MGMT 650 – Management Science and Decision Analysis
Final Preparation Guide
1. Key concepts of chapter 3
a. Sensitivity Analysis; Interpreting Management Scientist output reports
i. Range of optimality
ii. 100% rule
iii. Range of feasibility
iv. Dual price – what it means? How it can be used?
2. Key concepts of chapter 7
a. Transshipment problem and its Linear Programming formulation
b. Assignment problem and its Linear Programming formulation
3. Key concepts of chapter 8
a. Formulation of integer programs
b. Multiple choice constraints
c. K out of N alternatives constraints
d. Conditional and co-requisite constraints
4. Key concepts of chapter 9
a. Understanding of the shortest route problem
i. How can it be used for optimizing replacement policies (in-class
example) and scheduling purposes (HW #4 problem)
5. Key concepts of chapter 10
a. Understanding of activity slacks, critical activities, critical path, how much
activities can be delayed?
b. How is slack calculated?
c. Ability to interpret to Management Scientist outputs for project networks
d. Ability to set up project network diagrams with precedence relationships
between activities
e. Expected project duration with certain and uncertain activity times
6. Key concepts of chapter 14
a. Distinguishing between certainty, uncertainty, risk
b. Analysis of payoff tables
c. Decision trees: construction and interpretation
d. Calculating expected payoffs from decision tress and making decisions
e. Understanding of EVPI – what it means and how to calculate it
7. Key concepts of chapter 16
a. Moving averages, Weighted Moving Averages, Exponential smoothing –
how do they work?
b. Forecasting with linear trend time series
i. Interpretation of the trend equation
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c.
d.
e.
f.
ii. How to use trend equation to forecast for a given time period
Forecasting for time series with trend and seasonality
i. Interpretation of seasonal indices: what do they mean?
Forecasting accuracy measure - MSE
Ability to interpret to Management Scientist outputs
Ability to recognize different types of time series data
Please review all HW questions and solutions carefully.
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Sample Questions
1. (Chapter 3 – Sensitivity Analysis) Use the following Management Scientist output to
answer the questions.
LINEAR PROGRAMMING PROBLEM
MAX 31X1+35X2+32X3
S.T.
1) 3X1+5X2+2X3>90
2) 6X1+7X2+8X3<150
3) 5X1+3X2+3X3<120
OPTIMAL SOLUTION
Objective Function Value =
Variable
---------X1
X2
X3
Constraint
-------------1
2
3
763.333
Value
------13.333
10.000
0.000
Slack/Surplus
---------------0.000
0.000
23.333
Reduced Costs
-----------------0.000
0.000
10.889
Dual Prices
------------------0.778
5.556
0.000
OBJECTIVE COEFFICIENT RANGES
Variable
Lower Limit
------------ ------------------X1
30.000
X2
No Lower Limit
X3
No Lower Limit
Current Value
Upper Limit
---------------- --------------31.000
No Upper Limit
35.000
36.167
32.000
42.889
RIGHT HAND SIDE RANGES
Constraint
------------1
2
3
a.
Lower Limit
--------------77.647
126.000
96.667
Current Value Upper Limit
---------------- --------------90.000
107.143
150.000
163.125
120.000
No Upper Limit
Give the solution to the problem.
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b.
Which constraints are binding?
c.
What would happen to the optimal solution if the coefficient of x1
increased by 3?
d.
What would happen to the optimal solution if the right-hand side of
constraint 1 increased by 10?
2. (Chapter 3 – Sensitivity Analysis) Use the following Management Scientist output to
answer the questions.
MIN 4X1+5X2+6X3
S.T.
1) X1+X2+X3<85
2) 3X1+4X2+2X3>280
3) 2X1+4X2+4X3>320
Objective Function Value =
Variable
---------X1
X2
X3
Value
-------0.000
80.000
0.000
Constraint
------------1
2
3
Slack/Surplus
---------------5.000
40.000
0.000
400.000
Reduced Costs
-----------------1.500
0.000
1.000
Dual Prices
-------------0.000
0.000
-1.250
OBJECTIVE COEFFICIENT RANGES
Variable
---------X1
X2
X3
Lower Limit Current Value Upper Limit
--------------- ----------------- -------------2.500
4.000
No Upper Limit
0.000
5.000
6.000
5.000
6.000
No Upper Limit
RIGHT HAND SIDE RANGES
Constraint
Lower Limit Current Value
Upper Limit
------------- --------------- ----------------- --------------1
80.000
85.000
No Upper Limit
2
No Lower Limit
280.000
320.000
3
280.000
320.000
340.000
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a.
b.
c.
d.
e.
What is the optimal solution, and what is the value of the profit
contribution?
Which constraints are binding?
What are the dual prices for each resource? Interpret.
Compute and interpret the ranges of optimality.
Compute and interpret the ranges of feasibility.
3. (Chapter 10 – Project Scheduling) A set of activities in a project, their immediate
predecessors and expected times are listed below. A part of the Management Scientist
output has also been provided.
(a) Some activity slacks are given. Determine the slacks of the remaining activities.
(b) Which activities are critical and why?
(c) What is the project completion time?
(d) Can activity ‘I” be delayed without delaying the project’s completion? Justify your
answer.
4. (Chapter 8 – Linear Integer Programming) Grush Consulting has five projects to
consider. Each will require time in the next two quarters according to the table below.
Project
Time in first quarter
Time in second quarter
Revenue
A
5
8
12000
B
3
12
10000
C
7
5
15000
5
D
E
2
15
3
1
5000
20000
Revenue from each project is also shown. Develop a model whose solution would
maximize revenue, meet the time budget of 25 in the first quarter and 20 in the second
quarter, and not do both projects C and D.
5. (Chapter 8 – Linear Integer Programming) Chapter 8, problem 7 (from textbook)
6. (Chapter 16 – Forecasting) In each of the following scenarios, what in your opinion
(among Trend, Seasonality, Cycles and Irregular Variations) would be an accurate
representation of the following demand behavior? And why?
a) Demand for Mother’s day greeting cards
b) Demand for vacations on the moon
c) Demand for toothpaste at your local Stater Bros.
d) Demand for printer cartridges at Office Depot over the entire country
e) Demand for motel rooms inland in the wake of a hurricane alert along the Florida
Keys.
7. (Chapter 16 – Forecasting) The dean of a school of business is forecasting total student
enrollment for this year's summer session classes based on the following historical data,
and obtains the following linear trend equation based on the following data.
YEAR
Four years ago
Three years ago
Two years ago
Last year
TOTAL ENROLLMENT
2,000
2,200
2,800
3,000
F (t)
(a) Are enrollments increasing? If so, by how much each year?
(b) Forecast enrollments for this year and the following year. Assume t=1 corresponds to
4 years ago.
(c) Approximately when will the school have 4000 students?
(d) Actual enrollments this year are 3500. Determine the error in the dean’s forecast.
8. (Chapter 16 – Forecasting) The TIME SERIES VALUE column of the following
output from Management Scientist shows the number of actual storage shed sales at
Donna’s Garden Supply for Jan-Dec 2005. A 3-month moving average forecast appears
in the third column and the FORECAST ERROR is in the fourth column. Some values
are missing (indicated by “x”, “y”, and “z”).
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FORECASTING WITH MOVING AVERAGES
********************************
THE MOVING AVERAGE USES 3 TIME PERIODS
TIME PERIOD
===========
1
2
3
4
5
6
7
8
9
10
11
12
TIME SERIES VALUE
=================
10
12
x
16
19
23
26
30
28
y
16
14
FORECAST
========
11.67
13.67
16.00
19.33
22.67
26.33
28.00
25.33
20.67
FORECAST ERROR
==============
4.33
5.33
7.00
z
7.33
1.67
-10.00
-9.33
-6.67
(a) Determine the missing time series value for period 3.
(b) Determine the missing forecast error for period 7.
(c) Determine the missing time series value for period 10.
(d) Determine the 3-month moving average forecast for January 2006 (period 13).
(e) Determine the weighted 4-period MA forecast for period 13 using weights 0.4, 0.3,
0.2 and 0.1.
(f) If the actual time series value in period 13 turned out to be 20, then calculate the
exponential smoothing forecast for period 14 using a smoothing constant of 0.2 and the
forecast that you obtained in part (e).
9. (Chapter 14 – Decision Analysis) Gap Inc. is considering the possibility of opening a
new outlet in the South Coast Plaza, Costa Mesa, CA. The decision alternatives (small
outlet – decision alternative 1 and large outlet – decision alternative 2), probabilities for
good, average and bad markets (states of nature 1, 2 and 3, respectively), and the net
profits for each decision alternative and market condition are in the following
Management Scientist screenshot.
The Management Scientist output is as follows:
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(a) What size of the new outlet would you recommend and why?
(b) If Gap Inc. was certain of an “average market” at this location, which decision
alternative would be most suitable?
(c) Calculate the expected payoff under certainty.
10. (Chapter 7 – Transshipment and Assignment Problem) Develop the linear
programming formulation for this assignment problem.
Person
1
2
3
Task
A
9
12
11
B
5
6
6
C
4
3
5
D
2
5
7
8