Centre for Operations Excellence
The University of British Columbia
WHISTLER BLACKCOMB SKI AND SNOWBOARD SCHOOL (B)
(Revised August 11, 2003)
Michael Hiroshi leans back in his chair, peers out at the dusk settling over Whistler
Mountain and marvels at the sophisticated forecasting model that he just finished
developing. It is Sunday, February 26 and his forecasting model predicts that 56 skiers
will take private lessons tomorrow morning at Blackcomb. Further, his analysis revealed
that the root mean squared forecasting error was 3.2. A quick glance at his watch
indicated that it was 5:00pm. He still has not decided how many instructors to assign
tomorrow, and Happy Hour at the Garibaldi Lift Company Pub next to his office, was
due to end at 5:30pm!
Michael thought; “Should he accept the original master schedule number of 60, call four
scheduled instructors to tell them not to come into work tomorrow, or delve deeper into
analyzing this problem?” Pondering these alternatives, he recalled a prior conversation
with Rob Stern, the Ski School Director, in which his boss stressed new profit
maximization initiative at the Ski School. How is he supposed to do this? What about
ensuring that every person that wants a lesson gets one? What staffing level would help
achieve the maximum profit from the private ski lesson pods?
Understaffing and Overstaffing
The consequence of staffing level errors costs the Ski School money and other intangible
or indirect expenses. If there are too few instructors, potential revenue is lost; if there are
too many instructors, overage costs are incurred.
Revenue loss occurs every time a potential participant is turned away without being able
to take a lesson which is the case when too few instructors have been scheduled.
Stanley Tse prepared this case under the supervision of Professor Martin L. Puterman solely to provide
material for class discussion. The author does not intend to illustrate either effective or ineffective handling
of a managerial situation. The author may have disguised certain names and other identifying information to
protect confidentiality. The author would like to acknowledge David Fujimagari from the Whistler Blackcomb
Ski and Snowboard School and Isabelle Smith from the COE for all of their invaluable help.
The Centre for Operations Excellence prohibits any form of reproduction, storage, or transmittal of the
material in this case without prior written permission. To order copies or request permission to reproduce
materials, contact the Centre for Operations Excellence, Sauder School of Business, The University of
British Columbia, 2053 Main Mall, Vancouver, BC, V6T 1Z2; phone (604) 822-1800; fax (604) 822-1544; email info@coe.ubc.ca.
Copyright © 2000, The Centre for Operations Excellence
Version: 2003-08-11
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Revenue loss has two components; there is the loss of possible profit1 from not being able
to offer a lesson as well as a potential loss of goodwill. In fact, it is Ski School policy to
never turn away a request for a children’s lesson. More specifically, the potential profit
loss for the pod for the day is the number of people turned away times the profit per
lesson plus the value of goodwill.
Overage costs are incurred each time an instructor who has been called in does not have a
teaching assignment in the morning. The actual dollar cost is two hours of instructor
wages incurred for paying an instructor to standby for two hours. In this case the
instructor carries out minor chores around the ski slope such as snow shovelling and
routine trail maintenance so his or her time is not completely wasted, but if (s)he had not
been called in, the extra work would not have been done. Thus, if instructors are
scheduled and arrive in the morning, the Ski School must pay them for at least two hours
of time regardless if they teach lessons or not. The total overage cost for the pod for the
day is obtained by multiplying the number of excess instructors times the per instructor
standby cost.
Staffing
To avoid stocking out, or having too few instructors, pod supervisors normally take last
year’s demand as the predicted number of participants, add a buffer amount and staff to
that level. Michael’s concern is that this policy does not necessarily take into account the
profit maximization objective of the Ski School. Adding a large buffer places emphasis
on avoiding shortage costs, but it does not take into account the cost of having too many
instructors. When discussing this challenge over drinks last night, a fellow supervisor
said, “When we make our staffing decisions, we’re like bakers deciding how many loaves
of bread to bake for the next day. If we bake too many, we have to sell them at reduced
prices; if we don’t bake enough, we lose revenue. ” At this point Michael recalled a
conversation with a UBC operations professor who had described the “newsvendor
inventory model” to him.
The Newsvendor Inventory Model
Each day a person selling newspapers (a newsvendor) must decide on the number of
newspapers to order from a supplier for sale on the next day. Unfortunately the
newsvendor does not know tomorrow’s demand when placing the order but must trade
off between having too few and too many newspapers. What distinguishes the
newsvendor model from other inventory models is that inventory leftover at the end of
the day is not useful on the next day. Leftover newspapers are bought back by the
supplier at a lower cost then was originally paid. On the other hand if the newsvendor
had ordered too few papers, excess demand (and the resulting revenue) would be lost.
The Ski School’s staffing problem appears to fit this framework as the table below
shows.
1
Assume that profit per lesson is equal to the price of the lesson less the labour cost.
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The objective of the newsvendor model is to determine an order quantity that maximizes
profit and/or minimizes total cost.
To apply the newsvendor model, Michael requires an estimate of overage and underage
costs as well as some assessment of the probability distribution of the next day’s demand.
Thinking back on his forecasting exercise he recalled that he had available both a point
forecast of 56 and a forecasting root mean squared error of 3.2. So if he could determine
the shape of the forecasting error distribution he would be able to use the newsvendor
model results (see Exhibit 1) to determine an appropriate number of instructors for
Blackcomb private ski lessons tomorrow.
Characteristic
Single period decision
Perishable good
Cost of overage and shortage
Uncertain demand
No backordering
Similarity to Ski School
Must make staffing decision once
the day before
Instructor’s time is perishable (once
the lesson period is over, time is
gone forever)
Outlined above
Daily lesson demand variable and
uncertain
Once an instructor has been called
in, (s)he must be paid.
Michael’s assumptions






Assume only half-day lessons are offered.
A shortage in instructors causes lessons to be turned away.
Instructor wage rate is $35/hour.
Price of a private ski lesson is $300 (half-day, 3 hours).
Standby commitment is 2 hours.
Loss of goodwill assumed initially to be $0.
Questions
1. How would the results of Whistler-Blackcomb (A) help Michael obtain a probability
distribution of the next day demand for private lessons at Blackcomb Mountain?
Assume first that demand is normally distributed with mean and standard deviation
determined by the forecast.
2. Suppose that Michael chooses the staffing level equal to the forecast and that demand
follows a normal distribution with the mean equal to the forecast. What is the chance
that there are not enough instructors to staff all requests for lessons?
3. Use the newsvendor model to determine the number of instructors to schedule for
AM private ski lessons at Blackcomb Mountain on February 22 and February 26 that
maximizes expected profits. In each case, what is the probability that there are not
enough instructors to meet demand for these lessons?
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4. Comment on the suitability of using the normal distribution to model forecast errors.
What other approaches are possible?
5. Investigate the sensitivity of the staffing level to the value assigned to loss of
goodwill.
6. Describe how you would implement a staffing system for the entire Ski School which
has 36 lesson types. In particular what data should be captured, how should it be
stored and how should staffing levels be communicated to supervisors.
Exhibit 1: The Newsvendor Inventory Model
This model yields an order quantity Q* that minimizes the expected total shortage and
overage costs. The inputs to the newsvendor model are:
F(D) - the cumulative distribution function for the next day’s random demand; that is
the probability that the demand for newspapers is less than or equal to D.
G - Per unit profit (gain) from selling a newspaper (Selling price minus cost)
L - Per unit loss from not selling a newspaper that was ordered (Cost minus salvage
value)
The Key Result
Using probability theory, the expected profit (or loss) from choosing the order quantity
Q can be represented in equation form. The equation can be minimized by differentiating
it with respect to Q and setting the derivative equal to zero to obtain a value Q* that
maximizes expected profit. This value is given implicitly by the expression:
F (Q * ) 
G
(G  L)
The right-hand side of this expression is called the critical fractile (c). The number given
by the critical fractile (between 0 and 1) represents the fraction of demand (service level)
that the newsvendor should strive to meet each day to minimize expected cost. The
newsvendor chooses Q* to satisfy this equation. For example if G/(G+L) =.8, the
newsvendor orders sufficiently many newspapers to satisfy all demand with probability
0.8.
When demand follows a normal distribution, Q* is available in closed form as follows:
Q* = mean + zc *standard deviation
where zc denotes the (c*100)th percentile of the standard normal distribution, i.e, if c =.8,
then z.8 = 0.841 is the 80th percentile of the normal distribution.