Managing Capacity and Demand

McGraw-Hill/Irwin Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.

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. Explain what yield management is and

how it is applied.

11-2

Level Capacity and Chase Demand

Strategic Dimension Level Capacity Chase Demand

Customer Waiting Generally Low Moderate

Employee Utilization Moderate High

Labor-skill Level High Low

Labor Turnover Low High

Training Required per Employee High Low

Working Conditions Pleasant Hectic

Supervision Required Low High

Forecasting Long-run Short-run

11-3

Strategies for Matching Capacity and Demand for Services

MANAGINGDEMAND

PartitioningdemandDeveloping

complementaryservices

Establishingprice

incentivesDevelopingreservationsystems

Promoting off-peakdemand

Yieldmanagement

MANAGINGCAPACITY

Cross-training

employees

Increasingcustomer

participationSharingcapacity

Schedulingwork shifts

Creatingadjustablecapacity

Usingpart-time

employees

11-4

Customer-induced Variability Arrival: customer arrivals are

independent decisions not evenly spaced.

Capability: level of knowledge and skills vary resulting in some hand-holding.

Request: uneven service times result from unique demands.

Effort: level of commitment to coproduction or self-service varies.

Subjective Preference: personal preferences introduce unpredictability.

11-5

Strategies for ManagingCustomer-induced Variability

Type of Variability

Accommodation Reduction

Arrival Provide generous staffing Require reservations

Capability Adapt to customer skill levels

Target customers based on capability

Request Cross-train employees Limit service breadth

Effort Do work for customers Reward increased effort

SubjectivePreference

Diagnose expectations and adapt

Persuade customers to adjust expectations

11-6

Segmenting Demand at a Health Clinic

0

20

40

60

80

100

120

140

Mon. Tue. Wed. Thur. Fri.

BeforeSmoothingAfterSmoothing

Smoothing Demand by AppointmentScheduling

Day Appointments

Monday 84Tuesday 89Wednesday 124Thursday 129Friday 114

11-7

Discriminatory Pricing for Camping

Experience 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

11-8

Hotel Overbooking Loss Table

Number of Reservations Overbooked

No- Prob-shows ability 0 1 2 3 4 5 6 7 8

90 .07 0 100 200 300 400 500 600 700 800 9001 .19 40 0 100 200 300 400 500 600 700 8002 .22 80 40 0 100 200 300 400 500 600 7003 .16 120 80 40 0 100 200 300 400 500 6004 .12 160 120 80 40 0 100 200 300 400 5005 .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

11-9

Daily Scheduling ofTelephone 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

11-10

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 off

Nurse 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

11-11

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

11-12

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

11-13

Q

P

Price

Quantity

Consumer Surplus

Seats Available

Demand Curve

Airline Pricing for a Coach SeatTraditional Fixed Price

Total Revenue = PQ

11-14

Price

Quantity

P1

P2

P3

Q1 Q2 Q3

Consumer Surplus

Advanced

Purchase

Internet

Special

FullCoach

Demand Curve

Seats Available

Airline Pricing for a Coach SeatMultiple Pricing Using Yield Management

Total Revenue = P1Q1 + (Q2-Q1)P2 + (Q3-Q2)P3

11-15

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%

11-16

Demand Control Chart for a Hotel

0

50

100

150

200

250

300

350

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89

Days before arrival

Rese

rvat

ions

Expected Reservation Accumulation

2 standard deviation control limits

11-17

Yield Management Using the Critical Fractile Model

P d xC

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

( )

11-18

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? Go to http://en.wikipedia.org/wiki/Yield_management

and discuss the ethical issues associated with yield management.

11-19

Interactive Exercise

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

11-20