MAT/543 MAT543 MAT 543 WEEK 4 HOMEWORK

MAT 543 WEEK  4 HOMEWORK

Week 4 Homework

Homework

• Chapter 5: Exercises 5-1, 5-3, 5-5, and 5-6 (page 87 of the text)

REAL WORLD SCENARIO

Molly Adel is the director of University Health Services for Northern College, a large liberal arts college in the northeast. Northern College Health Services serves undergraduate and graduate students who live both on and off campus with a broad range of primary care services. In recent years, visit volume has been increasing, both during the academic year and the summer months. At times, the staffing and supply resources of the College’s Health Services have become strained. Molly has decided that it would be best to attempt to forecast upcoming visits to Health Services to better anticipate resource demands. She would like to understand the type and precision of each type of forecasting available to her. As director, she hears anecdotal stories of increased workloads from staff over the past 6 months. She believes there has been an increase in visits, but she would like to quantify these claims and attempt to understand if her own expert intuition of volume is a good substitute for a more analytic forecast.

LEARNING OBJECTIVE 1: TO DESCRIBE THE CONCEPT OF FORECASTING AS A MANAGERIAL TOOL

A forecast is an attempt to predict the future. Such attempts, however, are usually guesses of some form or another, as no one is able to see into the future or predict it with absolute certainty. Managers are not clairvoyant. They do not employ crystal balls or use fortune tellers as consultants. Yet managers must anticipate the future to prepare for it. Budgets are based upon forecasts. The number and type of employees are based upon present as well as future demands for service. Hiring and reductions in staff are based upon forecasts of the future.

Any forecast is, at best, an imprecise estimate. Few forecasts will be completely accurate, and so most contain some degree of inherent error. The challenge faced by managers and analysts is to minimize this error; or otherwise stated, managers must attempt to minimize the difference between what is predicted and what actually happens.

For example, if F = the forecast made yesterday of today’s temperature and TEMP = Today’s actual temperature, the only way F can equal TEMP (F = TEMP) is if:

    1. The Forecast was absolutely correct, or

    2. The formula is revised to be F = TEMP + E, where E is the positive or negative error of the forecast.

If today’s temperature was forecasted to be 65 degrees and the actual temperature is 65 degrees, then the error in the forecast would be zero. However, if the forecast for today’s temperature was 80 degrees, given the formula relationship, F = TEMP + E, the (E) error would be: E = 80 − 65 or 15 degrees.

Managers are very interested in methods that can minimize the error that is included in all forecasts. The challenge with forecasting is to strive for accuracy and come up with a “best” forecast, or one that employs the least amount of error. However, not all error is created equally. Error can be thought of as both systematic error—error that can be controlled for by the appropriateness and precision of the forecasting technique being used, and also random error—or error that is inherent in every forecast.

In our real world example, if Molly Adel did not account for the seasonal trends in visit volume to Northern College’s Health Services, she would be allowing systematic error to bias her forecasting estimates. At the same time, even if Molly did account for this variation, it is still possible that she could see a spike in visit volume over the summer months, for example, which could be entirely owing to random chance. This would be an example of random error, and there would be no way to predict its occurrence. The goal of all managers is to control for systematic error while being aware that random error is unpredictable and always possible.

LEARNING OBJECTIVE 2: TO DESCRIBE THE DIFFERENCE BETWEEN ANALYTIC AND NONANALYTIC FORECASTING

As the chapter title implies, forecasting is both an art and a science. To that end, there are two branches of forecasting: analytic, or statistical forecasting, and nonanalytic forecasting, often called judgmental, genius, or expert forecasting. Both have their merits and limitations.

Nonanalytic Forecasting

Judgment forecasting does not strictly imply making decisions based on intuition, although this can be the case. Most forms of this type of forecasting are both less accurate than analytic forecasting, and can be very labor intensive depending on the forecasting need.

For example, the Delphi method is a systematic method to collect opinions—usually from experts—and use these opinions in multiple round-robin cycles in an effort to arrive at a forecast that captures the essence of all the individuals (e.g., experts) used in the forecasting exercise. This type of effort may be good for forecasting a phenomenon that is relatively new, or for which there are little existing data, but it is not something one would use to predict the annual inventory for a services organization, for example.

Other examples of judgment or genius forecasting can be found in multiple forms—usually in newspapers or cable television when noted “experts” forecast the outcome of a certain situation, such as what stock performance will be, who will be wearing what next season, or what the new year will bring.

This chapter is not devoted to this type of forecasting. Except for the Delphi method, all forms of judgment forecasting are based upon individual opinion. Obviously, sometimes the individual will be right and other times wrong. It is important to remember that the challenge in forecasting is to minimize the error inherent in all forecasts. Judgment forecasting is often used to forecast far-off events that defy other approaches. Generally, the error inherent in judgment forecasting is considered large but unavoidable, although some have attempted to adjust for some of the inherent biases. (Harvey, N. “Improving judgmental forecasts,” in Principles of Forecasting: A Handbook for Researchers and Practitioners, J. Scott Armstrong (ed.), Kluwer Academic Publishers, 2001, 59–80.)

For example, consider an assignment to forecast the year when a cure will be available for HIV. The only reasonable and logical approach would be to identify either one or multiple experts and ask their opinion(s) on this question. The hypothesis is that the error in their forecasts will be less than the error in other forecasts because they are experts and have greater knowledge of this area than others. Before leaving judgment forecasting, it is important to note that sometimes the forecasting problem requires the use of judgment forecasting, such as with the example involving HIV. Judgment forecasting is still forecasting, even though it can be highly judgmental and not based upon mathematical models.

LEARNING OBJECTIVE 3: TO UNDERSTAND THE ASSUMPTIONS OF ANALYTIC FORECASTING

In contrast to nonanalytic forms of forecasting, analytic forecasting attempts to be more systematic and precise. This usually entails a mathematical approach to analyzing data to predict future outcomes and trends. Most forecasting problems faced by the health services manager can be accomplished using some form of analytic forecasting. Analytic forecasting methods are based on one of two assumptions. One is that the past is a reliable predictor of the future; and second is that the future can be predicted based on knowable cause-and-effect relationships. Each is examined in turn.

ASSUMPTION A: THE PAST CAN PREDICT THE FUTURE

This assumption is founded on the idea that future events are related to what has occurred in the past. Under this assumption analytic approaches are used to examine past and present events and extend or extrapolate the values of these past events forward. In using analytic approaches based upon this assumption, managers count on the past being a valid and reliable predictor of the future.

This assumption needs to be thoroughly considered by health services managers who use analytic forecasting approaches. For example, if the assignment is to forecast the number of patient days a hospital will generate (or produce) in the following month, basing the forecast on past patient-day production or generation seems appropriate because the past may be a reasonable predictor of the future. Examine the data in Figure 5-1. By a quick visual scan, if asked to predict the next month’s visits, most would place the forecast near 100. This, however, would be a visual judgment forecast. Instead there are methods to mathematically use past data to predict the future within some range of certainty. One question that first must be answered is, How far back should past data be included in making the forecast? Another is, How far into the future can and should one forecast given the data at hand? What if, for example, you were asked to forecast hospital patient days for the next 10 years? Ten years is a very long time in the future, and many unknown variables could affect the accuracy of such a distanced forecast. Given the ambiguity associated with such a long time interval, most health services managers would be very reluctant to base a 10-year forecast solely upon past data.

Chapter 6 will explore forecasting methods that are based on this assumption. They are:

    1. Extrapolations Using Averages

    2. Moving Averages as Forecasts

    3. Exponential Smoothing in Forecasting

^�z�K�