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Managing Capacity and Demand

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Learning Objectives

Describe the strategies for matchingcapacity and demand for services.

Recommend an overbooking strategy.

Use Linear Programming to prepare aweekly workshift schedule.

Prepare a work schedule for part-time

employees.Use yield management.

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Strategies for Matching Supply

and Demand for Services

DEMAND

STRATEGIES

Partitioning

demandDeveloping

complementary

servicesEstablishing

price

incentivesDeveloping

reservationsystems

Promoting

off-peak

demand

Yieldmanagement

SUPPLY

STRATEGIES

Cross-

trainingemployees

Increasingcustomer

participationSharing

capacity

Scheduling

work shifts

Creating

adjustable

capacityUsing

part-time

employees

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Segmenting Demand at a Health Clinic

60

70

80

90

100

110

120

130

140

1 2 3 4 5

Day of wee k

Per

centage

ofaverag

e

daily

physician

visit

s

Smoothing Demand by Appointment

Scheduling

Day Appointments

Monday 84

Tuesday 89

Wednesday 124

Thursday 129Friday 114

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Discriminatory Pricing for CampingExperience No. of Daily

type Days and weeks of camping season days fee

1 Saturdays and Sundays of weeks 10 to 15, plus 14 $6.00

Dominion Day and civic holidays

2 Saturdays and Sundays of weeks 3 to 9 and 15 to 19, 23 2.50

plus Victoria Day

3 Fridays of weeks 3 to 15, plus all other days of weeks 43 0.509 to 15 that are not in experience type 1 or 2

4 Rest of camping season 78 free

EXISTING REVENUE VS PROJECTED REVENUE FROM DISCRIMINATORY PRICING

Existing flat fee of $2.50 Discriminatory fee

Experience Campsites Campsites

type occupied Revenue occupied (est.) Revenue

1 5.891 $14,727 5,000 $30,000

2 8,978 22,445 8,500 21,250

3 6,129 15,322 15,500 7.750

4 4,979 12,447 . .

Total 25,977 $ 64,941 29,000 $59,000

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Hotel Overbooking Loss Table

Number of Reservations Overbooked

No- Prob-

shows ability 0 1 2 3 4 5 6 7 8 9

0 .07 0 100 200 300 400 500 600 700 800 900

1 .19 40 0 100 200 300 400 500 600 700 8002 .22 80 40 0 100 200 300 400 500 600 700

3 .16 120 80 40 0 100 200 300 400 500 600

4 .12 160 120 80 40 0 100 200 300 400 500

5 .10 200 160 120 80 40 0 100 200 300 400

6 .07 240 200 160 120 80 40 0 100 200 300

7 .04 280 240 200 160 120 80 40 0 100 200

8 .02 320 280 240 200 160 120 80 40 0 100

9 .01 360 320 280 240 200 160 120 80 40 0

Expected loss, $ 121.60 91.40 87.80 115.00 164.60 231.00 311.40 401.60 497.40 560.00

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Daily Scheduling of

Telephone Operator Workshifts

0

5

10

15

20

25

30

Time

Num

berofoperators

Scheduler program assigns

tours so that the number of

operators present each half

hour adds up to the number

required

Topline profile

12 2 4 6 8 10 12 2 4 6 8 10 12

Tour

0

500

1000

1500

2000

2500

Time

Calls

12 2 4 6 8 10 12 2 4 6 8 10 12

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LP Model for Weekly Workshift

Schedule with Two Days-off ConstraintObjective function:

Minimize x1 + x2 + x3 + x4 + x5 + x6 + x7

Constraints:

Sunday x2 + x3 + x4 + x5 + x6 3Monday x3 + x4 + x5 + x6 + x7 6

Tuesday x1 + x4 + x5 + x6 + x7 5

Wednesday x1 + x2 + x5 + x6 + x7 6

Thursday x1 + x2 + x3 + x6 + x7 5Friday x1 + x2 + x3 + x4 + x7 5Saturday x1 + x2 + x3 + x4 + x5 5

xi 0 and integer

Schedule matrix, x = day offOperator Su M Tu W Th F Sa

1 x x ...2 x x

3 ... x x

4 ... x x

5 x x

6 x x

7 x x

8 x x

Total 6 6 5 6 5 5 7

Required 3 6 5 6 5 5 5Excess 3 0 0 0 0 0 2

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Scheduling Part-time Bank Tellers

Objective function:Minimize x1+ x2+x3+x4+x5+x6+x7

Constraints:

Sunday x2+x3+x4+x5+x6 b1Monday x3+x4+x5+x6+x7 b2

0

1

2

3

4

5

6

7

Tellersr

equired

Mon. Tues. Wed. Thurs. Fri.

Two Full-time Tellers

54

1

3

2

1

4

3

2 1

5 2

Fri. Mon. Wed. Thurs Tues.

0

1

2

3

4

5

Tellersrequire

d

Decreasing part-time teller demand histogram

DAILY PART-TIME WORK SCHEDULE, X=workday

Teller Mon. Tues. Wed. Thurs. Fri.

1 x . x . x

2 x . . x x

3,4 x . . . x

5 . . x . x

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Seasonal Allocation of Rooms by

Service Class for Resort Hotel

First class

Standard

Budget

Percentage

ofcapac

ityallocated

to

differentservice

classes

60%

50% 30%

20%

50%

Peak Shoulder Off-peak Shoulder(30%) (20%) (40%) (10%)

Summer Fall Winter Spring

Percentage of capacity allocated to different seasons

30%20% 20%

10%30%

50% 30%

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Demand Control Chart for a Hotel

0

50

100

150

200

250

300

1 611

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

Days before arrival

Reservations

Expected Reservation Accumulation

2 standard deviation control limits

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Yield Management Using the

Critical Fractile Model

P d xC

C C

F D

p F

u

u o

( )( )

Where x= seats reserved for full-fare passengers

d= demand for full-fare tickets

p= proportion of economizing (discount) passengers

Cu = lost revenue associated with reserving one too few seats

at full fare (underestimating demand). The lost opportunity is the

difference between the fares (F-D) assuming a passenger, willing

to pay full-fare (F), purchased a seat at the discount (D) price.

Co = cost of reserving one to many seats for sale at full-fare

(overestimating demand). Assume the empty full-fare seat wouldhave been sold at the discount price. However, Co takes on two

values, depending on the buying behavior of the passenger who

would have purchased the seat if not reserved for full-fare.

if an economizing passenger

if a full fare passenger (marginal gain)

Expected value ofCo= pD-(1-p)(F-D) = pF - (F-D)

CD

F Do

( )

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Topics for DiscussionWhat organizational problems can arise from the

use of part-time employees?

How can computer-based reservation systems

increase service capacity utilization?What possible dangers are associated with

developing complementary services?

Will the widespread use of yield management

eventually erode the concept of fixed prices?

What possible negative effects can yield

management have on customer relations?

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Interactive Exercise

Watch the PowerPoint presentation

concerning the overbooking experience at

the Doubletree Hotel in Houston, Texas.

How could this situation been handled

differently?