1Operations Strategy 2Process Analysis 3Lean Operations 4Supply Chain Management

OM&PM/Class 6b 1

1 Operations Strategy

2 Process Analysis

3 Lean Operations

4 Supply Chain Management

5 Capacity Management in Services– Class 6b: Capacity Analysis and Queuing

» Why do queues build up?

» Performance measures for queuing systems

» The need for safety capacity

» Throughput of queuing system with finite buffer

» Pooling of capacity

6 Total Quality Management

7 Business Process Reengineering

Operations Management & Performance Modeling

OM&PM/Class 6b 5

Telemarketing at L.L.Bean

During some half hours, 80% of calls dialed received a busy signal.

Customers getting through had to wait on average 10 minutes for an available agent. Extra telephone expense per day for waiting was $25,000.

For calls abandoned because of long delays, L.L.Bean still paid for the queue time connect charges.

In 1988, L.L.Bean conservatively estimated that it lost $10 million of profit because of sub-optimal allocation of telemarketing resources.

OM&PM/Class 6b 6

Telemarketing: deterministic analysis

it takes 8 minutes to serve a customer

6 customers call per hour – one customer every 10

minutes

Flow Time = 8 min

Flow Time Distribution

Flow Time (minutes)

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OM&PM/Class 6b 7

Telemarketing with variability inarrival times + activity times

In reality service times– exhibit variability

In reality arrival times– exhibit variability

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OM&PM/Class 6b 8

Telemarketing with variability: The effect of utilization

Average service time = – 9 minutes

Average service time =– 9.5 minutes

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OM&PM/Class 6b 9

Why do queues form?

utilization: – throughput/capacity

variability: – arrival times

– service times

– processor availability

0123456789

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OM&PM/Class 6b 10

Industry Process AverageCycle Time

TheoreticalCycle Time

Process Efficiency

Life Insurance New PolicyApplication

72 hrs. 7 min. 0.16%

ConsumerPackaging

NewGraphicDesign

18 days 2 hrs. 0.14%

CommercialBank

ConsumerLoan

24 hrs. 34 min. 2.36%

Hospital PatientBilling

10 days 3 hrs. 3.75%

AutomobileManufacture

FinancialClosing

11 days 5 hrs 5.60%

Cycle Times in White Collar Processes

OM&PM/Class 6b 11

Queuing Systems to model Service Processes: A Simple Process

Sales Repsprocessing

calls

Incoming callsCalls

on Hold

Answered Calls

MBPF Inc. Call Center

Blocked Calls(Busy signal)

Abandoned Calls(Tired of waiting)

Order Queue“buffer” size K

OM&PM/Class 6b 12

What to manage in such a process?

Inputs– InterArrival times/distribution

– Service times/distribution

System structure– Number of servers

– Number of queues

– Maximum queue length/buffer size

Operating control policies – Queue discipline, priorities

OM&PM/Class 6b 13

Performance Measures

Sales– Throughput R

– Abandonment

Cost– Server utilization – Inventory/WIP : # in queue/system

Customer service– Waiting/Flow Time: time spent in queue/system

– Probability of blocking

OM&PM/Class 6b 14

Queuing Theory:Variability + Utilization = Waiting

Throughput-Delay curve:

Pollaczek-Khinchine Form:– Prob{waiting time in queue < t } = 1 - exp(-t / Ti ) where:

Variability

TheoreticalCycle Time

ActualAverageCycleTime, W

Utilization 100%

m

21

122pi

pi

CC

RT

mean service time

utilization effect

variability effectx x

OM&PM/Class 6b 15

Levers to reduce waiting and increase QoS: variability reduction + safety capacity

How reduce system variability?

Safety Capacity = capacity carried in excess of expected demand to cover for system variability– it provides a safety net against higher than expected arrivals

or services and reduces waiting time

OM&PM/Class 6b 16

Example 1: MBPF Calling Centerone server, unlimited buffer

Consider MBPF Inc. that has a customer service representative (CSR) taking calls. When the CSR is busy, the caller is put on hold. The calls are taken in the order received.

Assume that calls arrive exponentially at the rate of one every 3 minutes. The CSR takes on average 2.5 minutes to complete the reservation. The time for service is also assumed to be exponentially distributed.

The CSR is paid $20 per hour. It has been estimated that each minute that a customer spends in queue costs MBPF $2 due to customer dissatisfaction and loss of future business.– MBPF’s waiting cost =

OM&PM/Class 6b 17

Example 2: MBPF Calling Center limited buffer size

In reality only a limited number of people can be put on hold (this depends on the phone system in place) after which a caller receives busy signal. Assume that at most 5 people can be put on hold. Any caller receiving a busy signal simply calls a competitor resulting in a loss of $100 in revenue.

– # of servers c = 1

– buffer size K = 6 What is the hourly loss because of callers not being able to get

through?

OM&PM/Class 6b 18

Example 3: MBPF Calling CenterResource Pooling

2 phone numbers– MBPF hires a second CSR who is

assigned a new telephone number. Customers are now free to call either of the two numbers. Once they are put on hold customers tend to stay on line since the other may be worse ($111.52)

1 phone number: pooling– both CSRs share the same

telephone number and the customers on hold are in a single queue ($61.2)

Servers

Queue

ServerQueue

ServerQueue

50%

50%

OM&PM/Class 6b 19

Example 4: MBPF Calling CenterStaffing

Assume that the MBPF call center has a total of 6 lines. With all other data as in Example 2, what is the optimal number of CSRs that MBPF should staff the call center with?– c = 3

OM&PM/Class 6b 20

Class 6b Learning objectives

Queues build up due to variability.

Reducing variability improves performance.

If service cannot be provided from stock, safety capacity must be provided to cover for variability.

Tradeoff is between cost of waiting, lost sales, and cost of capacity.

Pooling servers improves performance.

OM&PM/Class 6b 21

National Cranberry Cooperative

Hourly Berry Arrivals

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OM&PM/Class 6b 22

Real Processes exhibit variability in order placement time and type

Histogram of Truck inter-delivery times

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Histogram of Truck Weights

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National Cranberry on Sept 23, 1970