The key idea of the Goal is to clarify the importance of strategic capacity planning and constraint management . The background of the goal is Alex Rogo manages a production plant which faces the bankrupt financial crisis. --After Alex’s conversation with Jonah, we know the goal of any business is to make money.

--Bottlenecks:
The book points out bottlenecks is one process in a chain of processes which is measured and controlled by variations on three measures: throughput, inventory and operational expense. And the bottleneck’s speed of production is what determines the speed of the other dependents. We should test quality control before going into the bottleneck because an hour lost at a bottleneck is an hour lost at the whole system. Focused on capacity, the company should increase throughput, decrease inventory and operational expense to make more money. During a hiking trip with Alex’s son, he produces a game for a few of the kids to demonstrate an ideal balance line of production. And we learned supply should be less than demand to make sure demand is going to decrease in market economy. --dependant events

a event is going to happen if and only if a series of events have happened --statistical fluctuation
the speed of the kids is not always same, production process is not always at the same speed. --break bottlenecks:
1. Identify the system's bottlenecks
2. how to get the most out of the bottleneck
3. Subordinate everything else to the above decision
4. Elevate the system's bottleneck
5. If the bottleneck has broken in the step 4 go back to step 1 --the proper way to manage any operation:
1.Identify what needs to be changed
2.Identify what are going to be changed to
3. How to execute the change

...ISyE3232
J. Reed
Stochastic Manufacturing and Service Systems
Fall 2005
Homework 7
November 22, 2005
Due at the start of class on Thursday, December 1st.
1. Suppose there are two tellers taking customers in a bank. Service times at a teller are independent, exponentially distributed random variables, but the ﬁrst teller has a mean service
time of 4 minutes while the second teller has a mean of 7 minutes. There is a single queue for
customers awaiting service. Suppose at noon, 3 customers enter the system. Customer A goes
to the ﬁrst teller, B to the second teller, and C queues. To standardize the answers, let us
assume that TA is the length of time in minutes starting from noon until Customer A departs,
and similarly deﬁne TB and TC .
(a) What is the probability that Customer A will still be in service at time 12:05?
(b) What is the expected length of time that A is in the system?
(c) What is the expected length of time that A is in the system if A is still in the system at
12:05?
(d) How likely is A to ﬁnish before B?
(e) What is the mean time from noon until a customer leaves the bank?
(f) What is the average time until C starts service?
(g) What is the average time that C is in the system?
(h) What is the average time until the system is empty?
(i) What is the probability that C leaves before A given that B leaves before A?
(j) What are the probabilities that A leaves last, B leaves last, and C leaves last?
(k)...

...ISYE 3770 B
Wednesday Jan 22
Quiz 1
Your name (please print): Solution Key
1.
Consider the following hybrid reliability system. The number in each box indicates the component’s
reliability (probability of working). Assume components fail independently. What is the probability that
the entire system works? (only write down the expression)
P(works) = P(A)*P(B) + P(C)*P(D)*P(E) – P(A)*P(B)*P(C)*P(D)*P(E)
= 0.7*0.7 + 0.8*0.8*0.8 – 0.7*0.7*0.8*0.8*0.8
2.
Finish the following Bayes theorem (only the basic version, not with total probability rule):
For two events A and B, with P(A) > 0 and P(B) > 0,
P(A|B) = P(B|A) * P(A) / P(B)
3.
The probability that a regularly scheduled flight departs on time is P(D)=0.83; the probability that it arrives
on time is P(A)=0.82; and the probability that it arrives on time given that it departed on time is
P(A|D)=0.94. Find the probability that a plane departs on time given that it arrives on time. (only write
down the expression)
P(D|A) = P(A|D)*P(D) / P(A) = 0.94*0.83 / 0.82
4.
A box contains 3 blue and 2 red pens while another box contains 2 blue and 5 red pens. A pen drawn at
random from one of the boxes turns out to be blue. What is the probability that it came from the first box?
(only write down the expression)
P(first|blue) = P(blue|first) * P(first)/P(blue)
= [3/(3+2) ]* [(3+2)/(3+2+2+5)] / [(3+2)/(3+2+2+5)]
5.
A random variable must be: (1) random, (2) variable (i.e. a...