HMGT 435 WK 4 DISC 4

CHAPTER

137

9FORECASTING

Learning Objectives

After reading this chapter, students will be able to

• articulate the importance of a good sales forecast, • describe the attributes of a good sales forecast, • apply demand theory to forecasts, and • use simple forecasting tools appropriately.

Key Concepts

• Making and interpreting forecasts are important jobs for managers. • Forecasts are planning tools, not rigid goals. • Sales and revenue forecasts are applications of demand theory. • Changes in demand conditions usually change forecasts. • Good forecasts should be easy to understand, easy to modify, accurate,

transparent, and precise. • Forecasts combine history and judgment. • Assessing external factors is vital to forecasting.

9.1 Introduction

Making and interpreting forecasts are important jobs for managers. Sales forecasts are especially important because many decisions hinge on what the organization expects to sell. Pricing decisions, staffing decisions, product launch decisions, and other crucial decisions are based on the organization’s revenue and sales forecasts.

Inaccurate or misunderstood forecasts can hurt businesses. The orga- nization can hire too many workers or too few. It can set prices too high or too low. It can add too much equipment or too little. At best, these sorts of forecasting problems will cut into profits; at worst, they may drive an orga- nization out of business.

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C o p y r i g h t 2 0 1 9 . H e a l t h A d m i n i s t r a t i o n P r e s s .

A l l r i g h t s r e s e r v e d . M a y n o t b e r e p r o d u c e d i n a n y f o r m w i t h o u t p e r m i s s i o n f r o m t h e p u b l i s h e r , e x c e p t f a i r u s e s p e r m i t t e d u n d e r U . S . o r a p p l i c a b l e c o p y r i g h t l a w .

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Economics for Healthcare Managers138

The consequences of bad or misapplied forecasts are particularly seri- ous in healthcare. For example, underestimating the level of demand in the short term may result in stock shortages at a pharmacy or too few nurses on duty at a hospital. In both cases, the healthcare organization will suffer financially and, more important, put patients at risk. It will suffer because the costs of meeting unexpected demand are high and because the long-term consequences of failing to meet patients’ needs are significant. The best out- come in this case will be unhappy patients; the worst outcome will be that physicians stop referring patients to the organization.

Overestimating sales can also have serious long-term effects. A hospital may add too many beds because its census forecast was too high. This surplus will depress profits for some time because the facility will have hired staff and added equipment to meet its overestimated forecast, and the costs of hir- ing and paying new employees and buying new equipment will substantially exceed actual sales profits. In extreme cases, bad forecasts may drive a firm out of business. A facility that borrows heavily in anticipation of higher sales that do not materialize may be unable to repay those debts. Bankruptcy may be the only option.

Sales and revenue forecasts are applications of demand theory. The fac- tors that change sales and revenues also change demand. The most important influences on demand are the price of the product, rivals’ prices for the prod- uct, prices for complements and substitutes, and demographics. Recognizing these influences can simplify forecasting considerably because it focuses our attention on tracking what has changed.

9.2 What Is a Sales Forecast?

A sales forecast is a projection of the number of units (e.g., bed days, visits, doses) an organization expects to sell. The forecast must specify the time frame, marketing plan, and expected market conditions for which it is valid.

A forecast is a planning tool, not a rigid goal. Conditions may change. If they do, the organization’s plan needs to be reassessed. Good management usually involves responding effectively to changes in the environment, not forging ahead as though nothing has shifted. In addition, fixed sales goals create incentives to behave opportunistically (that is, for employees to try to meet their goals instead of the organization’s goals). For example, sales staff may harm the organization by making overblown claims of a product’s effectiveness to meet their sales goals, even though their actions will harm the company in the long run. Alternatively, sales managers may bid on unprofit- able managed care contracts just to meet goals.

Whenever possible, a sales forecast should estimate the number of units expected to be sold, not revenues. The number of units to be sold

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Chapter 9: Forecast ing 139

determines staffing, materials, working capital, and other needs. In addition, costs often vary unevenly with volume. A small reduction in volume may save an entire shift’s worth of wages (thereby avoiding considerable cost), or an increase in sales may incur a small cost increase if it requires no additional staff or equipment.

The dollar volume of sales can vary in response to factors that do not affect the resources needed to produce, market, or service the sales. Dis- counts and price increases are examples of such factors. Revenues can vary even though neither volume nor costs change. Finally, managers can easily forecast revenue given a volume forecast. In general, managers should build their revenue estimates on sales volume estimates.

Good forecasts have five attributes. They should be

1. easy to understand, 2. easy to modify, 3. accurate (i.e., they contain the most probable actual values), 4. transparent about how variable they are, and 5. precise (i.e., they give the analyst as little wiggle room as possible).

These attributes often conflict. Managers may need to underplay how impre- cise simple forecasts are because their audience is not prepared to consider variation. As Aven (2013) points out, many decision makers are more com- fortable working with a single, precise estimate, even though it may be inac- curate. Precision and accuracy always conflict because a more precise forecast (80 to 85 visits per day) will always be less accurate than a less precise forecast (70 to 95 visits per day). Offering decision makers several precise scenarios is usually a good compromise. For example, busy decision makers generally can use a forecast such as “Our baseline forecast is 82 visits per day for the next three months, our low forecast is 75 visits per day, and our high forecast is 89 visits per day.”

Forecasting Supply Use

More and more healthcare institutions seek to reduce costs while increasing the quality of care.

Accurate forecasts of the use of medical supplies represent an important element of this effort. Overordering supplies drives up costs, and under- ordering supplies also can drive up costs and compromise care.

Case 9.1

(continued)

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Economics for Healthcare Managers140

9.3 Forecasting

All forecasts combine history and judgment. History is the only real source of data. For example, sales can be forecasted only on the basis of data on past sales of a product, past sales of similar products, past sales by rivals, or past

The stakes can be high. Caldwell Memorial Hos- pital, a 110-bed hospital in North Carolina, saved $2.62 million in less than six months by consolidat-

ing and eliminating excess supplies (Belliveau 2016). The hospital used a Lean approach to inventory management, which involves streamlining and simplifying the inventory and ordering systems.

In addition, a number of hospitals have expanded their use of just- in-time inventory management (Green 2015). This method reduces, but does not eliminate, the need for forecasting accuracy. Some supplies are highly specialized and are used intermittently, so they must be ordered well in advance. The savings can be substantial. Mercy Hos- pital in Chicago was able to reduce its inventory by 50 percent using just-in-time inventory management (Green 2015).

Discussion Questions • What share of hospital costs do supplies represent?

• Why would overordering supplies drive up costs?

• Why would underordering supplies drive up costs?

• Can you offer examples of Lean inventory management? Does it work well?

• Can you offer examples of just-in-time inventory management? Does it work well?

• Can you offer examples of supplies that have to be available at all times?

• What are the main challenges to making accurate forecasts of supply use in hospitals?

• How would you forecast supply use in the emergency department? Why?

• How would you forecast supply use in hospital clinics? Why?

• Would you use judgment in making these forecasts? Why?

• Would you use statistical models in making these forecasts? Why?

• How are supply chain forecasts different for hospitals than for retail? For manufacturing?

Case 9.1 (continued)

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Chapter 9: Forecast ing 141

sales in other markets. History is an imperfect guide to the future, but it is an essential starting point.

Judgment is also essential. It provides a basis for deciding what data to use, how to use the data, and what statistical techniques, if any, to use. In many cases (e.g., introductions of new products or new competitive situ- ations), managers who have insufficient data will have to base their forecasts mainly on judgment.

As mentioned in section 9.2, a forecast must specify the time frame, marketing plan, and expected market conditions for which it is valid. Changes in any of these factors will change the forecast.

A forecast applies to a given period. Extrapolating to a longer or shorter period is risky; conditions may change. The time frame varies accord- ing to the forecast’s use. For example, a staffing plan may need a forecast for only the next few weeks. Additional staff can be hired over a longer time horizon. In contrast, budget plans usually need a forecast for the coming year. Organizations usually set their budgets a year in advance on the basis of projected sales. Strategic plans usually need a forecast for the next several years. Longer forecasts are generally less detailed and less reliable, but manag- ers know to take these factors into account when they develop and use them.

Forecasts should be as short term as possible. A forecast for next month’s sales will usually be more accurate than forecasts for the distant future, which are likely to be less accurate because important facts will have changed. Your competitors today are likely to be your competitors in a month. Your competitors in two years are likely to be different from your competitors today, so a forecast based on current market conditions will be poor.

Marketing plan changes will influence the forecast. A clinic that increases its advertising expects visits to increase. A forecast that does not consider this increase will usually be inaccurate. Increasing discounts to phar- macy benefits managers should result in increased sales for a pharmaceutical firm. Again, a forecast that does not account for additional discounts will usu- ally be deficient. Any major changes in an organization’s marketing efforts should change forecasts. If they do not, the organization should reassess the usefulness of its marketing initiatives.

Changes in market conditions also influence forecasts. For example, a major plant closing would probably reduce a local plastic surgeon’s volume. Plant employees who had intended to undergo plastic surgery may opt to delay this elective procedure, and prospective patients who work for similar plants may defer discretionary spending in fear that they too may lose their jobs. Alternatively, a hospital closure will probably cause a competing hospital to forecast more inpatient days. Historical data have limited value in project- ing such an effect if a similar closure has not occurred in the past. Approval of a new drug by the Food and Drug Administration should cause a phar- maceutical firm to forecast a decrease in sales for its competing product. This

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Economics for Healthcare Managers142

sort of change in market conditions is familiar, and the firm’s marketing staff will probably draw on experience to predict the loss.

Analysts routinely use three forecasting methods: percentage adjust- ment, moving averages, and seasonalized regression analysis. If the data are adequate and the market has not changed too much, seasonalized regression analysis is the preferred method. However, whether the data are adequate and whether the market has changed too much are judgment calls.

Percentage adjustment increases or decreases the last period’s sales volume by a percentage the analyst deems sensible. For example, if a hospi- tal had an average daily census of 100 the previous quarter, and an analyst expects the census to fall an average of 1 percent per quarter, a reasonable forecast would be a census of 99. Because of its simplicity, managers often use percentage adjustment; however, this simplicity is also a shortcoming. In principle, a manager could choose an arbitrary percentage adjustment. Without some requirement that percentage adjustments be well justified, this approach may not yield accurate forecasts. For example, a manager might justify a request for a new position based on a forecast that average daily census will increase by 5 percent, even though the average daily census had been falling for the last 14 quarters. In addition, percentage adjustment does not allow for seasonal effects. (Seasonal effects are systematic tenden- cies for particular days, weeks, months, or quarters to have above- or below- average volume.)

Demand theory can be used to add rigor to percentage adjustments. For example, if the price of a product has changed, an estimate of the per- centage change in sales can be calculated by multiplying the percentage change in price by the price elasticity of demand. So, if an organization has chosen to raise prices by 3 percent and faces a price elasticity of demand of −4, sales will drop by 12 percent. Similar calculations can be used if the price of a substitute, the price of a complement, or consumer income has changed.

The moving-average method uses the average of data from recent periods to forecast sales. This method works well for short-term forecasts, although it tends to hide emerging trends and seasonal effects. Exhibit 9.1 shows census data and a one-year moving average for a sample hospital.

Exhibit 9.1 also illustrates the calculation of a seasonalized regression format. Excel was used to estimate a regression model with a trend (a vari- able that increases in value as time passes) and three quarter indicators. The variable Q1 has a value of 1 if the data are from the first quarter; otherwise, its value is 0. Q2 equals 1 if the data are from the second quarter, and Q3 equals 1 if the data are from the third quarter. For technical reasons, the aver- age response in the fourth quarter is represented by the constant. A negative regression coefficient for trend indicates that the census is in a downward trend. The results also show that the typical third-quarter census is smaller

percentage adjustment An adjustment that increases or decreases the average of the past n periods. (The adjustment is essentially a best guess of what is expected to happen in the next year.)

moving average The unweighted mean of the previous n data points.

seasonalized regression analysis A least squares regression that includes variables to identify subperiods (e.g., weeks) that historically have had above- or below-trend sales.

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Chapter 9: Forecast ing 143

Quarter Census Moving Average First Second Third Trend

1 99 1 0 0 1

2 109 0 1 0 2

3 101 0 0 1 3

4 107 0 0 0 4

5 104 104.0 1 0 0 5

6 116 105.3 0 1 0 6

7 100 107.0 0 0 1 7

8 106 106.8 0 0 0 8

9 103 106.5 1 0 0 9

10 107 106.3 0 1 0 10

11 90 104.0 0 0 1 11

12 105 101.5 0 0 0 12

13 102 101.3 1 0 0 13

14 94 101.0 0 1 0 14

15 98 97.8 0 0 1 15

16 104 99.8 0 0 0 16

17 99 99.5 1 0 0 17

18 105 98.8 0 1 0 18

19 94 101.5 0 0 1 19

20 102 100.5 0 0 0 20

21 100 100.0 1 0 0 21

22 100.3

Seasonalized Regression Model

Coefficient t-statistic

Intercept 108.811 40.90 R2 = 0.55

First quarter −3.968 −1.53 F(4,20) = 4.98

Second quarter 0.732 0.27 p = 0.01

Third quarter −8.534 −3.16

Trend −0.334 −2.16

EXHIBIT 9.1 Census Data for a Sample Hospital

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Economics for Healthcare Managers144

than average because the coefficient for Q3 is large, negative, and statistically significant.

The forecast based on seasonalized regression analysis is calculated as follows: 108.811 + (−0.334 × 22) + 0.732. Here, 108.811 is the estimate of the constant, −0.334 is the estimate of the trend coefficient, 22 is the quarter to which the forecast applies, and 0.732 is the estimate of the Q2 coefficient. Therefore, the seasonalized forecast is 102.2, slightly higher than the forecast based on the moving average. Overall the seasonalized forecast is a little more accurate than the one-year moving average. The mean absolute deviation for the regression is 2.3 for periods 5 through 21, and the mean absolute deviation for the moving average is 4.0.

Exhibit 9.2 shows an overview of the forecasting process. The main message of this exhibit is that a forecast is one part of the overall product management process. In addition, the forecast will change as managers’

mean absolute deviation The average absolute difference between a forecast and the actual value. (It is absolute because it converts both 9 and −9 to 9. The Excel function =ABS( ) performs this conversion.)

Assess internal and external factors.

Develop an initial forecast.

Develop an initial marketing strategy and then modify the forecast and marketing strategy until they are consistent.

Monitor sales, internal factors, external factors, and the marketing strategy.

Modify the forecast and marketing strategies as needed.

EXHIBIT 9.2 An Overview of the Forecasting

Process

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Chapter 9: Forecast ing 145

assessments of relevant internal factors (e.g., cost and quality), external fac- tors (e.g., the competitive environment and payment levels), and the market- ing plan change.

A naïve forecast uses the value for the last period as the forecast for the next period—in other words, a 0 percent adjustment forecast. Exhibit 9.3 shows an example of a naïve forecast. A moving-average forecast uses the average of the last n values, where n is the number of preceding values used in the forecast. For example, the first entry in the Two-Period Moving-Average Forecast column in exhibit 9.3 equals (189 + 217) ÷ 2, or 203.

To compare forecasting techniques, analysts sometimes use the mean absolute deviation, which is the average of the forecast’s absolute deviations from the actual value. (When using the absolute deviation, it does not mat- ter if a value is higher or lower than the actual value; all the deviations are positive numbers.) For April through July, the naïve forecast in exhibit 9.3 has a mean absolute deviation of 12.0, and the two-period moving-average forecast has a mean absolute deviation of 12.1. From this perspective, the naïve forecast performs a little better.

These (and other) mechanistic forecasting methods do not allow man- agers to explore how changes in the environment are likely to affect sales. How would changes in insurance coverage change sales? Naïve forecasts and moving-average forecasts are little help in such situations.

9.4 What Matters?

Assessment of external factors (i.e., factors beyond the organization’s con- trol) is vital to forecasting. General economic conditions are a prime example. Expected inflation and interest rates are good indicators of the state of the

Month Sales Naïve

Forecast Two-Period Moving-

Average Forecast

February 189

March 217 189

April 211 217 203

May 239 211 214

June 234 239 225

July 243 234 236.5

EXHIBIT 9.3 Simple Forecasting Techniques: Naïve and Moving-Average Forecasts

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Economics for Healthcare Managers146

economy. Local market conditions, such as business rents and local wages, also play an important role.

Government actions also can have a major impact on healthcare firms. For example, changes in Medicare rates affect most healthcare firms. Alter- natively, regulations can have a significant effect on costs. Expansion of Med- icaid eligibility can have major effects on some hospitals and minor effects on others. Keep in mind that these sorts of changes will also affect most of your competitors, but forecasters would be ill advised to ignore changes in government policy.

The plans of key competitors must also be considered. Closure of a competing clinic or hospital can increase volume significantly and quickly. Introduction of a generic drug can have a dramatic effect on a pharmaceuti- cal manufacturer. Changes in competitors’ pricing policies can have a major impact on sales.

Technological change is always an important issue. If a rival gains a technological advantage, your sales can drop sharply. For example, if a rival introduces minimally invasive coronary artery bypass graft surgery, admis- sions to your cardiac unit will probably drop significantly until you adopt similar technology. In other cases, your own advances may affect sales of substitute products. For example, introduction of highly reliable magnetic resonance imaging may sharply reduce the demand for conventional colo- noscopy. Keep in mind, however, that if you do not introduce technologies that add value for your customers, someone else will. A decision not to introduce an attractive product because it will cannibalize sales is usually a mistake.

Finally, although markets usually change slowly, differences in general market characteristics (e.g., median income and percentage with insurance coverage) may be important in forecasting sales of a new product.

Assessment of internal factors (i.e., factors within an organization’s control) is also vital to forecasting. For example, existing production may limit sales, or production may have limited sales in the past. If so, changes in capacity or productivity need to be considered. Changes in the availability of resources and personnel can also have a powerful effect on sales. For many healthcare organizations, the entry or exit of a key physician can dramatically shape volume. In addition, changes in the size, support, composition, and organization of the sales staff can affect sales dramatically. For instance, a small drug firm may experience a large increase in sales if one of its products is marketed by a larger firm’s sales staff.

Failures or improvements in key systems can also have dramatic effects on sales. Breakdowns in a clinic’s phone or scheduling system may drive away potential customers. Fixing the phone system, in contrast, might be the most effective marketing campaign the clinic ever launched.

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Chapter 9: Forecast ing 147

Mistakes to Avoid When Making Forecasts

Business plans require a sales forecast. Scott Fishman, the CEO of Envisage, sees three common mistakes in business plans (Fishman 2015):

• They forecast “hockey stick” revenue growth.

• They forecast smoothly rising trend lines.

• They lack convincing evidence of market size.

A “hockey stick” forecast—a revenue graph shaped like a hockey stick—involves limited revenues initially followed by explosive growth. It is a potentially effective sales technique to use in discussions with executives and investors because it suggests that the business oppor- tunity might be extremely valuable.

In contrast, smoothly rising trend lines do not seem plausible from an economic standpoint. The number of customers and their consump- tion of any product is typically finite. Furthermore, any true blockbuster product will attract competition.

Every new product faces a complex environment: features and benefits, competitive environment, regulatory conditions, payment models, distribution, pricing, market positioning, and so forth. A genu- inely new product will have multiple unknowns in its market. If there are no unknowns, it is not really a new product. A convincing forecast demands market research, an honest recognition of what is not known, and a strategy for resolving some of the unknowns.

Discussion Questions • What is problematic about a “hockey stick” forecast?

• Can you find an example of a product that displayed “hockey stick” revenue growth?

• What is problematic about a forecast with a smoothly rising trend line?

• Can you find an example of a product that displayed smoothly rising revenue growth?

• From an economic point of view, what is implausible about smoothly rising trend lines?

Case 9.2

(continued)

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Economics for Healthcare Managers148

9.5 Conclusion

Making and interpreting forecasts are important tasks for healthcare manag- ers. Not only are most crucial decisions based on sales forecasts, but also the consequences of overestimating or underestimating demand can be cata- strophic. Overestimating demand can put the financial future of an organiza- tion at risk, whereas underestimating demand can compromise the care of patients and harm the organization’s reputation.

Analysts should apply demand theory to their sales forecasts to better recognize changes. Demand theory limits what analysts need to consider: the price of the product, the price of substitutes, and the price of complements. The key idea of demand theory is that the out-of-pocket price drives most consumer demand. The amount the consumer has to pay depends largely on the terms of the insurance contract. Is the product covered? What is the required copayment? Changes in the answers to these two questions can shift sales sharply. The same concerns affect the prices of substitutes. The most important substitutes are similar products offered by rivals, but other prod- ucts that meet some of the same needs should also be considered.

Demographic factors are important. Population size, income per capita, the age distribution of the population, the ethnic makeup of the population, and the insurance coverage of the population are some examples. Although vital, demographic factors tend to be stable in the short term. Demographics are much more important in long-range forecasts.

“Prediction is very difficult, especially if it’s about the future.” This saying, noted in chapter 4, reveals a core truth about forecasting: You often will be wrong. Knowing that, a shrewd manager will make decisions that can be modified as conditions change. The shrewd manager will also know which

• Can you find an example of a product that wildly underperformed early forecasts?

• Can you find an example of a product that wildly overperformed early forecasts?

• What external factors might cause below-forecast sales? Above- forecast sales?

• What internal factors might cause below-forecast revenues? Above- forecast revenues?

• What are examples of new products with uncertain prospects in healthcare?

Case 9.2 (continued)

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Chapter 9: Forecast ing 149

data are likely to be the most problematic or most variable and will monitor those data carefully.

Management decisions require sales forecasts. Off-the-cuff forecasts often fail to consider key factors and can lead to risky decisions. Imper- fect forecasts can be used to make decisions as long as you recognize that your predictions will sometimes be wrong and you structure your decisions accordingly.

Exercises

9.1 The table lists visits for each of the four clinics operated by your system. You anticipate that volumes will increase by 4 percent next year. Forecast the number of visits for each clinic, and explain what assumptions underlie your forecasts. For example, are you sure that all the clinics can serve additional clients?

Period Clinic 1 Clinic 2 Clinic 3 Clinic 4 Total

This year 16,640 41,600 24,960 33,280 116,480

Next year ? ? ? ? 121,139

9.2 Your data for the clinics in exercise 9.1 suggest that clinic 2 is operating at capacity and is highly efficient. Its output is unlikely to increase. Furthermore, clinic 4 has unused capacity but is unlikely to attract additional patients. How would these facts change your answer to the question in exercise 9.1? Continue to assume that overall volume will rise to 121,139.

9.3 You estimate that the price elasticity of demand for clinic visits is −0.25. You anticipate that a major insurer will increase the copayment from $20 to $25. This insurer covers 40,000 of your patients, and those patients average 2.5 visits per year. What is your forecast of the change in the number of visits?

9.4 A major employer has just added health insurance coverage for its employees. Consequently, 5,000 of your patients will pay a $30 copayment rather than the list price of $100 per visit. These patients average 2.2 visits per year. You believe the price elasticity of demand is between −0.15 and −0.35. What is your forecast of the change in the number of visits?

9.5 The following table shows data on asthma-related visits. Is there evidence that these visits vary by quarter? Can you detect a trend?

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Economics for Healthcare Managers150

A powerful test would be to run a multiple regression in Excel. (To do this, you will need the free Analysis ToolPak for your version of Excel. Microsoft [2018] offers guidance on how to load and use the Analysis ToolPak.) To test for quarterly differences, create a variable called Q1 that equals 1 if the data are for the first quarter and 0 otherwise, a variable called Q2 that equals 1 if the data are for the second quarter and 0 otherwise, and a variable called Q4 that equals 1 if the data are for the fourth quarter and 0 otherwise. (Because you will accept the default, which is to have a constant term in your regression equation, do not include an indicator variable for Quarter 3.) Also create a variable called Trend that increases by 1 each quarter.

Year Q1 Q2 Q3 Q4

2014 1,513 1,060

2015 1,431 1,123 994 679

2016 1,485 886 1,256 975

2017 1,256 1,156 1,163 1,062

2018 1,200 1,072 1,563 531

2019 1,022 1,169

9.6 Your marketing department estimates that Medicare urology visits equal 5 − (1.0 × C) + (−6.5 × TO) + (5 × TR) + (0.01 × Y). Here, C denotes the Medicare copayment (now $20), TO is waiting time in your clinic (now 30 minutes), TR is waiting time in your competitor’s clinic (now 40 minutes), and Y is per capita income (now $40,000). a. How many visits do you anticipate? b. Medicare’s allowed fee is $120. What revenue do you anticipate? c. What might change your forecast of visits and revenue?

9.7 Because of fluctuations in insurance coverage, the average price paid out of pocket (P) by patients of an urgent care center varied, as the table shows. The number of visits per month (Q) also varied, and an analyst believes the two are related. The analyst also thinks the data show a trend. Run a regression of Q on P and Period to test these hypotheses. Then use the estimated parameters a, b, and c and the values of Month and P to predict Q (number of visits). The prediction equation is Q = a + (b × Month) + (c × P).

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Chapter 9: Forecast ing 151

Month 1 2 3 4 5 6 7 8 9 10 11 12

P $21 $18 $15 $24 $18 $21 $18 $15 $20 $19 $24 $20

Q 193 197 256 179 231 214 247 273 223 225 198 211

9.8 Use the data in exercise 9.7 to answer these questions: a. Calculate the naïve estimator, which is Qt = Qt − 1. b. Calculate the two-period moving-average forecast. c. Calculate the mean absolute deviation for the regression forecast,

the naïve forecast, and the two-period moving-average forecast. d. Which forecast seems to perform the best? Why?

9.9 Sales data are displayed in the table.

Month Sales Month Sales

February 224 January 260

March 217 February 284

April 211 March 280

May 239 April 271

June 234 May 302

July 243 June 286

August 238 July 297

September 243 August 301

October 251 September 309

November 259 October 314

December 270

a. Calculate the naïve estimator, which is Salest = Salest − 1. b. Calculate the two-period and three-period moving averages. c. Calculate the mean absolute deviation for each of the forecasting

methods. 9.10 A pharmaceutical company produces a sinus medicine. Monthly sales

(in thousands of doses) for the past three years are shown in the table on the next page.

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Economics for Healthcare Managers152

a. Develop a regression model that allows for trend and seasonal components. Obtain the Excel output for this model.

b. Calculate a two-period moving-average forecast. c. Compare the mean absolute deviations for these approaches. d. Use one of these models to forecast sales for each month of

year 3.

References

Aven, T. 2013. “On How to Deal with Deep Uncertainties in a Risk Assessment and Management Context.” Risk Analysis 33 (12): 2082–91.

Belliveau, J. 2016. “How a Small Hospital Developed Lean Supply Chain Manage ment.” RevCycle Intelligence. Published September 6. https://revcycle intelligence .com /news/how-a-small-hospital-developed-lean-supply-chain-management.

Fishman, S. 2015. “3 Mistakes to Avoid When Forecasting the Market for Your Medical Device.” Med Device Online. Published September 21. www.med deviceonline.com/doc/mistakes-to-avoid-when-forecasting-the-market-for -your-medical-device-0001.

Green, C. 2015. “Hospitals Turn to Just-in-Time Buying to Control Supply Chain Costs.” Healthcare Finance. Published May 6. www.healthcarefinancenews .com/news/hospitals-turn-just-time-buying-control-supply-chain-costs.

Microsoft. 2018. “Use the Analysis ToolPak to Perform Complex Data Analysis.” Accessed September 18. https://support.office.com/en-us/article/use-the -analysis-toolpak-to-perform-complex-data-analysis-6c67ccf0-f4a9-487c-8dec -bdb5a2cefab6.

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

6,788 8,020 1,848 410 586 2,260 2,232 8,018 9,384 6,916 5,698 6,940

9,136 7,420 3,350 1,998 1,972 3,572 4,506 10,474 13,358 8,232 8,218 10,248

9,628 7,826 3,528 2,126 2,070 3,762 4,754 11,010 14,040 8,646 8,634 10,782

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