they can get free printing, as Carlson does not provide for this facility. Hence, data we have in this research might be significantly different compared to other buildings in UW-Whitewater. Furthermore, as the findings are done in autumn semester, the pattern of consumption might be different for different semester.

6 Recommendations for Further Research

Further research needs starting with open-ended questions regarding what items are consumed in campus and in which building. Hence, a more comprehensive research should be done. Another thing is the importance of using the same respondent in computing the time series forecasting also may help to increase the reliability of the research. One other recommendation also came up to our mind is the usability of UW-Whitewater's information system in providing required information such as how many papers are printed during one semester by one student. Tracking each time one student logs in into the UW-Whitewater system and prints is a way to implement this suggestion.

Bibliography

1. Hair, J. J., Babin, B., Money, A. H., & Samouel, P. (2003). Essentials of Business Research Methods. John Wiley & Sons, Inc.
2. Hugos, M. (2003). Essentials of Supply Chain Management. John Wiley & Sons, Inc.
3. Kress, G. (1985). Practical Techniques of Business Forecasting: Fundamentals and Applications for Marketing, Production, and Financial Managers. Quorum Books - Greenwood Press.
4. Makridakis, S., & Wheelwright, S. C. (1989). Forecasting Methods for Management (5 ed.). John Wiley & Sons.
5. Makridakis, S., Wheelwright, S. C., & McGee, V. E. (1983). Forecasting: Methods and Applications (2 ed.). John Wiley & Sons, Inc.
6. Sekaran, U. (2003). Research Methods for Business: A Skill-building Approach. New York: John-Wiley & Sons, Inc.
7. Tersine, R. J. (1994). Principles of Inventory and Materials Management (4 ed.). PTR Prentice-Hall, Inc.

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