DEVELOPMENT OF A DEMAND FORECASTING MODEL FOR A SUMMER FOOD SERVICE PROGRAM SPONSORED BY THE UNITED STATES DEPARTMENT OF AGRICULTURE

Transcription

1 DEVELOPMENT OF A DEMAND FORECASTING MODEL FOR A SUMMER FOOD SERVICE PROGRAM SPONSORED BY THE UNITED STATES DEPARTMENT OF AGRICULTURE by MICHELLE MIN-HSUEH LIN, B.S. A THESIS IN RESTAURANT, HOTEL, AND INSTITUTIONAL MANAGEMENT Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE Approved December,

2 S ^^/'' "f^^^ J Z, ^.- ACKNOWLEDGEMENTS ' / ' ^ C&:}-^- This thesis is the result of a collaborative effort. Although I labored very diligently to complete this research, I readily concede this undertaking would not have been possible without the advice and help I received from others. It is these individuals, whose support and assistance was so generously given, that I acknowledge and to whom I give thanks. Dr. Linda C. Hoover has been tremendously helpful in the professional advice and support she has so freely given to me, and I express thanks to Dr. Julia T. Poynter for her valuable assistance, also. I sincerely appreciate the kind support I received as well from Dr. Ronald H. Bremer, whose advice in helping me with data analysis was indispensable. For her gracious assistance in giving me access to the Summer Food Service Program data I used in this study, I convey my sincere gratitude to Debora Phillips. With their limitless love and support, my family in Taiwan also helped me to complete my Master's degree. I take special pride in dedicating this thesis to my late father, whose encouragement motivated me to achieve my goal.

3 TABLE OF CONTENTS ACKNOWLEDGEMENTS LIST OF TABLES LIST OF FIGURES ii vi vii CHAPTER I. INTRODUCTION Background Statement of the Problem Purpose of the Study Research Questions Definitions Research Assumptions Research Limitations Contribution of Proposed Study II. REVIEW OF LITERATURE Forecasting in Food Service Operations... Commercial Operations Non-commercial Operations Importance of Forecasting: The Impact on Food Production Management Controlling Labor Costs Controlling Food Costs Maximizing Customer Satisfaction... Elements of Food Service Forecasting... Historical Records Pattern of Demand Forecasting Time Periods Demand Forecasting Models Types of Forecast Methods iii

4 Criteria for Forecasting Models... Measuring the Accuracy of Forecast Models III. METHODOLOGY Pilot Study Sites Data Collection Treatment of Data Data Analysis Phase I--Selection of an Appropriate Forecast Model Phase II--Evaluation of Menu and Daily Indices on the Accuracy of a Forecast Model IV. RESULTS AND DISCUSSION Pattern of Time Plots Accuracy of Forecast Models The Most Appropriate Forecast Method... Alpha Analysis Daily Index Menu Index Recommendation to SFSP in West Texas... Comparison of Results V. CONCLUSIONS Major Findings of the Study Impact of the Study Limitation of the Results Recommendations for Further Research... Summary IV

5 REFERENCES APPENDICES A. SUMMER FOOD SERVICE PROGRAM FOOD PRODUCTION RECORD B. DATA ANALYSIS SPREADSHEET C. ESTIMATED NUMBER OF MEALS FOR PREPARATION.. D. SELECTED COLUMNS OF RAW DATA AND TIME PLOTS. V

6 LIST OF TABLES. Ranking values of forecast methods based on objective and subjective analysis for pattern of time plot.. Example for one site: Ranking values for accuracy of forecast methods based on MAD, MAPE, and RMSE.. Example for one site: Selection of an appropriate forecast method based on pattern, accuracy, and simplicity. Trend analysis of time plots for meals served at SFSP sties. Seasonality analysis of time plots for meals served at SFSP sites. Analysis of RMSE by forecast method for meals served at SFSP sites. Analysis of MAD by forecast method for meals served at SFSP sites. Analysis of MAPE by forecast method for meals served at SFSP sites. Comparison of mean ranking score for appropriateness of the forecast methods for breakfast and lunch. Comparison of mean alpha for different patterns of time plot for breakfast and lunch. Forecast error measures with adjustment of daily index for breakfast. Forecast error measures with adjustment of daily index for lunch. Breakfast menu index analysis for selected sites of SFSP. Lunch menu index analysis for selected sites of SFSP VI

7 LIST OF FIGURES. Final selection of forecast method for breakfast.. Final selection of forecast method for lunch.... Alpha distribution for simple exponential smoothing method. Menu index analysis of breakfast. Menu index analysis of lunch Vll

8 CHAPTER I INTRODUCTION Background In the very competitive and dynamic environment that most businesses face, forecasting is a beneficial tool and an indispensable strategy for business survival. Success in analyzing and forecasting customer demand for a given good or service can mean the difference between profit or loss for an accounting period and, ultimately, the success or failure of the business itself. Chandler and Trone () noted that forecasting is the starting point for all budgeting. Forecasting also is used to predict daily sales, utilizing past data which is adjusted for factors such as management judgement, economic considerations, and current trends. The main purpose of forecasting is to predict future events that could potentially affect the success of an operation. All facets of management rely on the estimates and predictions developed through forecasting. Therefore, the primary focus of forecasting is to determine customer demand for an organization's goods or services (Webster, ). Forecasting in the food service industry is invaluable to various aspects of operations. The food service manager needs to forecast sales in order to plan staff schedules and

9 make food and supply purchases. Over-forecasting means that the demand is less than the forecast, which results in wasted resources. On the other hand, under-forecasting will result in employee stress and customer dissatisfaction. Thus an accurate forecast is the goal of a food service manager who strives to achieve a successful business (Messersmith & Miller, ). Food service operations can be classified as either a commercial or non-commercial. They also can be classified as either for-profit or non-profit. Regardless of the nature of the food service operation, all food service managers operate within fairly clear financial limits. Therefore, any technique that can help to improve operational efficiency by getting a more accurate picture of demand and by limiting waste would be extremely helpful. Many federal funded food programs are non-commercial/ non-profit operations. Cost control is extremely important in this type of operation. The Summer Food Service Program (SFSP), a Child Nutrition Program funded by the United States Department of Agriculture (USDA), is such a program. The purpose of the SFSP is to provide children with nutritious food during the summer when school is not in session. As a federally funded program, with limited funding and non-profit attributes, SFSP has a critical need for forecasting.

10 In Texas, the SFSP is administered by the Texas Department of Human Services (TDHS) Special Nutrition Program (SNP). There were agencies involved in operating the SFSP in Texas in. Although more than % of the. million Texas school children qualified to receive benefit from this Child Nutrition Program, only about.% of those children actually received summer meals. The SFSP provided. million meals to children in (Summer Food Service Program: Orientation & Organizing Guide, ). The successful operation of the SFSP will bring more opportunities for children to receive nutritional meals in the summer time. Children's Enterprises Incorporated (CEI), a private non-profit organization, currently operates the SFSP throughout a vast geographic area in west Texas. CEI has operated to cafeterias in low-income areas in this area each summer since. Through this program, free breakfast and lunch meals are provided daily for children years old and younger. Children and youth are not charged for meals and do not complete any paperwork. They may receive second servings, if they desire. The menu is standardized in an eleven-day cycle, but substitutions occur to provide for better inventory usage. The breakfast menu must include a serving of milk, fruit, and bread or cereal. The lunch menu must include a serving of meat, bread, two

11 fruits and/or vegetables, and milk (Summer Food Service Program Handbook, ). The locations of the CEI cafeterias are usually in schools, but they also may be located at local youth agencies or churches. CEI employs cafeteria workers from local schools to operate the meal service. This provides employment opportunities for school personnel during summer months and benefits CEI's SFSP by utilizing experienced employees and established kitchen facilities. The service period for the SFSP is usually from the week after the regular school year ends until two weeks to one month prior to the beginning of the regular school year. Most sites operate for six to twelve weeks during the summer (Summer Food Service Program: Orientation & Organizing Guide, ). Food inventory must be consumed by the end of the summer for three reasons. One reason is the distance involved in travelling from sites to the administrative office, which can be up to miles. A second reason for eliminating the inventory is that the administrative office has limited space to store these supplies. Finally, because of the short shelf life and spoilage of some of the items, they would not be usable for the following year's program (Phillips, personal communication, October, ). The SFSP is an example of a food service operation that could benefit greatly from forecasting techniques. The

12 administrator and staff of CEI have expressed a need for a more precise forecasting method but no literature was found to assist in choosing a forecast method for SFSP. Plans for staffing and purchasing have been made by the "best guess" method. Each year program plans are made based on the number of children that were served during the previous year. When a new cafeteria is opened, the forecast is made based on past experience with other communities of similar size. No mathematical methods have been applied to this operation. The initial supplies and groceries for each site are purchased by the Lubbock administrative staff at the beginning of the summer. Later, food service managers from each cafeteria prepare weekly grocery orders based on their judgement and previous experience and submit the orders to the administrative office. This procedure lacks any scientific basis. These orders may be modified by the administrative staff, again, based on judgement and previous experience and not mathematical methods. Current operations do not incorporate a forecasting method because of the following reasons: () the staff at each cafeteria site lack forecasting skills, () the program does not have a forecasting system available for the staff at each site to follow, () the program runs in a very short time span, and training time is limited, and () since employees may change from one summer to the other, the

13 program is not willing to train the staff in how to use a complex forecasting technique. It is not practical for the administrative staff in Lubbock to calculate daily forecasts since this would require at least two long distance calls per site each day. Statement of the Problem The SFSP in west Texas, utilizing the "best guest" forecast method, has confronted major operational problems and has a great need to implement a forecasting technique to solve this problem. Therefore, finding an accurate and efficient forecasting method is very important for this operation. Purpose of the Study The purpose of this study was to explore the application of appropriate forecasting methods to an existing food service operation. This study compared different models of forecasting and selected an appropriate forecasting method based on three criteria: the pattern of demand, the accuracy, and the simplicity of the model. The specific objectives of this study were to:. screen patterns of time plots of each site to determine if there was a trend or seasonality in the past data.

14 . compare the accuracy of various forecast models for both individuals and aggregate data,. analyze the procedures required for each forecast model being tested and rate its simplicity,. recommend the best forecast model for the SFSP based on pattern, accuracy, and simplicity, and. determine if the menu item or the day of the week affects demand, and. create a worksheet which allows food service operations to apply the forecast method recommended as a result of the study. The forecasting method selected must be a simple one that does not rely on computer resources or extensive training, in order to keep the cost of training and hardware investment minimal. As a result of this study, CEI will have the ability to plan, purchase, and staff more efficiently. Research Ouestions The research questions to be addressed by this study were:. What is the menu preference of the SFSP in the past three years?. What is the demand trend along the operational period?

15 . What is the most accurate forecast model for each CEI cafeteria site for breakfast and lunch?. What is the most accurate forecast method for the aggregate data of the combined cafeteria settings?. Based on the calculation procedure required for each testing forecast models, what is the simplest forecast method?. Based on findings from questions,,, and, what is the best method for demand forecasting to achieve more efficient and effective planning of staffing and purchasing for the SFSP in west Texas?. Does the menu item and demand trend affect the accuracy of forecasting? Definitions "Best Guess" Method--The current forecast method used by the staff of the SFSP operated by CEI's is based on no mathematical forecasting method. The estimation of forecasting is based on the forecaster's previous experience and intuition (Phillips, personal communication, October, ). Daily Index--Daily index is the ratio of the total servings from one weekday (for example, Monday) to the total servings from the whole week (Wheelwright & Makridakis, ).

16 Demand--The desire to purchase a good or service (Nisberg, ). The demand mentioned in this study is the actual serving count for each meal of the SFSP. Demand Trend--Demand trend identifies the gradual increase or decrease in demand (Wheelwright & Makridakis, ). Forecasting--Spears () explained forecasting as the art and science of estimating future events by combining intuitive interpretation of data with the use of mathematical models. The primary purpose of this study is to predict the meal service count for each meal of the SFSP operated by CEI in west Texas. Forecast Model--The forecast model is the technique that either utilizes a mathematical or non-mathematical methods to estimate the forecast (Chase & Aquilano, ). Mathematical Forecasting--A quantitative forecasting technique that requires a certain formula to calculate the forecast demand (Wheelwright & Makridakis, ). Menu Preference Index--This index is the proportion or percentage of servings of one menu item to the total servings (Messersmith & Miller, ). Over-forecasting--The estimation of forecasting is higher than the actual demand (Messersmith & Miller, ). Pattern of Demand--The pattern of demand is the trend, cycle, or seasonality appeared on the time plot (Chase & Aquilano, ).

17 Scatter Plot--A scatter plot displays a statistical relationship between two metric-variables (Cryer & Miller, ). Seasonality--A pattern of demand occurs routinely in certain intervals of time (Wheelwright & Makridakis, ). Time Series--A time series is a series of measurements taken at successive points in time (Iman & Conover, ). Time Plot--A time plot is a plot of the time series values versus time with successive points connected (Bremer, personal communication, June, ). Under-forecasting--The forecasting is under estimated which leads to running out of food items for the meal service (Messersmith & Miller, ). Research Assumptions The assumptions for this research were:. The economic base of the community do not affect the demand patterns.. The population in the city where each site is located will stay the same in the long term.. One site in the program has the same attributes as another in considering demand patterns.. The demand for July th would be the same forecast value as calculated by using simple exponential smoothing method. July th is excluded as a workday because it is a national holiday.

18 Research Limitations The ability to generalize the results of this study was limited by the following constraints:. This research analyzed only one contractor of the SFSP in the state of Texas.. The sites under study were suburban and rural locations. Since urban sites were not included, the results might not be applicable to these environments. Contribution of Proposed Study The food service industry is currently undergoing tremendous change as the cost of operations continues to rapidly climb for both non-commercial and commercial operations. Because of the strong pressure on operating margins and the need to control expenses and stay within budgets, forecasting can be a tremendous benefit to both large and small food service operations. Despite the strong need for forecasting in food service, the application of forecasting models is quite limited. Forecasting is critical for the SFSP due to its limited funding and short time span. This study identified a simple but realistic demand forecast model for the SFSP, that may well be applicable for other short time frame food service operations.

19 CHAPTER II REVIEW OF LITERATURE Forecasting in Food Service Operations Commercial Operations Restaurants Forecasting demand for goods and services is critical for effective and efficient restaurant operations. Accurate forecasting results in effective cost control which assists profitability in restaurant operations. Despite the benefits of using a forecasting method, recent research (Repko & Miller, ) has revealed that few food service operations use forecasting. Restaurant operators, however, report a need for improvement in both training and application of forecasting methods (Repko & Miller, ). The review of literature revealed that food service managers do not use forecasting techniques because they do not fully understand how to use them. Airline Food Service Forecasting of airline meals is based on the number of passengers. Pedrick, Babakus, and Richardson's () study found that airline customers comment that the number of in flight airline meals is generally underestimated. Because of the time constraints in estimating an accurate count of passengers, forecasting the number of meals needed on a

20 flight is difficult. Also, considerations of meal variety and special meal requirements add to the difficulty of forecasting. Non-commercial Operations Health Care Facilities Food Service In the past, health care operators did not pay adequate attention to forecasting primarily because they did not have a strong economic incentive to do so. Costs associated with inadequate forecasting were passed on to their customers. However Reyna, Kwong, and Li () stated that under a third-party reimbursement system, payments are based on amounts set by the government for each service. This change in the payment method, plus rising costs and increasing competition, have made hospital operations more budget conscious. Health care managers are now looking for ways to cut costs. Therefore, forecasting has become an essential part of health care food service management. College and University Food Service Forecasting is especially important in college and university food service operations which are usually nonprofit. Repko and Miller () conducted a survey in to assess the need for current application of forecasting in college and university food service operations. The study revealed that % of the respondents valued forecasting as

21 very important. Respondents also indicated a need for improvement in training and application in the area of forecasting. A similar study was conducted by Miller and Shanklin (b). In their research, educators responded that forecasting was an important tool for managers of food service operations and that continuing training was necessary in this area. Child Nutrition Programs The Summer Food Service Program (SFSP), funded by the United States Department of Agriculture (USDA), was created by Public Law - in. This law was amended in under Public Law -. The purpose of the SFSP is to provide children with a nutritious meal during the summer months when they are out of school and would not normally receive the free or reduced price meals. The program was initially called the Special Food Service Programs for Children. SFSP operations throughout the country are usually operated by school districts, city parks and recreation departments, or other non-profit organizations. Many sites offer summer school, workshops or field trips for children. For example, in, Columbia, Missouri, offered a summer program for children that included crafts, health and nutrition education, swimming, sports activities, and field trips in addition to the SFSP. The summer program provided

22 physical activities as well as nutritional meals for children during the summer (Gibson, ; Ott, ; Summer Feeding, ). The regulations for SFSP has become more and more restricted. The regulations in ("Summer Food Service Program", ) state that only lower income neighborhoods may participate in the SFSP or participants must qualify for a minimum income level. Current law defines the low income area as an area in which one-half or more of the children are from families with income at or below % of poverty. This regulation was implemented to prevent program abuses, but also has resulted in fewer sites qualifying for the program. Increasing restrictions to operate a SFSP means that the forecasting is critical for the success of operating the SFSP (Summer Food Program Restricted, ). Importance of Forecasting: The Impact on Food Production Management Controlling Labor Costs Accurate forecasting of customer demands is critical for realizing effective labor cost control. Pavesic () and Wacker () indicated that accurate forecasting is one of the prerequisites for labor cost control. Managers schedule labor according to forecasts. Thus, accurate forecasts can result in cost effective scheduling.

23 Controlling Food Costs Over estimating demand (over-forecasting) leads to overproduction and results in extra costs. Messersmith and Miller () stated that the problem with over-forecasting is the cost of unused prepared food which includes labor associated with handling, such as wrapping, storing, recording, and replanning. Rehandling and discarding menu items are also hidden costs of over-forecasting. Maximizing Customer Satisfaction Under-forecasting leads to under production. This can result in customer dissatisfaction if they do not receive their menu choices. The cost of under-forecasting may be minor, but the cost of losing customers is significant. Underproduction also can cause high stress for cooks, service employees, and managers (Messersmith & Miller, ). Elements of Food Service Forecasting Historical Records Historical records are the most important element in forecasting. As stated previously, forecasting is the prediction of a future event based on past data. Therefore, complete data and information are required in order to forecast effectively. Spears () indicated that reliable forecasting depends on accurate and complete

24 records. The better the data available to a forecaster, the more accurate the forecast will be. Therefore, it is the responsibility of the forecaster to get as much historical data and current information as possible before making a forecast. Pattern of Demand The main task in forecasting is to analyze past data to predict a future event. The forecaster must consider the pattern of past data when making projections. The easiest way to produce a forecast is to compute the average past demand and use it to estimate the future demand. The pattern of demand includes random variation, trend lines, seasonal influence, and cyclical elements (Chase & Aquilano, ). Random Variation Effective forecasting assumes a regular predictable pattern of demand can be accurately determined. When random variations occur, mostly caused by chance events, the predictive power of forecasting is greatly weakened. Forecasters are challenged by this type of demand. Random events that can disrupt forecasting include strikes, earthquakes, wars, and changes in weather (Jarrett, ). Having a complete data record is very important to making an effective forecast. Chandler and Trone () indicated

25 that having a complete data record the first months of operations is most crucial for small businesses. Trend Line According to Chase and Aquilano (), four types of trend line demand distributions are: linear trend, S-curve trend, asymptotic trend, and exponential trend. Demand distribution in a linear trend or horizontal pattern indicates a straight continuous relationship. Schonberger and Knod () stated that trend lines define a positive or negative shift in series value over a certain time period. A straight line demand distribution shows stable sales. Chase and Aquilano () noted that S-curve trends indicate the demand of the service through the stages of development, growth, and maturity. Asymptotic trends indicate the highest demand growth at the beginning of the service period and then taper off. Exponential trends indicate that the demand has explosive growth. Seasonal Influence Seasonal variation usually occurs within one year and recurs annually (Schonberger & Knod ). Wheelwright and Makridakis () indicated that seasons may be -month intervals, -day intervals, one-week intervals, or even - hour intervals. Seasonal patterns of demand are a good indicator for making long range forecasts.

26 Cyclical Elements Cyclical factors are very difficult to predict because the time span may be unknown or the cause of the cycle may not be considered (Chase & Aquilano, ). Examples of cyclical factors include political elections, war, economic conditions, or sociological pressures. Wheelwright and Makridakis () stated that a cyclical pattern of demand is similar to a seasonal pattern, but the length of a single cycle is generally longer than one year. Schonberger and Knod () explained that a cyclical pattern may be recurring and often spans several years. Forecasting Time Periods Forecasting involves two types of elements: model development and production demand. Most food service operations refuse to use quantitative forecast methods due to misunderstanding the time required in preparing a forecast or not knowing how to properly use the methods. Most quantitative forecast models require time, personnel, and equipment to calculate the output. Some regression forecast models require a specific period of time to initiate the model. Developing any forecasting system requires time and human effort. Repko and Miller's () study found that very few food service operators used mathematical models for forecasting demand. Their research revealed that judgment based on the past records was the

27 most frequently used forecasting method and that production demand was determined one week in advance. Their study implied that food service operators are limited to forecasting methods that are simple and fast. Long-term Forecasting A long-term forecast fits neatly into the corporate strategic planning process. Long-range forecasting generally predicts two to five years into the future. It is used in business planning for production, research, capital planning, plant location and expansion, and advertising decisions. This type of forecasting is generally broad in scope and often employs qualitative analysis (Dilworth, ). Intermediate-term Forecasting The time span for intermediate-term forecasting is generally in the range of one season to two years. It is most commonly used in aggregate planning such as in capital and cash budgets, sales planning, production planning, production and inventory budgeting. Intermediate-range forecasting usually uses numerical methods (Dilworth, ). Short-term Forecasting Short-term forecasting usually predicts future events for one season, one day, or one year. It is used for short-

28 term control, which includes adjustment of production and employment levels, purchasing, job scheduling, project assignment, and overtime decisions. Methods of short-term forecasting include trend extrapolation, graphicalprojection, personal judgement, and exponential smoothing (Dilworth, ). Demand Forecasting Models Types of Forecast Methods A forecast can range from simply using a "guesstimate" to complex mathematical methods. Two general categories of forecast methods are: () qualitative and () quantitative approaches. The qualitative approach, sometimes referred to as the subjective or judgmental method, is based on subjective assessments. Quantitative, objective, or mathematic methods include two subgroups of models, time series and causal models (Chase & Aquilano, ; Jarrett, ; Wheelwright & Makridakis, ). Oualitative or Subjective Forecasting Methods The major characteristic of the qualitative approach to forecasting is human judgment and intuition in an ad hoc manner. forecast. It is sometimes the simplest and fastest way to This method involves using only subjective judgement without expressing the forecast in numerical terms. Qualitative forecasting methods include the Delphi

29 technique, jury of executive opinion, field sales force, aggregate subjective forecasts, as well as other methods. Delphi Technique Adam and Ebert () stated that "The Delphi technique is a group process intended to achieve a consensus forecast, often a technological forecast" (p. ). Jarrett () explained that the Delphi method involves using the subjective opinion of experts to predict the future direction of economic sectors. This type of technique avoids direct interpersonal relations and has worked successfully as a method of technological forecasting. The Jury of Executive Opinion The jury of executive opinion approach is one of the simplest and most widely used forecasting methods (Wheelwright & Makridakis, ; Wilson & Daubek, ). Wheelwright and Makridakis () explained that the jury of executive opinion approach consists of corporate executives sitting around a table and deciding as a group what their best estimate is of future demand. The advantages of this type of method are that it provides a quick and easy forecast; it does not require complicated statistics; and it brings together a variety of specialized opinions. The drawback of this approach is that since estimators are in personal contact with another, the weight assigned to each

30 executive's assessment will depend in large part on the role and personality of that executive in the organization. Field Sales Force The field sales force technique requires each sales representative to estimate the sales within his or her territory. This method utilizes input from persons in direct contact with the customer and the field sales force. This method is most suited for a new product. The advantage of this approach is that it uses the specialized knowledge of those closest to the marketplace. The down side for this method is that it involves individual biases. Often salespeople are poor estimators and are either overly optimistic or overly pessimistic (Dilworth, ). Aggregate Subjective Forecasts The aggregate subjective forecast method is the easiest and fastest way to estimate demand forecasting. Research has found that aggregate subjective forecasts are more accurate than the individual forecast (Ashton & Ashton, ; Makridakis & Winkler, ). Also, weighing individual forecasts differentially produces better aggregate forecasts. Armstrong () stated that expert opinion is useful in estimating current status; combining forecasts from extrapolation and judgment methods has been shown to be highly effective.

31 Other Subjective Methods Other subjective methods include nominal group technique, expert opinions, panel consensus, visionary forecast, and historical analysis. Basically, these subjective methods are based on a person or a group's intuition in making predictions rather than the scientific calculation of future events (Adam & Ebert, ; Armstrong, ; Makridakis, ; Webster, ). Ouantitative or Objective Forecasting Methods Mathematical forecasting techniques may be effective in food service operations to control costs, increase productivity, and maximize profits (Miller, Thompson, & Orabella, ). Quantitative forecast methods generally divide into two types: the time series model and the causal model. Time Series Models Time series models assume that patterns reoccur over time (Wheelwright & Makridakis, ). Examples of time series models include naive, simple average, simple moving average, weighted moving average, seasonal index, and exponential smoothing techniques. Studies have found that very few food service operations utilize quantitative methods in doing forecasting (Miller, McCahon, & Bloss,

32 ; Miller & Shanklin, a; Repko & Miller, ; Reyna, Kwong, & Li, ). The Naive method uses the most recent information available as the actual forecast value. For example, if a forecast is being prepared for a time horizon of one period, the most recent actual value would be used as the forecast for the next period. The formula for a Naive forecast is simply: F = D Ft+i = The forecast for period t + i, t = Present period, i = The number of periods ahead being forecast, Dt = The latest actual value. The Naive model assumes that there is no pattern in the data series to be forecast (Wheelwright & Makridakis, ). Miller, McCahon, and Miller's () study illustrated that the Naive model was the least accurate model when applied to food service forecasting. However, some studies have indicated that the Naive model based on the judgment of past data, most recent demand, and intuitive estimate is utilized by the majority of the food service operators (Miller & Shanklin, a; Repko & Miller, ). The other type of Naive model considers the possibility of seasonality in the series (Wheelwright & Makridakis, ). This type of model uses the most recent seasonally adjusted value as a forecast for the next seasonally

33 adjusted value. The equation for the Naive with seasonality model of forecast is based on the following: ^j where Sj = the seasonal adjustment index for season j (or season j + i). Miller, McCahon, and Miller () utilized both the Naive and the Naive with seasonality models in their study and found that the Naive with seasonality model has a smaller error than the pure Naive model. Simple Average. The simple average method is the average of past data in which the demands of all previous periods are equally weighted (Adam & Ebert, ). The average demand may be a continuous average or seasonal average. The example of a continuous average is averaging past consecutive days demand to estimate future demand (Bails & Peppers, ). An example of a seasonal average is utilizing the past Monday's average to estimate the future demand (Messersmith & Miller, ). It is calculated as follows: Ft = (Di + D Dn) /n Di = the demand in the most recent period, D = the demand that occurred two periods ago, Dn = the demand that occurred n-periods ago.

34 Hanke and Reitsch () suggested that simple average method should be used when the data set has no trend, seasonality, or other systematic patterns. Simple Moving Average. A simple moving average combines the demand data from several of the most recent periods, their average being the forecast for the next period (Adam & Ebert, ). The simple moving average method generally takes to past values of a like day of the week to forecast the future demand. Each week, the oldest demand is dropped and the most recent is added (Messersmith & Miller, ). The formula for a simple moving average is simply: n ^ ^ where t=i is the oldest period, and t=n is the most recent period in the n-period average. Hanke and Reitsch () indicated that the simple moving average model handles trend and seasonality better than the simple average model. Chase and Aquilano () indicated that the simple moving average model is useful in removing the random fluctuations. They recommended the simple moving average model for short-term forecasting. Repko and Miller () found that the moving average is the most frequently used quantitative forecast method. Simple

35 moving average method is suggested for short-term forecasting (Miller, McCahon, & Miller, ). Weighted Moving Average. Unlike the simple moving average method that gives equal weight to each component of the moving average database, a weighted moving average allows a weighted constant to be assigned to each element, so that the sum of all weights equals one (Chase & Aquilano, ). This method allows the forecaster to adjust the effects of past data. Typically, higher weights are assigned to more recent periods (Schonberger & Knod, ). The equation for the weighted moving average is as following: n t Z> t^t where E'^t=i t=i where Ct = Weighted constant, and s C^ s.. Seasonal Index. Moving average methods estimate forecasting by smoothing the past data. The seasonal index method, however, takes the seasonal factor into consideration when calculating the forecast (Schonberger & Knod, ). Simple Exponential Smoothing. Exponential smoothing models are easy and often used in operations management (Adam & Ebert, ; Gardner & Dannenbring, ). Simple

36 exponential smoothing models average the past data by assigning a weighted constant (Gardner & Dannenbring, ). The weighted constant or smoothing coefficient, a, is between and. (Schonberger & Knod, ). The weighted scheme applies the greatest weight to the most recently observed values and lesser weights to the older values. The formula for the simple exponential smoothing is: Ft+i = adt + (l-a)ft An alternative way of writing this equation can be: Ft.i = Ft+ Q?(Dt-FJ. In this form, the new forecast equals the old forecast plus a. times the error (Dt - Ft) from the old forecast. If Of is close to, the new forecast will include a substantial adjustment for any error that occurred in the preceding forecast. Conversely, when a. is close to, the new forecast will not show much adjustment for a previous forecast error. Therefore, the effect of a large or small a. is important to the adjustment of the previous forecast error (Wheelwright & Makridakis, ). Wheelwright and Makridakis' () study showed that an of. yields better forecasts than larger values of a. Also, Schonberger and Knod () suggested that a. should be in the range of. to.. Their experiment showed that exponential smoothing is more accurate than the moving average method. Makridakis et al.'s () empirical studies demonstrated that exponential smoothing is quite

37 accurate compared with more complex forecasting methods such as the Box-Jenkins model. Adaptive Exponential Smoothing. In adaptive exponential smoothing, the smoothing coefficient, a, is not fixed but allowed to fluctuate over time based upon the pattern of demand changed (Adam & Ebert, ). The adaptive exponential smoothing model is most effective if it is computer assisted (Messersmith & Miller, ). A tracking signal is utilized to adjust the value of the a. It is used to indicate the existence of any positive or negative bias in the forecast. The cumulative forecast error is called the running sum of forecast error (RSFE). The tracking signal is then the RSFE divided by the mean absolute deviation (MAD) (Schonberger & Knod, ): RSFE Tracking signal = MAD. Double Exponential Smoothing (Brown's Exponential Smoothing). While single exponential smoothing of past data estimates the forecast, it does not take the trend factor into calculation. The double exponential smoothing was introduced by R. G. Brown. This method yields results which consider the trend observed values (Jarrett, ). Jarrett indicated that Brown's exponential smoothing is more accurate than either single exponential smoothing or moving average. The calculation for this type of method would be most effectively done with computer assistance.

38 Holt's Exponential Smoothing. Similar to Brown's exponential smoothing. Holt's exponential smoothing is not just an adjustment to trends but a two-parameter model. A growth factor is added to the smoothing equation (Jarrett, ). Bails and Peppers () stated that these two parameters must be quantified, although the trial and error process of finding the best combination of parameters may be costly and time-consuming. The formula of this model includes three equations (Hanke & Reitsch, ):. The Simple Exponential Smoothing formula: Ft,i= Q?Dt + (l-q?)ft.. The trend estimate: Tt.i=i(Ft.i- Ft) + (l-is)tt.. Forecast for n periods into the future: Ft+n= Ft+i + ntt+i /= Smoothing constant for trend estimate Tt+i= Trend estimate n=periods to be forecasted into future Ft+n= Forecast for n periods into future. Studies indicate that Holt's procedure is preferred over Brown's exponential smoothing (Gardner & Dannenbring, ; Jarrett, ). Winter's Exponential Smoothing. While Brown's exponential smoothing included a trend factor and Holt's method added a growth factor. Winter's exponential smoothing is based on the three components of a pattern: randomness/

39 cyclic contrast, linearity, and seasonality (Wheelwright & Makridakis, ). This method employs these three parameters {a, (, & ) through a trial and error approach. Computer software is very helpful in this type of analysis. The formulas for this method are the following (Hanke & Reitsch, ):. The exponentially smoothed series: F,=a-^^{l-a) (F,., + r,.,).. The seasonality estimate:,=p^m-p)s,_^.. The trend estimate: T,-y{F,-F,.^)^{l-y)T,_^^. Forecast for P periods in the future: F,^p={F,-PT,)S, where: St = seasonality estimate, St-p = average experience of seasonality estimated, smoothed to period t-p, y = smoothing constant for trend estimate, p= number of seasons.

40 Ft^p= forecast for p periods into future. Causal Models Causal models find the exact form of the relationship between independent variables and the dependent variable. The dependent variable is what the researcher would like to predict, and the independent variables are the variables that affect the value of the dependent variable. There are two types of causal models: linear regression and multiple regression (Cryer & Miller, ; Iman & Conover, ). Armstrong () suggested that causal methods are used only if historical data are available. Linear Regression The linear regression model in forecasting estimates the nature of the relationship between a dependent variable and an independent variable. The dependent variable, Y, is the one to predict, and the independent variable, X, is the one used to help in the prediction. A simple regression model can be expressed in the form of a straight line with the following equation: Y = lo + P^X + e where /So and (^ are parameters that represent, respectively, the Y intercept and slope of the regression curve and e is the random variable between the value of the independent variable and the regression line (Jarrett, ).

41 Multiple Regression When there is more than one independent variable, such relationships are called multiple relationships. Hanke and Reitsch () defined that "Multiple regression is the use of more than one independent variable to predict a dependent variable" (p. ). The equation for multiple regression is as follows: Y= /So + /SA + (,X, +... / X, + e where /i, (,...^^ are the regression coefficients explaining the association between the independent and dependent variables (Jarrett, ). Because of the cost and tedious labor involved in multiple regression analysis, computer programs are needed. Combining Subjective and Objective Forecasting Models Several studies have found that simple mathematic methods, such as Naive, simple exponential smoothing and simple moving average, are as accurate as sophisticated models, such as double exponential smoothing and simple linear regression (Armstrong, ; Georgoff & Murdick, ; Mahmoud, ; Miller, McCahon, & Bloss, ; Miller, McCahon, & Miller, ; Shahabuddin, ; Wheelwright & Makridakis, ). It is believed that quantitative methods out-perform qualitative methods (Carbone & Gorr, ; Mahmoud, ). However some studies found that quantitative methods are not

42 consistently superior in accuracy to judgmental methods (Lawrence, ; Lawrence, Edmundson, & O'Connor, ). Although subjective methods are more widely used by operations than objective methods, the latter approach is more accurate than subjective methods (Dalrymple, ; Georgoff & Murdick, ). Some researchers claim that combining forecasts is more desirable than using forecasts that are prepared by an individual method (Shahabuddin, ; Wilson & Allison-Koerber, ; Wilson & Daubek, ). Because any individual method is difficult to identify, they add that the accuracy of a combined forecast depends on which methods and how many are used. Criteria for Forecasting Models Cost of Model According to Spears (), the cost of a forecasting model includes both the development and operational cost. Development costs relate to constructing the model, validating the forecast stability, and writing or securing a computer program. Operational costs include costs incurred after the model is developed and as it is used. Georgoff and Murdick () stated that the Naive model is the most inexpensive to implement and maintain. Moving average and exponential smoothing techniques require moderate expenditures. Adaptive smoothing and regression models are very expensive.

43 The cost of error is another factor to consider in the selection of a model. Over-forecasting may increase the food cost and under-forecasting may result in customer dissatisfaction. The goal of a forecaster is to reach the optimal region where cost and accuracy can be a trade-off (Adam & Ebert, ). Relevancy of Past Data Spears () stated that the general assumption in most forecasting is that past behavioral patterns and relationships will be repeated in the future. In other words, past data will influence future events only if there is a clear relationship between the past and future. Forecasting Lead Time Forecasting lead time varies according to the type of operations. Perishable product requires short-term lead time. time. Canned goods, however, allow a more flexible lead Lawrence, Edmundson, and O'Connor () found that the judgmental method is superior to the mathematic method only if there are long lead times. Studies found that simple mathematic methods require a short lead time. (Jarrett, ; Mentzer & Cox, ; Wheelwright & Makridakis, ; Wilson & Allison-Koerber, ). Regression models are suggested in long-range forecasting (Mentzer & Cox, ; Wilson & Allison-Koerber, ).

44 Degree of Stability The pattern of demand influences the choice of a model. Different types of operations have different types of behavioral patterns. Moving average and simple exponential smoothing methods are best for stable data forecasting (Georgoff & Murdick, ; Miller, McCahon, & Miller, ; Wilson & Allison-Koerber, ). A simple moving average method will perform better than simple exponential smoothing in forecasting an unstable data pattern (Miller, McCahon, & Miller, ). Wilson and Allison-Koerber () indicated that regression models can handle complex patterns. Availability of Equipment and Facilities Repko and Miller () indicated that computers are reliable tools for improving forecast accuracy. Georgoff and Murdick () stated that computer facilities are not essential for all qualitative techniques. It is helpful to have computing facilities for simple mathematic methods. A computer is essential for adaptive exponential smoothing, regression, and Box-Jenkins models. Skills of Personnel Another consideration in selecting a forecasting model is the degree of skill required to compute the results. Wilson and Allison-Koerber's () study indicated that simple exponential smoothing techniques is less

45 sophisticated than Holt's exponential smoothing, Winter's exponential smoothing, and linear regression models. The multiple regression model and Box-Jenkins, however, are the most complex forecast techniques. They require the expertise and training of personnel within the organization. Accuracy Accuracy is the last and the most important concern in judging the quality of a forecast. Lawrence () indicated that there are two main issues concerning forecast accuracy. The first is whether quantitative techniques are significantly more accurate than judgmental methods and secondly, which quantitative techniques are best. An expensive and sophisticated model is not necessarily more accurate than a less expensive and simpler model. Multiple regression is believed to be the best forecast model when it is used alone (Forst, ; West, ; Wilson & Allison- Koerber, ; Wilson & Daubek, ). Studies found that forecast accuracy improved when more methods are involved (Armstrong, ; Lawrence, Edmundson, & O'Connor, ; Makridakis, ; Reyna, Kwong, & Li, ; West, ; Wilson & Allison-Koerber, ). However, too many methods may mean confusion. How to select the right methods and make good combinations is a challenge to the decision support system (West, ).

46 Measuring the Accuracy of Forecast Models The goal of a forecaster is to minimize the forecast error. Thus, the error or deviation is defined as: Error = actual - forecast or Et = Dt - Ft Et = Error for period t (Schonberger & Knod, ). Some of the most common indicators of accuracy are the bias, mean absolute deviation (MAD), mean square error (MSE), root mean square error (RMSE), and mean absolute percentage error (MAPE) (Adam & Ebert, ). Bias One of the methods to measure error is called bias, which is the average of errors, and is given in the following equation: n j: (F,-D,) Bias=^^ n where Ft = Forecast for period t, Dt = Actual demand that occurred in period t. Bias indicates the directional tendency of forecast errors. For example, if a forecast has been overestimating constantly, it will have a positive value of bias.