Matching Supply with Demand:An Introduction to Operations Management

Gérard Cachon ChristianTerwiesch

All slides in this file are copyrighted by Gerard Cachon and Christian Terwiesch. Any instructor that adopts Matching Supply with

Demand: An Introduction to Operations Management as a required text for their course is free to use and modify these slides as desired. All others must obtain explicit written permission from the authors to

use these slides.

Trauma center moves to diversion status once all servers are busy (incoming patients are directed to other locations)

Figure 7.1.: Process flow diagram for trauma center

3 trauma bays

Figure 7.2.: Implied utilization vs probability of having all servers utilizedImplied utilization

Probabilitythat all serversare utilized

m=1m=2

m=5 m=10

m=200

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

m=3

Figure 7.3: Impact of buffer size on the probability Pm for various levels of implied utilization as well as on the throughput of the process in the case of one single server

0

0.1

0.2

0.3

0.4

0.5

1 2 3 4 5 6 7 8 9 10 11

Probabilitythat system isfull, Pm

Increasing levelsof utilization

Size of the buffer space

Percentageof demand rate

Increasing levelsof utilization

Size of the buffer space

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11

Figure 7.4.: Impact of waiting time on customer loss

Average wait time [seconds]

Fraction of customer lost

Inflow

Figure 7.5.: A serial queuing system with three resources

Outflow

Outflow of resource 1 =Inflow of resource 2

Upstream Downstream

Inflow

Figure 7.6.: The concepts of blocking and starving

Outflow

Activity completed

Outflow

Resource is blocked

Inflow

Resource is starvedActivity notyet completed Empty space for a flow unit

Space for a flow unit with a flow unitin the space

Figure 7.7.: Flow rate compared at four configurations of a queuing system

Sequential system, no buffersCycle time=11.5 minutes

Sequential system, one buffer space eachCycle time=10 minutes

(1) (1)

Sequential system, unlimited buffersCycle time=7 minutes; inventory “explodes”

Horizontally pooled systemCycle time=19.5/3 minutes=6.5 minutes

6.5 min/unit 7 min/unit 6 min/unit

6.5 min/unit 7 min/unit 6 min/unit

6.5 min/unit 7 min/unit 6 min/unit

3 resources, 19.5 min/ unit each

Waitingproblem Loss

problem

Pure waitingproblem, all customersare perfectly patient.

All customers enter the process,some leave due totheir impatience

Customers do notenter the process oncebuffer has reached a certain limit

Customers are lostonce all servers arebusy

Same if customers are patient Same if buffer size=0

Same if buffer size is extremely large

Figure 7.8.: Different types of variability problems