Sixteenth-Century ReformationThe Reformation beg.docx

Sixteenth-Century Reformation
The Reformation began as a protest by churchmen and scholars
against existing Church practices and their own superiors.
These reformers did not view their actions as a “break with the
church,” but as a challenge to papal authority.
The Sixteenth-Century ReformationI. The Luther AffairII.
Luther’s MessageIII. Religious Pluralism: Responses to the
Reformers
I. The Luther Affair1. Who was Martin Luther?2. The
Indulgence Controversy3. Luther’s Political Protection:
Frederick Duke of Saxony (An Imperial Elector)4. A Public
AffairLeipzig Disputation (1519)On the Freedom of a Christian
(1520)The Diet of Worms (1521); a meeting of the Imperial
representative assembly
II. Luther’s Message1. The Problem of Salvation2. Human
Nature and Human Relations to God3. Sola fide (Salvation by
Faith Alone): A Radical Emphasis on Faith over WorksFaith is

the unmerited gift of God’s grace4. Sola scriptura (Scripture
Alone): The Importance of the Bible over Tradition5. From
Seven Sacraments to Two
5. From Seven Sacraments to Two1. Baptism2. Confirmation
(X)3. Eucharist/Communion-->Lord’s Supper4.
Penance/Confession (X)5. Last Rites/Anointing the Sick (X)6.
Ordination/Holy Orders (X)7. Marriage (X)
III. Religious Pluralism: Responses to the Reformers1. Papal
Response2. Popular ResponseThe Printing Revolution“The
Reformation of the Cities”3. Disputes Among the
ReformersWhat was a sacrament and how should it be
understood?A Priesthood of All Believers?
IV. Social and Political Consequences of the Reformation1. The
“Priesthood of all Believers”2. “Reformation of the Cities”3.
The Radical ReformationAnabaptists (Re-baptizers)4. The
German Peasants’ Revolt (1525)5. Reformation of the
PrincesDiet of Speyer 1526; emperor allows princes to decide
religion in their territoriesFormation of Protestant Defensive
Alliance (Schmalkaldic League 1531)
3. The Radical ReformationAnabaptists (many diverse
groups)Adult baptismSought to create “Holy

Communities”Separation from the State (refused to serve in
government, swear oaths, pay taxes, fight in armies)Elimination
of private property & shared wealthMillenarianism (End of the
World) Melchior Hoffman
4. German Peasants’ WarMid to late 1524 spontaneous rural
demonstrations and formation of peasant assemblies and then
armed and organized bands1525 appeal to the “Word of God” as
justification of the revolt and creation of supra-territorial
alliances “Christian Assembly” and “Christian Union of
Swabia”Peasant DemandsEconomic burdens: rents, fees,
services, taxes, and tithesInfringement of local self-
governmentReligious reformResponse of the Princes and Lords
ResponseConcessions and Coercion and Military Force mid to
late 1525
English Monarchs: A Reformation From Above?Henry VIII
(1509-1547)Parliamentary Act of Supremacy 1534; Opponents
executed (Thomas More)Confiscation of monastic property
1536/45Pilgrimage of Grace Uprisings (1536-37)Edward VI
(1547-1553)Banned “superstitious practices” (Church Alters)
1547Act of Uniformity & Convocation of the Clergy endorsed
Book of Common Prayer (1549); produced uprisingsCreed:
Forty-Two Articles (Bishop Thomas Cranmer)
Henry’s Wives and ChildrenCatherine of Aragon; marriage
annulledMaryAnne Boleyn; executed for adultery, incest, and
witchcraftElizabeth IJane Seymour; died in childbirthEdward
VIAnne of Cleves; marriage annulledCatherine Howard;
executed for infidelity (Catholic Howard family, niece of the

Duke of Norfolk)Catherine Parr; survived Henry
IE413 Fall 2011 1
♣ ♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣
IE 413 Engineering OR I
Homework #5
Due Thursday, November 12, 2015
♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣
Part I: Transportation Problem
Las Cruces Academy can store 200 files on hard drive, 100 files
in USB flash drive, and
300 files on DVD. Users want to store 300 word-processing
files, 100 packaged-program
files, and 100 data files. Each month a typical word-processing
file is accessed nine times;
a typical packaged-program file, five times; and a typical data
file, three times. When a
file is accessed, the time it takes for the file to be retrieved
depends on the type of file and
on the storage medium (see table below).
Storage Medium
Time (Minutes)
Word Processing Packaged Program Data
Hard Drive 5 4 7
USB Flash Drive 3 2 1
DVD 10 8 5

If the goal is to minimize the total time per month that users
spend accessing their files,
determine the linear programming model formulation that can
be used to determine
where files should be stored (4 points).
Part II: Assignment Problem
Consider the assignment problem having the following cost
table:
Task
1 2 3 4
Assignee
A 8 7 5 7
B 6 5 3 4
C 7 8 4 6
D 6 6 5 6
a. Determine the linear programming model formulation to
minimize the total
assignment cost (2 points).
b. Manually apply the Hungarian algorithm to find the optimal
assignment (2 points).
Part III. Read the attached reading material (i.e., pages 413 –
417 of Hillier &

Lieberman’s OR text, 10th edition), and write a one-page
summary report. The summary
should be typed, double-spaced with 1" margins on all sides. Be
concise in your writing
and consult technical writing references as needed. The body of
the summary report
should include the sections outlined as follows: (1) Summary of
the Chapter’s main point;
(2) Your opinion of the Chapters including the most important
information you learned
(2 points).
Hillier−Lieberman:
Introduction to Operations
Research, Ninth Edition
9. Network Optimization
Models
Text 407© The McGraw−Hill
Companies, 2010
9.8 A NETWORK MODEL 399
■ 9.8 A NETWORK MODEL FOR OPTIMIZING A PROJECT’S
TIME-COST TRADE-OFF
Networks provide a natural way of graphically displaying the
flow of activities in a major
project, such as a construction project or a research-and-
development project. Therefore,
one of the most important applications of network theory is in
aiding the management of

such projects.
In the late 1950s, two network-based OR techniques—PERT
(program evaluation
and review technique) and CPM (critical path method)—were
developed independently
to assist project managers in carrying out their responsibilities.
These techniques were de-
signed to help plan how to coordinate a project’s various
activities, develop a realistic
schedule for the project, and then monitor the progress of the
project after it is under way.
Over the years, the better features of these two techniques have
tended to be merged into
what is now commonly referred to as the PERT/CPM technique.
This network approach
to project management continues to be widely used today.
One of the supplementary chapters on the book’s website, Chap.
22 (Project Man-
agement with PERT/CPM), provides a complete description of
the various features of
PERT/CPM. We now will highlight one of these features for
two reasons. First, it is a
network optimization model and so fits into the theme of the
current chapter. Second, it
illustrates the kind of important applications that such models
can have.
The feature we will highlight is referred to as the CPM method
of time-cost trade-
offs because it was a key part of the original CPM technique. It
addresses the follow-
ing problem for a project that needs to be completed by a
specific deadline. Suppose
that this deadline would not be met if all the activities are

performed in the normal
manner, but that there are various ways of meeting the deadline
by spending more
money to expedite some of the activities. What is the optimal
plan for expediting
some activities so as to minimize the total cost of performing
the project within the
deadline?
The general approach begins by using a network to display the
various activities and
the order in which they need to be performed. An optimization
model then is formulated
that can be solved by using either marginal analysis or linear
programming. As with the
other network optimization models considered earlier in this
chapter, the special structure
of the problem makes it relatively easy to solve efficiently.
This approach is illustrated below by using the same prototype
example that is car-
ried through Chap. 22.
A Prototype Example—the Reliable Construction Co. Problem
The RELIABLE CONSTRUCTION COMPANY has just made
the winning bid of $5.4 mil-
lion to construct a new plant for a major manufacturer. The
manufacturer needs the plant to
go into operation within 40 weeks.
Reliable is assigning its best construction manager, David
Perty, to this project to help
ensure that it stays on schedule. Mr. Perty will need to arrange
for a number of crews to
perform the various construction activities at different times.

Table 9.7 shows his list of
the various activities. The third column provides important
additional information for co-
ordinating the scheduling of the crews.
For any given activity, its immediate predecessors (as given in
the third col-
umn of Table 9.7) are those activities that must be completed by
no later than
the starting time of the given activity. (Similarly, the given
activity is called an
immediate successor of each of its immediate predecessors.)
Models
Text408 © The McGraw−Hill
Companies, 2010
400 CHAPTER 9 NETWORK OPTIMIZATION MODELS
■ TABLE 9.7 Activity list for the Reliable Construction Co.
project
Immediate Estimated
Activity Activity Description Predecessors Duration
A Excavate — 2 weeks
B Lay the foundation A 4 weeks
C Put up the rough wall B 10 weeks

D Put up the roof C 6 weeks
E Install the exterior plumbing C 4 weeks
F Install the interior plumbing E 5 weeks
G Put up the exterior siding D 7 weeks
H Do the exterior painting E, G 9 weeks
I Do the electrical work C 7 weeks
J Put up the wallboard F, I 8 weeks
K Install the flooring J 4 weeks
L Do the interior painting J 5 weeks
M Install the exterior fixtures H 2 weeks
N Install the interior fixtures K, L 6 weeks
For example, the top entries in this column indicate that
1. Excavation does not need to wait for any other activities.
2. Excavation must be completed before starting to lay the
foundation.
3. The foundation must be completely laid before starting to put
up the rough wall, and
so on.
When a given activity has more than one immediate
predecessor, all must be finished be-
fore the activity can begin.
In order to schedule the activities, Mr. Perty consults with each
of the crew supervi-
sors to develop an estimate of how long each activity should
take when it is done in the
normal way. These estimates are given in the rightmost column
of Table 9.7.
Adding up these times gives a grand total of 79 weeks, which is
far beyond the dead-
line of 40 weeks for the project. Fortunately, some of the

activities can be done in par-
allel, which substantially reduces the project completion time.
We will see next how the
project can be displayed graphically to better visualize the flow
of the activities and to
determine the total time required to complete the project if no
delays occur.
We have seen in this chapter how valuable networks can be to
represent and help an-
alyze many kinds of problems. In much the same way, networks
play a key role in dealing
with projects. They enable showing the relationships between
the activities and succinctly
displaying the overall plan for the project. They also are helpful
for analyzing the project.
Project Networks
A network used to represent a project is called a project
network. A project network
consists of a number of nodes (typically shown as small circles
or rectangles) and a
number of arcs (shown as arrows) that connect two different
nodes.
As Table 9.7 indicates, three types of information are needed to
describe a project.
1. Activity information: Break down the project into its
individual activities (at the de-
sired level of detail).
2. Precedence relationships: Identify the immediate
predecessor(s) for each activity.
3. Time information: Estimate the duration of each activity.

The project network should convey all this information. Two
alternative types of project
networks are available for doing this.
Models
Companies, 2010
One type is the activity-on-arc (AOA) project network, where
each activity is represented
by an arc. A node is used to separate an activity (an outgoing
arc) from each of its immedi-
ate predecessors (an incoming arc). The sequencing of the arcs
thereby shows the precedence
relationships between the activities.
The second type is the activity-on-node (AON) project network,
where each activity
is represented by a node. Then the arcs are used just to show the
precedence relationships
that exist between the activities. In particular, the node for each
activity with immediate
predecessors has an arc coming in from each of these
predecessors.
The original versions of PERT and CPM used AOA project
networks, so this was the

conventional type for some years. However, AON project
networks have some important
advantages over AOA project networks for conveying the same
information.
1. AON project networks are considerably easier to construct
than AOA project networks.
2. AON project networks are easier to understand than AOA
project networks for inex-
perienced users, including many managers.
3. AON project networks are easier to revise than AOA project
networks when there are
changes in the project.
For these reasons, AON project networks have become
increasingly popular with practi-
tioners. It appears that they may become the standard format for
project networks. There-
fore, we will focus solely on AON project networks, and will
drop the adjective AON.
Figure 9.28 shows the project network for Reliable’s project.2
Referring also to the
third column of Table 9.7, note how there is an arc leading to
each activity from each of
its immediate predecessors. Because activity A has no
immediate predecessors, there is
an arc leading from the start node to this activity. Similarly,
since activities M and N have
no immediate successors, arcs lead from these activities to the
finish node. Therefore, the
project network nicely displays at a glance all the precedence
relationships between all
the activities (plus the start and finish of the project). Based on

the rightmost column of
Table 9.7, the number next to the node for each activity then
records the estimated dura-
tion (in weeks) of that activity.
The Critical Path
How long should the project take? We noted earlier that
summing the durations of all the
activities gives a grand total of 79 weeks. However, this isn’t
the answer to the question
because some of the activities can be performed (roughly)
simultaneously.
What is relevant instead is the length of each path through the
network.
A path through a project network is one of the routes following
the arcs from
the START node to the FINISH node. The length of a path is the
sum of the (es-
timated) durations of the activities on the path.
The six paths through the project network in Fig. 9.28 are given
in Table 9.8, along with
the calculations of the lengths of these paths. The path lengths
range from 31 weeks up
to 44 weeks for the longest path (the fourth one in the table).
So given these path lengths, what should be the (estimated)
project duration (the to-
tal time required for the project)? Let us reason it out.
Since the activities on any given path must be done in sequence
with no overlap, the
project duration cannot be shorter than the path length.

However, the project duration can
be longer because some activity on the path with multiple
immediate predecessors might
2Although project networks often are drawn from left to right,
we go from top to bottom to better fit on the
printed page.
Models
Text410 © The McGraw−Hill
Companies, 2010
have to wait longer for an immediate predecessor not on the
path to finish than for the
one on the path. For example, consider the second path in Table
9.8 and focus on activ-
ity H. This activity has two immediate predecessors, one
(activity G) not on the path and
one (activity E ) that is. After activity C finishes, only 4 more
weeks are required for ac-
tivity E but 13 weeks will be needed for activity D and then
activity G to finish. There-
fore, the project duration must be considerably longer than the
length of the second path
in the table.

However, the project duration will not be longer than one
particular path. This is
the longest path through the project network. The activities on
this path can be per-
formed sequentially without interruption. (Otherwise, this
would not be the longest path.)
402 CHAPTER 9 NETWORK OPTIMIZATION MODELS
■ TABLE 9.8 The paths and path lengths through Reliable’s
project network
Path Length
START �A�B�C�D�G�H�M� FINISH 2 � 4 � 10 � 6 � 7
� 9 � 2 � 6 � 40 weeks
START �A�B�C�E�H�M� FINISH 2 � 4 � 10 � 4 � 9 � 2
� 2 � 6 � 31 weeks
START �A�B�C�E�F�J�K�N� FINISH 2 � 4 � 10 � 4 �
5 � 8 � 4 � 6 � 43 weeks
START �A�B�C�E�F�J�L�N� FINISH 2 � 4 � 10 � 4 �
5 � 8 � 5 � 6 � 44 weeks
START �A�B�C�I�J�K�N� FINISH 2 � 4 � 10 � 7 � 8 �
4 � 6 � 6 � 41 weeks
START �A�B�C�I�J�L�N� FINISH 2 � 4 � 10 � 7 � 8 �
5 � 6 � 6 � 42 weeks
A
B
C
ED
G

H
M
K
N
L
J
F
I
START 0
FINISH
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
L.
M.
N.

Activity Code
Excavate
Foundation
Rough wall
Roof
Exterior plumbing
Interior plumbing
Exterior siding
Exterior painting
Electrical work
Wallboard
Flooring
Interior painting
Exterior fixtures
Interior fixtures
2
4
10
74
5
8
5
6
4
0

2
9
7
6
■ FIGURE 9.28
The project network for the
Reliable Construction Co.
project.
Models
Companies, 2010
Therefore, the time required to reach the FINISH node equals
the length of this path. Fur-
thermore, all the shorter paths will reach the FINISH node no
later than this.
Here is the key conclusion.
The (estimated) project duration equals the length of the longest
path through
the project network. This longest path is called the critical

path.3 (If more than
one path tie for the longest, they all are critical paths.)
Thus, for the Reliable Construction Co. project, we have
Critical path: START �A�B�C�E�F�J�L�N� FINISH
(Estimated) project duration � 44 weeks.
Therefore, if no delays occur, the total time required to
complete the project should be
about 44 weeks. Furthermore, the activities on this critical path
are the critical bottleneck
activities where any delays in their completion must be avoided
to prevent delaying proj-
ect completion. This is valuable information for Mr. Perty,
since he now knows that he
should focus most of his attention on keeping these particular
activities on schedule in
striving to keep the overall project on schedule. Furthermore, to
reduce the duration of
the project (remember that the deadline for completion is 40
weeks), these are the main
activities where changes should be made to reduce their
durations.
Mr. Perty now needs to determine specifically which activites
should have their du-
rations reduced, and by how much, in order to meet the deadline
of 40 weeks in the least
expensive way. He remembers that CPM provides an excellent
procedure for investigat-
ing such time-cost trade-offs, so he will use this approach to
address this question.
We begin with some background.

Time-Cost Trade-Offs for Individual Activities
The first key concept for this approach is that of crashing.
Crashing an activity refers to taking special costly measures to
reduce the dura-
tion of an activity below its normal value. These special
measures might include us-
ing overtime, hiring additional temporary help, using special
time-saving materials,
obtaining special equipment, etc. Crashing the project refers to
crashing a num-
ber of activities in order to reduce the duration of the project
below its normal value.
The CPM method of time-cost trade-offs is concerned with
determining how much
(if any) to crash each of the activities in order to reduce the
anticipated duration of the
project to a desired value.
The data necessary for determining how much to crash a
particular activity are given
by the time-cost graph for the activity. Figure 9.29 shows a
typical time-cost graph. Note
the two key points on this graph labeled Normal and Crash.
The normal point on the time-cost graph for an activity shows
the time (dura-
tion) and cost of the activity when it is performed in the normal
way. The crash
point shows the time and cost when the activity is fully crashed,
i.e., it is fully
expedited with no cost spared to reduce its duration as much as
possible. As an
approximation, CPM assumes that these times and costs can be

reliably predicted
without significant uncertainty.
For most applications, it is assumed that partially crashing the
activity at any level will
give a combination of time and cost that will lie somewhere on
the line segment between
3Although Table 9.8 illustrates how the enumeration of paths
and path lengths can be used to find the critical
path for small projects, Chap. 22 describes how PERT/CPM
normally uses a considerably more efficient pro-
cedure to obtain a variety of useful information, including the
critical path.

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