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Operations Management Waiting LinesPowerPoint Presentation

Operations Management Waiting Lines

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**Leo** - Follow User

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Operations Management Waiting Lines. Example: A Deterministic System. Questions: Can we process the orders? How many orders will wait in the queue? How long will orders wait in the queue? What is the utilization rate of the facility?. A Deterministic System: Example 1.

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### Operations ManagementWaiting Lines

Example: A Deterministic System

- Questions:
- Can we process the orders?
- How many orders will wait in the queue?
- How long will orders wait in the queue?
- What is the utilization rate of the facility?

Utilization

- Arrival rate = 1/10 per minutes
- Processing rate = time 1/9 per minute
- Utilization – AR/PR = (1/10)/(1/9) = 0.9 or 90%
- On average 0.9 person is in the system

Known but Uneven Demand: Example 2

- What if arrivals are not exactly every 10 minutes?
- Let’s open the spreadsheet.

A Deterministic System: Example 2

Observations:

- Utilization is below 100% (machine is idle 14% of the time).
- There are 1.12 orders (on average) waiting to be processed.

A Deterministic System: Example 2

- Why do we have idleness (low utilization) and at the same time orders are waiting to be processed?
- Answer: Variability

Known but Uneven Demand: Example 2

- How to measure variability?
- Coefficient of variation:
CV = Standard Deviation / Mean

Uncertain Demand (Interarrival times): Example 3

- The interarrival time is either 5 periods with probability 0.5 or 15 periods with probability 0.5
- Notice that the mean interarrival time is 10. (mean interarrival = 0.5 * 15 + 0.5 * 5 = 10)

- The service time is 9 periods (with certainty).
- The only difference between example 3 and 1 is that the interarrival times are random.

Uncertain Demand ( Example 3Interarrival times): Example 3

(Recall that in Example 1, no job needed to wait.)

Uncertain Demand (Inter-arrival times): Example 3 Example 3

- Suppose we change the previous example and assume:
- Inter-arrival time 17 0.5 probability
- Inter-arrival time 3 0.5 probability
- Average inter-arrival times as before 10 min.

Uncertain Demand ( Example 3Interarrival times): Example 3

The effect of variability: higher variability in inter-arrival times results in higher average # in queue.

Can we reduce demand variability/ Example 3uncertainty?

- Can we manage demand?
- What are other sources of variability/uncertainty?

Uncertain Demand (Inter-arrival times) Example 3

- Up to now, our service time is exactly 9 minutes.
- What will happen to waiting-line and waiting-time if we have a short service time (i.e., we have a lower utilization rate)?
- What will happen if our service time is longer than 10 minutes?

Key Concepts and Issues Example 3

- The factors that determine the performance of the waiting lines:
- Variability
- Utilization rate
- Risk pooling effect

Rule 1 Example 3

- In general, if the variability, or the uncertainty, of the demand (arrival) or service process is large, the queue length and the waiting time are also large.

Rule 2 Example 3

- As the utilization increases the waiting time and the number of orders in the queue increases exponentially.

Rule 3 Example 3

- In general, pooling the demand (customers) into one common line improves the performance of the system.

Arrival Rate at an Airport Security Check Point Example 3

What is the queue size?

What is the capacity utilization?

Flow Times with Arrival Every 6 Secs Example 3

What is the queue size?

What is the capacity utilization?

Flow Times with Arrival Every 6 Secs Example 3

What is the queue size?

What is the capacity utilization?

Flow Times with Arrival Every 6 Secs Example 3

What is the queue size?

What is the capacity utilization?

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