Multi-Stage Control and Scheduling
Lecturer: Stanley B. Gershwin
Denitions
Events may be controllable or not, and predictable
or not.
controllable uncontrollable
predictable loading a part
lunch
unpredictable
?
machine failure
Denitions
Scheduling is th
Optimization
Lecturer: Stanley B. Gershwin
Purpose of
Optimization
Choosing the best of a set of alternatives.
Applications:
investment, scheduling, system design, product
design, etc., etc.
Optimization is sometimes called mathematical
programming .
Pur
Probability
Lecturer: Stanley B. Gershwin
Probability and
Statistics
Trick Question
I ip a coin 100 times, and it shows heads ever y time.
Question: What is the probability that it will show
heads on the next ip?
Probability and
Statistics
Probability = S
Quality / Quantity Interactions
Lecturer: Stanley B. Gershwin
Goals of Talk
To show that there is great advantage in treating
quality and quantity simultaneously in the design
and operation of manufacturing systems.
To report on M IT research.
Collaborato
Queues
Lecturer: Stanley B. Gershwin
Stochastic
processes
t is time.
X () is a stochastic process if X (t) is a random
variable for ever y t.
t is a scalar it can be discrete or continuous.
X (t) can be discrete or continuous, scalar or vector.
Stocha
Introduction to Simulation
Lecturer: Stanley B. Gershwin
What is
Simulation?
A computer simulation is a computer program .
that calculates a hard-to-calculate quantity using
statistical techniques; OR
that models the behavior of a system by imitating
in
Single-part-type, multiple stage systems
Lecturer: Stanley B. Gershwin
Flow Line
. also known as a Production or Transfer Line.
M1
B1
M2
Machine
B2
M3
B3
M4
B4
M5
B5
M6
Buffer
Machines are unreliable.
Buffers are nite.
In many cases, the operation time
Statistical Inference
Lecturer: Prof. Duane S. Boning
1
Agenda
1. Review: Probability Distributions & Random Variables
2. Sampling: Key distributions arising in sampling
Chi-square, t, and F distributions
3. Estimation:
Reasoning about the population base
Toyota Production System
Lecturer: Stanley B. Gershwin
TPS
Primary source: Toyota Production System by Yasuhiro
Monden
See also: Decoding the DNA of the Toyota Production
System by Steven Spear and H. Kent Bowen, Harvard
Business Review , September-Octo
Useful Distributions
Chuan Shi
Suppose we have a population X N (, 2 ), and x1 , x2 , , xn is a n size sample of the
population. The mean and variance of the sample are given as:
x=
n
n
1
1
xi and s2 =
(xi x)2
n i=1
n 1 i=1
(1 )
The following distributio
Single-stage, multiple-part-type systems
Lecturer: Stanley B. Gershwin
Setups
Setup: A setup change occurs when it costs more
to make a Type j par t after making a Type i par t
than after making a Type j par t.
Examples:
Tool change (when making holes)
Material Requirements Planning
Lecturer: Stanley B. Gershwin
MRP Overview
Primary source: Factory Physics by Hopp and
Spearman.
Basic idea: Once the nal due date for a product is
known, and the time required for each production
step is known, then inter
Probability Estimation Through the Indicator Function
System Reliability Example With Crystal Ball
Same Seed to Compare Alternatives
Modeling Correlation Between Random Numbers
Option Pricing using Crystal Ball
Probability Estimation Through E[IA]
Pr
X, Y independent cov(X, Y ) = 0
Assume random variables X and Y are discrete. That is, assume that there is a nite or
denumerable sample space which is a set of i and a set of quantities xi and yi dened.
Denition X and Y are independent if
prob(X = x) and
Forecasting
Lecturer: Prof. Duane S. Boning
Rev 8
1
Regression Review & Extensions
Single Model Coefficient: Linear Dependence
Slope and Intercept (or Offset):
Polynomial and Higher Order Models:
Multiple Parameters
Key point: linear regression can b
Notes for Lecture 3
Chuan Shi
Example of Independence
A = cfw_i = 2 or 3 ;
B = cfw_ j = 1 or 5 or 6 .
Thus, we have
A B = cfw_(2,1), (3,1), (2, 5), (3, 5), (2, 6), (3, 6) .
So, we can compute the following:
P ( A) = 12 / 36 = 1/ 3 ;
P ( B) = 18 / 36 = 1 /
Manufacturing Systems Overview
Lecturer: Stanley B. Gershwin
http:/web.mit.edu/manuf-sys
http:/web.mit.edu/chuanshi/www/
Background
HP Printer Case
In 1993, the ink-jet printer market was taking off
explosively, and manufacturers were competing
intensive
Inventory
Lecturer: Stanley B. Gershwin
Storage
Storage is fundamental in nature, management, and
engineering.
In nature, energy is stored. Life can only exist if the
acquisition of energy can occur at a different time from the
the expenditure of energy
KKT Examples
Stanley B. Gershwin
Massachusetts Institute of Technology
The purpose of this note is to supplement the slides that describe the Karush-Kuhn-Tucker
conditions. Neither these notes nor the slides are a complete description of these conditions;
LP Example
Stanley B. Gershwin
Massachusetts Institute of Technology
Consider the factory in Figure 1 that consists of three parallel machines. It makes a single
product which can be produced using any one of the machines. The possible material ows are
in
M/M/1 Queue
Chuan Shi
We learned M/M/1 queue in Queueing lectures. For an M/M/1 queue, there is one server with an
exponential service rate . The arrival rate to the system is < . In addition, the waiting area is
innite. Particularly, we derive that the a
MEIE-4262: MANUFACTURING PROCESSES
HOMEWORK1
Sec-10; Spring Semester 2016
Due: Mon 10-Oct 2016
Basics of metal casting
Question-1
What are the effects of mold materials on fluid flow and heat transfer?
Question-2
Which of the following considerations are