# Operations Management Waiting Lines - PowerPoint PPT Presentation

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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 Management Waiting Lines

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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?

### 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?

### 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 (Interarrival times): Example 3

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

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

• Suppose we change the previous example and assume:

• Inter-arrival time170.5 probability

• Inter-arrival time 30.5 probability

• Average inter-arrival times as before 10 min.

### Uncertain Demand (Interarrival times): Example 3

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

### Can we reduce demand variability/uncertainty?

• Can we manage demand?

• What are other sources of variability/uncertainty?

### Uncertain Demand (Inter-arrival times)

• 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

• The factors that determine the performance of the waiting lines:

• Variability

• Utilization rate

• Risk pooling effect

### Rule 1

• 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

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

### Rule 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

What is the queue size?

What is the capacity utilization?

### Flow Times with Arrival Every 6 Secs

What is the queue size?

What is the capacity utilization?

### Flow Times with Arrival Every 6 Secs

What is the queue size?

What is the capacity utilization?

### Flow Times with Arrival Every 6 Secs

What is the queue size?

What is the capacity utilization?