Some Key Terms OIM305 #1 Spring2019 Priyank Term
Definition / Symbol
Cycle Time
(time / unit)
Average time for completion of a unit at a
production step or process
Throughput Rate
(units / time)
Average number of units processed over a
time interval
Bottleneck
Process stage with the smallest throughput
rate
Capacity
Effective
Capacity
Units per unit time that go through each
step and entire process (overall process
capacity; 𝑅𝑅)
If there is an operational construct or
constraint that necessitates correction in
capacity calculation of a task, then
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶
effective capacity = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹
Remarks
Capacity of process = Capacity of
Bottleneck
𝑇𝑇; Average time that a unit takes to go
Throughput Time
through the entire process (including
(time)
waiting time)
Work in Process
(units)
Little’s Law
Utilization
Arrival Rate
(units / time)
Average Interarrival Time
Service Rate
(units / time)
Average Service
Time
Utilization of
Queue’s
Resources
Level of
Satisfaction (S)
𝐼𝐼; Average number of units in the system
at a point in time
𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊 𝑖𝑖𝑖𝑖 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃
Throughput Time = 𝑇𝑇ℎ𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟ℎ𝑝𝑝𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
Time resource is active / total time
Capacity of Bottleneck
resource is available = Capacity of task
(Lambda) ; For M/M/x queues, it is the
rate of the exponential distribution of
inter-arrival times
Also, termed as the expected time
1
between arrivals = 𝐸𝐸(𝑇𝑇) = 𝜆𝜆
(Mu) &micro;; For M/M/x queues, it is the rate
of the exponential distribution of service
times
Also, termed as the expected time taken to
1
process a service request = 𝐸𝐸(𝑆𝑆) = 𝜇𝜇
𝜆𝜆
(Rho)  = 𝑠𝑠𝑠𝑠, where s denotes number of
servers = 1, 2, 3…
= Perception (P) – Expectation (E)
𝐼𝐼 = 𝑅𝑅 ∗ 𝑇𝑇
Never exceeds 100%
If inter-arrival times are
exponentially distributed with rate ,
then number of arrivals follow a
Poisson distribution (with rate )
Stability Condition: 𝜌𝜌 &lt; 1;
Idle Time = 1 − 𝜌𝜌
The Psychology of Waiting
OIM 305 – Spring 2019 – Useful Terms – Arora