Variability and the OM triangle

Question 1

DISCRETE RV

Answer 1

Countable Values: The outcomes are finite or countably infinite (e.g., 0, 1, 2, …).

Question 2

CONTINUOUS RV

Answer 2

Values are uncountable and can take any value within a range (e.g., height, temperature).

Question 3

Cumulative Distribution Function (CDF)

Answer 3

describes the probability that a random variable 𝑋 takes on a value less than or equal to a certain value
x. P(X≤x) is the probability that
𝑋 is less than or equal to 𝑥
x.

Question 4

PREDICTABLE VARIABILITY

Answer 4

Knowable changes in input or capacity rates. Can be controlled by making changes to the system.

Question 5

UNPREDICTABLE VARIABILITY

Answer 5

Unknowable changes in input and or capacity rates. Expressed with probabilty distribution

Question 6

PREDICTABLE AND UNPREDICTABLE VARIABILITY

Answer 6

Both types of variability exist simultaneously

Question 7

What are the effects of input variability without a buffer ?

Answer 7

1. Input may be wasted - Resources are underutilized due to inefficiencies
2. Reduced throughput - The overall output of the process decreases
3. Lower throughput leads to - Lost customers and revenue, customer disatisfaction, Less utilization of resources

Question 8

When the arrival rate of customers is unpredictable, what could you do to increase throughput?

Answer 8

Add Buffer or Increase Capacity

Question 9

THE OPERATIONS MANAGEMENT (OM) TRIANGLE

Answer 9

1. CAPACITY - The ability to handle increased production or demand
2. INVENTORY - Resources held to buffer against variability or demand fluctuations
3. INFORMATION - Knowledge about the system and its variability to improve decision making

Question 10

STRATEGIES TO RESPOND TO VARIABILITY

Answer 10

1. INVENTORY- Let the queue (inventory) build up to absorb variability. This approach deals with variability by holding extra resources, but it can increase costs or delay flow time.
2. CAPACITY- Increase capacity to handle higher variability.
3. INFORMATION - Reduce uncertainty by understanding and predicting variability. This strategy minimizes reliance on buffers and optimizes the process based on data.

Question 11

Iq

Answer 11

Queue length

Question 12

Tq

Answer 12

Waiting time

Question 13

Ts

Answer 13

Service Time

Question 14

Flow Time ( 𝑇 )

Answer 14

Total time a customer spends in the system, including both waiting (𝑇𝑞) and service (𝑇𝑠).
𝑇 = 𝑇𝑞 + 𝑇𝑠

Question 15

Throughput Rate (λ)

Answer 15

Rate at which customers/items are processed (flow rate through the system).

Question 16

Inventory (𝐼)

Answer 16

Total number of customers/items in the system:
𝐼= 𝐼𝑞 + 𝐼𝑠

Question 17

Little’s Law

Answer 17

Iq =λTq (Inventoryinqueue)
𝐼𝑠 = 𝜆𝑇𝑠 (Inventoryinservice)
𝐼 =𝜆𝑇 (Totalinventoryinthesystem)

Question 18

μ

Answer 18

Service rate (processing capacity of the server)

Question 19

Utilization (ρ)

Answer 19

Represents how much of the server’s capacity is being utilized:
𝜌 = 𝜆 /𝜇
The system is stable when
𝜌 < 100%

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Question 20

Safety Capacity

Answer 20

SafetyCapacity = μ − λ

The difference between the server’s capacity and the actual arrival rate

Question 21

K

Answer 21

Buffer Capacity

Question 22

C

Answer 22

Number of servers in the resource pool