Managing Capacity and Demand

Learning Objectives

Describe the strategies for matching capacity and demand for services.

Recommend an overbooking strategy. Use Linear Programming to prepare a

weekly workshift schedule. Prepare a work schedule for part-time

employees. Use yield management.

Strategies for Matching Supply and Demand for Services

DEMANDSTRATEGIES

PartitioningdemandDeveloping

complementaryservices

Establishingprice

incentivesDevelopingreservationsystems

Promoting off-peakdemand

Yieldmanagement

SUPPLYSTRATEGIES

Cross-training

employees

Increasingcustomer

participationSharingcapacity

Schedulingwork shifts

Creatingadjustablecapacity

Usingpart-time

employees

Segmenting Demand at a Health Clinic

60

70

80

90

100

110

120

130

140

1 2 3 4 5

Day of week

Perc

enta

ge o

f ave

rage

dail

y ph

ysici

an vi

sits

Smoothing Demand by AppointmentScheduling

Day Appointments

Monday 84Tuesday 89Wednesday 124Thursday 129Friday 114

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 0.50

9 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

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 0 100 200 300 400 500 600 700 800

2 .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

Daily Scheduling of Telephone Operator Workshifts

0

5

10

15

20

25

30

Time

Num

ber o

f ope

rato

rs

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

Cal

ls

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

LP Model for Weekly Workshift Schedule with Two Days-off Constraint

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

Constraints: Sunday x2 + x3 + x4 + x5 + x6

3 Monday 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 5 Friday x1 + x2 + x3 + x4 + x7

5 Saturday 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 … … … … … xTotal 6 6 5 6 5 5 7Required 3 6 5 6 5 5 5Excess 3 0 0 0 0 0 2

Scheduling Part-time Bank Tellers

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

Constraints: Sunday x2+x3+x4+x5+x6 b1

Monday x3+x4+x5+x6+x7 b2

0

1

2

3

4

5

6

7

Tel

lers

req

uire

d

Mon. Tues. Wed. Thurs. Fri.

Two Full-time Tellers

54

1

32

1

432 1

5 2

Fri. Mon. Wed. Thurs Tues. 0

1

2

3

4

5

Te

llers

re

qu

ired

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

Ideal Characteristics for Yield Management

Relatively Fixed Capacity Ability to Segment Markets Perishable Inventory Product Sold in Advance Fluctuating Demand Low Marginal Sales Cost and High

Capacity Change Cost

Seasonal Allocation of Rooms by Service Class for Resort Hotel

First class

Standard

Budget

Per

cent

age

of c

apac

ity a

lloca

ted

to d

iffer

ent s

ervi

ce c

lass

es

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%

Demand Control Chart for a Hotel

0

50

100

150

200

250

300

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86

Days before arrival

Rese

rvat

ions

Expected Reservation Accumulation

2 standard deviation control limits

Yield Management Using the Critical Fractile Model

P d x

C

C C

F D

p Fu

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 seatsat full fare (underestimating demand). The lost opportunity is the difference between the fares (F-D) assuming a passenger, willingto 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 twovalues, depending on the buying behavior of the passenger whowould have purchased the seat if not reserved for full-fare. if an economizing passenger if a full fare passenger (marginal gain)Expected value of Co = pD-(1-p)(F-D) = pF - (F-D)

CD

F Do

( )

Topics for Discussion What 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?

Interactive Exercise

Watch the PowerPoint presentation concerning the overbooking experience at the Doubletree Hotel in Houston, Texas. How could this situation been handled differently?