OM3 C07 Solved Problems

Solved Problem
An inspection station for assembling printers receives 40
printers/hour and has two inspectors, each of whom can inspect
30 printers per hour. What is the utilization of the inspectors?
What service rate would be required to have a target utilization of
85 percent?
The labor utilization at this inspection station is calculated to be
40/(2 × 30) = 67%. If the utilization rate is 85%, we can
calculate the target service rate by solving the equation:
85% = 40/(2 × SR)
1.7 × SR = 40
SR = 23.5 printers/hour
Process Design and Resource Utilization
• The average number of entities completed per unit time—
the output rate—from a process is called throughput.
Throughput might be measured as parts per day, transactions per
minute, or customers per hour, depending on the context.
A bottleneck is the work activity that effectively limits throughput of the
entire process.
Identifying and breaking process bottlenecks is an important part of
process design and improvement, and will increase the speed of the
process, reduce waiting and work-in-process inventory, and use
resources more efficiently.
Little’s Law
Flow time, or cycle time, is the average time it takes to
complete one cycle of a process.
Little’s Law is a simple formula that explains the
relationship among flow time (T ), throughput (R ), and
work-in-process (WIP ).
Work-In-Process = Throughput × Flow Time
WIP = R × T
If we know any two of the three variables, we can compute the third.
Solved Problem
Suppose that a voting facility processes an average of
50 people per hour and that, on average, it takes 10
minutes. What is the average number of voters in the
process? for each person to complete the v
WIP = R  T
= 50 voters/hr  (10 minutes/60 minutes per hour)
= 8.33 voters
Solved Problem
Suppose that the loan department of a bank takes an
average of 6 days (0.2 months) to process an
application and that an internal audit found that about
100 applications are in various stages of processing at
any one time. Using Little’s Law, we see that T = 0.2
and WIP = 100. What is the throughput? the v
R = WIP/T = 100 applications/0.2 months
= 500 applications per month
Solved Problem
Suppose that a restaurant makes 400 pizzas per week,
each of which uses one-half pound of dough, and that
it typically maintains an inventory of 70 pounds of
dough. In this case, R = 200 pounds per week of
dough and WIP = 70 pounds. What is the average flow
T = WIP/R = 70/200
= 0.35 weeks, or about 21/2 days.

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