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ISM 270. Service Engineering and Management Lecture 7: Forecasting and Managing Service Capacity. Announcements. Project Proposal Due today Homework 4 due next week $15 check for ‘Responsive Learning Technologies’ Final four weeks: Capacity Planning Outsourcing Capacity Management Game

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Ism 270

ISM 270

Service Engineering and Management

Lecture 7: Forecasting and Managing Service Capacity


Announcements

Announcements

  • Project Proposal Due today

  • Homework 4 due next week

  • $15 check for ‘Responsive Learning Technologies’

  • Final four weeks:

    • Capacity Planning

    • Outsourcing

    • Capacity Management Game

    • Project Presentations


Today

Today

  • Capacity Management

  • QueueingModels

  • Introduction to R


Managing waiting lines queueing models

Managing Waiting Lines – Queueing Models


Essential features of queuing systems

Essential Features of Queuing Systems

Renege

Arrival

process

Queue

discipline

Departure

Calling

population

Service

process

Queue

configuration

No future

need for

service

Balk


Arrival process

Arrival Process

Arrival

process

Static

Dynamic

Random

arrivals with

constant rate

Random arrival

rate varying

with time

Facility-

controlled

Customer-

exercised

control

Accept/Reject

Price

Appointments

Reneging

Balking


Distribution of patient interarrival times

Distribution of Patient Interarrival Times


Temporal variation in arrival rates

Temporal Variation in Arrival Rates


Poisson and exponential equivalence

Poisson and Exponential Equivalence

Poisson distribution for number of arrivals per hour (top view)

One-hour

1 2 0 1 interval

Arrival Arrivals Arrivals Arrival

62 min.

40 min.

123 min.

Exponential distribution of time between arrivals in minutes (bottom view)


Queue configurations

Queue Configurations

Multiple Queue Single queue

Take a Number

Enter

3

4

2

8

6

10

12

7

11

9

5


Queue discipline

Queue Discipline

Queue

discipline

Static

(FCFS rule)

Dynamic

selection

based on status

of queue

Selection based

on individual

customer

attributes

Number of

customers

waiting

Round robin

Priority

Preemptive

Processing time

of customers

(SPT rule)


Queuing formulas

Queuing Formulas

Single Server Model with Poisson Arrival and Service Rates: M/M/1

1. Mean arrival rate:

2. Mean service rate:

3. Mean number in service:

4. Probability of exactly “n” customers in the system:

5. Probability of “k” or more customers in the system:

6. Mean number of customers in the system:

7. Mean number of customers in queue:

8. Mean time in system:

9. Mean time in queue:


Queuing formulas cont

Queuing Formulas (cont.)

Single Server General Service Distribution Model: M/G/1

Mean number of customers in queue for two servers: M/M/2

Relationships among system characteristics (Little’s Law for ALL queues):


Congestion as

Congestion as

100

10

8

6

4

2

0

With:

  • Then:

0 0

0.2 0.25

0.5 1

0.8 4

0.9 9

0.99 99

0 1.0


Single server general service distribution model m g 1

Single Server General Service Distribution Model : M/G/1

1. For Exponential Distribution:

2. For Constant Service Time:

3. Conclusion:

Congestion measured by Lqis accounted for equally by

variability in arrivals and service times.


Queuing system cost tradeoff

Queuing System Cost Tradeoff

Let: Cw = Cost of one customer waiting in queue for an hour

Cs = Hourly cost per server

C = Number of servers

Total Cost/hour = Hourly Service Cost + Hourly Customer Waiting Cost

Total Cost/hour = Cs C + Cw Lq

Note: Only consider systems where


General queuing observations

General Queuing Observations

1. Variability in arrivals and service times contribute equally to

congestion as measured by Lq.

2. Service capacity must exceed demand.

3. Servers must be idle some of the time.

4. Single queue preferred to multiple queue unless jockeying

is permitted.

5. Large single server (team) preferred to multiple-servers if

minimizing mean time in system, WS.

6. Multiple-servers preferred to single large server (team) if

minimizing mean time in queue, WQ.


Managing capacity and demand

Managing Capacity and Demand


Segmenting demand at a health clinic

Segmenting Demand at a Health Clinic

Smoothing Demand by Appointment

Scheduling

Day Appointments

Monday 84

Tuesday 89

Wednesday 124

Thursday 129

Friday 114


Hotel overbooking loss table

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

Daily Scheduling of Telephone Operator Workshifts

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

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


Lp model for weekly workshift schedule with two days off constraint

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

Schedule matrix, x = day off

Operator Su M Tu W Th F Sa

1 xx … … … … ... 2 … xx … … … …

3 … ... xx … … …

4 … ... xx … … …

5 … … … … xx …

6 … … … … xx …

7 … … … … xx …

8 x … … … … … x

Total 6 6 5 6 5 5 7

Required 3 6 5 6 5 5 5

Excess 3 0 0 0 0 0 2


Seasonal allocation of rooms by service class for resort hotel

Seasonal Allocation of Rooms by Service Class for Resort Hotel

First class

Standard

Budget

20%

20%

20%

30%

50%

30%

50%

60%

Percentage of capacity allocated

to different service classes

50%

30%

30%

10%

Peak Shoulder Off-peak Shoulder

(30%) (20%) (40%) (10%)

Summer Fall Winter Spring

Percentage of capacity allocated to different seasons


Demand control chart for a hotel

Demand Control Chart for a Hotel

Expected Reservation Accumulation

2 standard deviation control limits


Yield management using the critical fractile model

Yield Management Using the Critical Fractile Model

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 would

have 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 of Co = pD-(1-p)(F-D) = pF - (F-D)


Statistical analysis in r

Statistical Analysis in R

  • Homework 4 is designed to introduce you to analysis using R


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