NEW MEXICO INSTITUTE OF

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NEW MEXICO INSTITUTE OF MINING AND TECHNOLOGY
Department of Management Management Science for
Engineering Management (EMGT 501) Fall, 2005
Instructor Toshi Sueyoshi (Ph.D.) HP
address www.nmt.edu/toshi E-mail
Address toshi_at_nmt.edu Office
Speare 143-A
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1. Course Description The purpose of this
course is to introduce Management Science (MS)
techniques for manufacturing, services, and
public sector. MS includes a variety of
techniques used in modeling business applications
for both better understanding the system in
question and making best decisions.
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MS techniques have been applied in many
situations, ranging from inventory management in
manufacturing firms to capital budgeting in large
and small organizations. Public and Private
Sector Applications
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The main objective of this graduate course is to
provide engineers with a variety of decisional
tools available for modeling and solving problems
in a real business and/or nonprofit context. In
this class, each individual will explore how to
make various business models and how to solve
them effectively.
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2. Texts -- The texts for this course
(1) Anderson, Sweeney and Williams An
Introduction to Management Science,
South-Western (2) Chang Yih-Long, WinQSB ,
John WileySons
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3. Grading
In a course, like this class, homework problems
are essential. We will have homework
assignments. Homework has significant weight.
The grade allocation is separated as
follows Homework 20
Mid-Term Exam
40 Final Exam
40 The usual scale (90-100A,
80-89.99B, 70-79.99C, 60-69.99D) will be used.
Please remember no makeup exam.
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4. Course Outline Week Topic(s)
Text(s) 1
Introduction and Overview Ch. 12
2 Linear Programming Ch. 34
3 Solving Linear Programming Ch.
5 4 Duality Theory Ch.
6 5 No Class 6 Project
Scheduling PERT-CPM Ch. 10 7
Inventory Models Ch.
11 8 Review for Mid-Term EXAM

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Week Topic(s)
Text(s) 9 Waiting Line Models Ch. 13
10 Waiting Line Models Ch. 13
11 Decision Analysis Ch. 14
12 Multi-criteria Decision Ch. 15 13 No
Class 14 Forecasting Ch. 16
15 Markov Process Ch. 17
16 Review for FINAL EXAM
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Linear Programming (LP) A mathematical method
that consists of an objective function and many
constraints. LP involves the planning of
activities to obtain an optimal result, using a
mathematical model, in which all the functions
are expressed by a linear relation.
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A standard Linear Programming Problem
Maximize subject to
Applications Man Power Design, Portfolio Analysis
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Simplex method A remarkably efficient solution
procedure for solving various LP problems.
Extensions and variations of the simplex method
are used to perform postoptimality analysis
(including sensitivity analysis).
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(a) Algebraic Form
(0)
(1)
(2)
(3)
(b) Tabular Form
Coefficient of
Basic Variable
Eq.
Right Side
Z
(0)
1 -3 -5 0 0 0 0 0 1 0 1
0 0 0 0 2 0 0 1 0 12 0
3 2 0 0 1 18
(1)
(2)
(3)
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Duality Theory An important discovery in the
early development of LP is Duality Theory. Each
LP problem, referred to as a primal problem is
associated with another LP problem called a dual
problem. One of the key uses of duality theory
lies in the interpretation and implementation of
sensitivity analysis.
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PERT (Program Evaluation and Review
Technique)-CPM (Critical Path Method) PERT and
CPM have been used extensively to assist project
managers in planning, scheduling, and controlling
their projects. Applications Project
Management, Project Scheduling
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START
0
Critical Path 2 4 10 4 5 8 5 6 44
weeks
A 2
B
4
10
C
D
6
I
7
4
E
5
F
G
7
8
J
H
9
L
K
5
4
M
2
N
6
FINISH
0
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Decision Analysis An important technique for
decision making in uncertainty. It divides
decision making between the cases of without
experimentation and with experimentation.
Applications Decision Making, Planning
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decision fork chance fork
Drill
Oil 0.14
f
Unfavorable 0.7
c
0.85 Dry
Sell
b
Do seismic survey
Oil 0.5
g
Drill
0.3 Favorable
0.5 Dry
d
Sell
a
Oil 0.25
h
Drill
0.75 Dry
e
No seismic survey
Sell
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Markov Chain Model A special kind of a
stochastic process. It has a special property
that probabilities, involving how a process will
evolve in future, depend only on the present
state of the process, and so are independent of
events in the past. Applications Inventory
Control, Forecasting
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Queueing Theory This theory studies queueing
systems by formulating mathematical models of
their operation and then using these models to
derive measures of performance.
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This analysis provides vital information for
effectively designing queueing systems that
achieve an appropriate balance between the cost
of providing a service and the cost associated
with waiting for the service.
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Served customers
Queueing system
Queue
S S Service S facility S
C C C C
Customers
C C C C C C
Served customers
Applications Waiting Line Design, Banking,
Network Design
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Inventory Theory This theory is used by both
wholesalers and retailers to maintain inventories
of goods to be available for purchase by
customers. The just-in-time inventory system is
such an example that emphasizes planning and
scheduling so that the needed materials arrive
just-in-time for their use. Applications
Inventory Analysis, Warehouse Design
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Economic Order Quantity (EOQ) model
Inventory level
Batch size
Time t
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Forecasting When historical sales data are
available, statistical forecasting methods have
been developed for using these data to forecast
future demand. Several judgmental forecasting
methods use expert judgment. Applications Future
Prediction, Inventory Analysis
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The evolution of the monthly sales of a product
illustrates a time series
10,000 8,000 6,000 4,000 2,000 0
Monthly sales (units sold)
1/99 4/99 7/99 10/99 1/00 4/00 7/00
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Introduction to MS/OR MS Management Science OR
Operations Research Key components (a)
Modeling/Formulation (b)
Algorithm (c) Application
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Management Science (MS) (1) A discipline that
attempts to aid managerial decision making by
applying a scientific approach to managerial
problems that involve quantitative factors. (2)
MS is based upon mathematics, computer science
and other social sciences like economics and
business.
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General Steps of MS Step 1 Define problem and
gather data Step 2 Formulate a mathematical
model to represent the problem Step
3 Develop a computer based procedure
for deriving a solution(s) to the
problem
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Step 4 Test the model and refine it as
needed Step 5 Apply the model to analyze the
problem and make recommendation
for management Step 6 Help implementation
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Linear Programming (LP)
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1 LP Formulation (a) Decision Variables
All the decision variables are non-negative. (b)
Objective Function Min or Max (c) Constraints
s.t. subject to
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2 Example
A company has three plants, Plant 1, Plant 2,
Plant 3. Because of declining earnings, top
management has decided to revamp the companys
product line. Product 1 It requires some of
production capacity in Plants
1 and 3. Product 2 It needs Plants 2 and 3.
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The marketing division has concluded that the
company could sell as much as could be produced
by these plants. However, because both products
would be competing for the same production
capacity in Plant 3, it is not clear which mix of
the two products would be most profitable.
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The data needed to be gathered 1. Number of
hours of production time available per week in
each plant for these new products. (The available
capacity for the new products is quite
limited.) 2. Production time used in each plant
for each batch to yield each new product. 3.
There is a profit per batch from a new product.
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Production Time per Batch, Hours
Production Time Available per Week, Hours
Product
1 2
Plant
1 2 3
4 12 18
1 0 0 2 3 2
Profit per batch
3,000 5,000
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of batches of product 1 produced per week
of batches of product 2 produced per week
the total profit per week Maximize subject
to
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Graphic Solution
10
8
6
4
Feasible region
2
0 2 4 6 8
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10
8
6
4
Feasible region
2
0 2 4 6 8
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10
8
6
4
Feasible region
2
0 2 4 6 8
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10
8
6
4
Feasible region
2
0 2 4 6 8
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Maximize
Slope-intercept form
8
6
4
2
0 2 4 6 8 10
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4 Standard Form of LP Model
Maximize
s.t.
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5 Other Forms The other LP forms are the
following 1. Minimizing the objective
function 2. Greater-than-or-equal-to
constraints
Minimize
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3. Some functional constraints in equation
form 4. Deleting the nonnegativity constraints
for some decision variables
unrestricted in sign
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6 Key Terminology (a) A feasible solution is a
solution for which all constraints are
satisfied (b) An infeasible solution is a
solution for which at least one constraint
is violated (c) A feasible region is a
collection of all feasible solutions
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(d) An optimal solution is a feasible solution
that has the most favorable value of the
objective function (e) Multiple optimal
solutions have an infinite number of
solutions with the same optimal objective
value
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Multiple optimal solutions
Example
Maximize
Subject to
and
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Multiple optimal solutions
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Every point on this red line segment is optimal,
each with Z18.
4
2
Feasible region
0 2 4 6 8 10
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(f) An unbounded solution occurs when the
constraints do not prevent improving the
value of the objective function.
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Case Study - Personal Scheduling
UNION AIRWAYS needs to hire additional customer
service agents. Management recognizes the need
for cost control while also consistently
providing a satisfactory level of service to
customers. Based on the new schedule of flights,
an analysis has been made of the minimum number
of customer service agents that need to be on
duty at different times of the day to provide a
satisfactory level of service.
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Time Period Covered
Minimum of Agents needed
Shift
Time Period
1 2 3 4 5
48 79 65 87 64 73 82 43 52 15
600 am to 800 am 800 am to1000 am 1000 am to
noon Noon to 200 pm 200 pm to 400 pm 400 pm
to 600 pm 600 pm to 800 pm 800 pm to 1000
pm 1000 pm to midnight Midnight to 600 am




Daily cost per agent
170 160 175 180 195
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The problem is to determine how many agents
should be assigned to the respective shifts each
day to minimize the total personnel cost for
agents, while meeting (or surpassing) the service
requirements. Activities correspond to shifts,
where the level of each activity is the number of
agents assigned to that shift. This problem
involves finding the best mix of shift sizes.
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of agents for shift 1 (6AM - 2PM) of
agents for shift 2 (8AM - 4PM) of agents for
shift 3 (Noon - 8PM) of agents for shift 4
(4PM - Midnight) of agents for shift 5 (10PM
- 6AM)
The objective is to minimize the total cost of
the agents assigned to the five shifts.
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Min s.t.
all
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Total Personal Cost 30,610