Slide 1 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.

Slide 2 Variability – Throughput Loss

Slide 3 Lessons from Call Center Case: The Three Enemies of Operations Additional costs due to variability in demand and activity times Is associated with longer wait times and / or customer loss Requires process to hold excess capacity (idle time) Variability Use of resources beyond what is needed to meet customer requirements Not adding value to the product, but adding cost Reducing the performance of the production system 7 different types of waste WasteWorkValue- adding WasteWorkValue- adding Waste Inflexibility Additional costs incurred because of supply demand mismatches Waiting customers or Waiting (idle capacity) Capacity Customer demand

Slide 4 From Theory to Practice: How Many Patients will be Cured? Accidents Happen Ambulance Arrives Emergency Room Care Process Actual flows are determined by rolling the dice (1…6) Round 1: patients die if they are not taken care of in the same round Round 2: patients can be moved forward in the next round How many patients will be cured after 10 rounds?

Slide 5 Different Models of Variability Waiting problems Utilization has to be less than 100% Impact of variability is on Flow Time Loss problems Demand can be bigger than capacity Impact of variability is on Flow Rate Pure waiting problem, all customers are perfectly patient. All customers enter the process, some leave due to their impatience Customers do not enter the process once buffer has reached a certain limit Customers are lost once all servers are busy Same if customers are patientSame if buffer size=0 Same if buffer size is extremely large Variability is always bad – you pay through lower flow rate and/or longer flow time Buffer or suffer: if you are willing to tolerate waiting, you don’t have to give up on flow rate

Slide 6 Macro Economic Trends Driving Emergency Room Crowding and Ambulance Diversion Data from L. Green; general accounting office 20% of US hospitals are on diversion status for more than 2.4 hours per day Increase in ER visits 40% of patients admitted through the ER Decrease in number of emergency departments Consequences: –Long wait times (see waiting time analysis) –Loss of throughput (requires new analysis)

Slide 7 Analyzing Loss Systems Trauma center moves to diversion status once all servers are busy incoming patients are directed to other locations Resources 3 trauma bays (m=3) Demand Process One trauma case comes in every 3 hours (a=3 hours) a is the interarrival time Exponential interarrival times Service Process Patient stays in trauma bay for an average of 2 hours (p=2 hours) p is the service time Can have any distribution What is P m, the probability that all m resources are utilized?

Slide 8 Analyzing Loss Systems: Finding P m (r) Define r = p / a Example: r= 2 hours/ 3 hours r=0.67 Recall m=3 Use Erlang Loss Table Find that P 3 (0.67)= Given P m (r) we can compute: Time per day that system has to deny access Flow units lost = 1/a * P m (r) r = p / a m

Slide 9 Probability{all m servers busy}= Erlang Loss Table

Slide 10 Implied utilization Probability that all servers are utilized m=1 m=2 m=5 m=10 m= m=3 Implied utilization vs probability of having all servers utilized: Pooling Revisited