Download Professor Jonathan Eckstein

Professor Jonathan Eckstein
Operations Management, 33:623:386:01/02
School of Business – New Brunswick
Rutgers University
Practice Problems for Second Midterm Exam
You will have 80 minutes. You will write all answers in the “blue books” provided. The
exam will have two questions. One will be spreadsheet question and the other an algebra
question. They will be on different topics.
Allowed materials:
A single “cram sheet” in your own handwriting (both sides allowed)
A dictionary (if English is not your first language)
A calculator
The following are relevant sample problems from past exams. Note that until a few years
ago, we covered a lot more material in less depth in this part of the course. So, many of the
older exam questions that are still relevant are pretty easy.
Also, on this exam, I will probably also ask you about some elementary simulation material.
Many of the simulation practice questions here originally used the @Risk software package
instead of YASAI, so there are some differences in the simulation report formats.
The Fall 2001 second midterm consisted of questions 14, 15, and 16.
1: Choosing a Class Schedule
Shelly Shaw is a marketing senior in the business program at Relatively Normal University
(RNU). With the help of her roommate Anny Litical, Shelly is trying to decide what courses to
take next semester. Shelly has identified ten possible courses she might want to take and has
assigned a “point score” between 1 and 10 to each one, with 10 indicating the most desirable
course, and 1 the least. The “homework” column is an estimate of the average hours of
homework assigned per week.
1
2
3
4
5
6
7
8
9
10
Course
Intermediate Marketing (section 1)
Intermediate Marketing (section 2)
Intermediate Marketing (section 3)
International Marketing
Market Research
Internet Marketing Project
Sales Management
Advanced MIS for Non-Majors
Cases in International Management
Chinese I
Practice Questions for Midterm Exam 2
Instructor Credits Homework Points
Time
Neisgye
3
6
10 MW 10:30AM
Meeney
3
8
8
MW 1:30PM
Yewslis
3
5
4
MW 3:00PM
Neisgye
4
5
9
MW 3:00PM
Keiskware
3
8
7
TTh 10:30AM
Jones
4
7
9
MW 10:30AM
Bosman
3
4
8
TTh 1:30PM
Phillips
3
5
7
TTh 10:30AM
Hunter
3
4
6
TTh 3:00PM
Chen
4
8
6
MW 1:30PM
-- 1 --
Fall 2001
Shelly has to take at least 14 and at most 17 credits, and wants an average homework load no
more than 30 hours per week. She has to take Intermediate Marketing, but can choose any
section. She must also take at least one Marketing elective, and at least one general elective.
The marketing electives are International Marketing, Market Research, Internet Marketing
Project, and Sales Management. The general electives are Advanced MIS for Non-Majors, Cases
in International Management, and Chinese I. The university will not let Shelly register for two
courses that meet at the same time.
Write an algebraic integer programming model for choosing a schedule that has the
highest possible total point score, subject to the constraints described above. Clearly define
your variables. The total point score of a schedule is the sum of the point scores of the
classes being taken.
2: Staffing a Class Schedule
P.J. Scramm, chairman of the marketing department of Understaffed State University (USU), is
in the process of assigning instructors to courses for next term. He has concluded that he must
hire temporary instructors for three sections of Introduction to Marketing (“Intro”), three
sections of Intermediate Marketing (“Intermediate”), two sections of International Marketing
(“International”), and one section of Market Research.
The table on the following page shows the available temporary instructors, listed by last name.
A “” appears whenever an instructor is able to teach a given course, and a “--” means the
instructor cannot teach the course. “Hiring cost” gives the cost (in thousands of dollars) of hiring
the instructor for a semester. “Max sections” is the maximum number of sections that can be
assigned to an instructor once he or she is hired. The instructor’s pay remains the same even if
he or she teaches fewer sections than the maximum.
Instructor: Mulholland Makeshwari Tseng Furtig Worth Ramirez Jackson
Intro
--




Intermediate
-





International
-----

Market Research
----


35
45
32
25
27
35
30
Hiring Cost
2
3
2
2
2
3
2
Max Sections
The chairman is trying to use the spreadsheet model below to decide which temporary instructors
to hire. His objective is to spend as little money as possible, while staffing all the sections. The
“--” cells contain zero, but are formatted to display as “--”. Shaded-in cells contain formulas
(whose values are not shown, except for B28). One of the constraints used in the Solver is
B15:H18 <= B23:H26.
Practice Questions for Midterm Exam 2
-- 2 --
Fall 2001
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Intro
Intermediate
International
Market Research
Hiring Cost
Max Sections
I
Sections
Mulholland Makeshwari Tseng Furtig Worth Ramirez Jackson Needed
1
1
-1
-1
1
3
1
1
1
-1
1
1
3
-1
1
----2
-1
1
--1
-1
35
45
32
25
27
35
30
2
3
2
2
2
3
2
1 if Hired, else 0
Mulholland Makeshwari Tseng Furtig Worth Ramirez Jackson
0
0
1
1
1
1
0
Intro
Intermediate
International
Market Research
Total
B
C
D
E
F
G
H
Number of Sections Taught
Mulholland Makeshwari Tseng Furtig Worth Ramirez Jackson
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
Total
Logical Upper Bounds on Number of Sections Taught
Mulholland Makeshwari Tseng Furtig Worth Ramirez Jackson
Intro
Intermediate
International
Market Research
Total Cost
119
(a) What formula should you put in cell I15, to compute the total number of sections of
“Intro” taught by the temporary instructors? Make sure your answer will yield correct
results for the other courses when copied to cells I16:I18.
(b) What formula should you put in cell B19, to compute the total number of sections
taught by Mulholland? Make sure your answer will produce correct results for the
other instructors if copied to cells C19:H19.
(c) What formula should you put in cell B23, to provide a logical upper bound on the
number of sections of “Intro” taught by Mulholland? Make sure your answer will
produce correct results for all the other instructor-class combinations if copied to all
the other cells in the block B23:H26.
(d) What target cell should you use in the Solver? Should you maximize or minimize it?
What are all the changing cells?
Practice Questions for Midterm Exam 2
-- 3 --
Fall 2001
(e) What are all the constraints? Should you check “assume nonnegative”?
(f) Assume you want a solution within 0.2% of the best possible. Should you check
“assume linear model”? How would you set the “precision” Solver parameter? How
would you set the “tolerance” Solver parameter?
(g) Suppose you are informed of new seniority rules imposed by a recently-negotiated labor
contract. The effect of these Rules is that Ramirez cannot be hired unless both
Makeshwari and Worth are hired. What constraint(s) would you add to the Solver to
comply with this restriction?
3: Hiring Consultants
Your firm is forming a panel of three to five consultants to advise it on its latest product
development project. Each candidate to be on the panel has been classified as being competent
in one or more areas of expertise: computer systems (CS), management (MGMT), marketing
(MKT), and operations analysis (OA). There must be at least one panelist competent in each
area of expertise, except for marketing, for which there must be at least two. The following table
describes the available candidates:
Hourly Rate Expertise
$ 250
CS, MGMT, MKT
Joe Nowital
$ 150
CS, OA
John Ecklestone
$ 125
CS
Mary Hacker
$
185
MGMT, MKT
Phil Saftee
$ 200
MGMT, OA
Max Bradley
$ 190
MGMT, MKT, OA
Sarah Lyddle
Due to an old academic squabble, Max Bradley and Sarah Lyddle dislike one another. If one of
them is hired, the other cannot be.
Algebraically formulate an integer program that will find a panel that meets all the
constraints above and has the lowest cost, where cost is defined to be the sum of the hourly
rates of the consultants hired. Clearly define your variables.
4: Producing Trucks
Atlas Truck Body has three products, a flatbed truck, a moving van, and a tanker truck. There
are at most seven days left before the plant shuts down for its annual vacation, and Atlas wants to
make the most possible profit within that time. Data on the three products are as follows:
Flatbed
3
Minimum Production, if any Produced
Profit per Unit $ 2,000
1
Labor Days per Unit
Practice Questions for Midterm Exam 2
-- 4 --
Moving Van
2
$ 5,000
2
Tanker
2
$ 7,000
3
Fall 2001
If Atlas makes any flatbeds, they must make at least three. They may also make more than three
if they wish, but if they decide to produce less than three, then they cannot produce any.
Similarly, if Atlas produces any moving vans, they must produce at least two, and a similar
restriction applies to tankers. Each flatbed truck takes one day to produce and yields a profit of
$2,000. The table gives similar information for moving vans and tankers.
Atlas is trying to use the following (partially filled in) spreadsheet model to find the highestprofit production plan from now until the shutdown. Partially completed trucks will not be
considered as contributing to profits for the period. Atlas wants a solution within 0.1% of
optimal.
Parts (a), (b), and (c) concern the correct completion of the spreadsheet model.
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Minimum Production, if any Produced
Profit per Unit
Labor Days per Unit
Total Days Available
B
C
Flatbed Moving Van
3
2
$ 2,000 $
5,000 $
1
2
D
Tanker
2
7,000
3
7
Maximum Possible Production
Produce Any?
Production
Logical Lower Bound
Logical Upper Bound
Profit
Labor Usage
=SUMPRODUCT(B11:D11,B3:D3)
=SUMPRODUCT(B11:D11,B4:D4)
(a) [5 points] Cell B8 is intended to contain the maximum number of flatbeds that could
be produced in the days available before the shutdown (in cell B6), assuming that no
other kinds of trucks are made. What formula would you enter in cell B8? Make sure
your answer could simply be copied to C8 and D8 to calculate similar values for
moving vans and tankers, respectively.
(b) [10 points] What values would you enter in cells B13 and B14 to give lower and upper
limits on the production of flatbeds? Make sure your answers will yield correct
answers for moving vans and tankers when copied to C13:C14 and D13:D14,
respectively.
(c) [15 points] Indicate the Solver settings and options you would use to solve this model.
What is the “target cell”? Should you maximize or minimize it? What are the
changing cells? What are all the constraints? Should you “assume linear model”?
How should you set the “tolerance” in the Solver options?
(d) [20 points] Algebraically formulate this problem as an integer program. Include
clear, complete definitions of the decision variables.
Practice Questions for Midterm Exam 2
-- 5 --
Fall 2001
5: Fruit-of-the-Month Club
Every year, the Fruit-of-the-month club sends a small free holiday gift assortment to its most
loyal customers. For this year's assortment, the club is considering a selection drawn from the
following fruits:
Description
Cost
Desirability Rating
Maximum Allowed
Kiwi
$0.50
2
1
Kumquat
$0.75
2
1
Apple
$0.35
1
2
Carambola
$1.00
3
2
The total desirability rating of the assortment must be at least 5. For example, it would be
feasible to send one kiwi, one kumquat, and one apple, with a desirability of 2 + 2 + 1 = 5. It
would also be feasible to simply send two carambolas, with a desirability of 2  3 = 6.
You would like to concoct an assortment that has the lowest possible cost while conforming to
this desirability criterion (and also to the "maximum allowed" numbers above).
Algebraically formulate this problem as an integer program. Include definitions of the
decision variables.
6: Safe-T-Flow, Inc.
Safe-T-Flow, Inc. make specialty valves for the power generation and transportation industries.
Presently, they have three products: valve types 1, 2, and 3. All valves are made in lots of 100
units, and the firm has the capacity to produce a total of up to 5 lots this month. The three
different types of valves have the following properties:
Valve
Type
1
2
3
Profit
Setup Cost per Lot
$5,000
$ 5,000
$3,000
$ 4,000
$7,000
$ 6,000
Maximum
Number
of Lots
2
2
3
Suppose that Safe-T-Flow is trying to use the following spreadsheet model to make its decision:
Practice Questions for Midterm Exam 2
-- 6 --
Fall 2001
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
B
C
Valve
Type
Setup Cost
1
5000
2
3000
3
7000
Valve
Type
1
1
2
0
3
1
Valve
Type
1
2
3
Total:
Profit
per Lot
5000
2
4000
2
6000
3
Make
Any?
D
Maximum
Number
of Lots
E
F
Capacity
Limit
5
How
Many?
2
<=
0
<=
3
<=
Total: =SUM(D10:D12)
Limit
?????
?????
?????
Cash Flows
=C4*D10-B4*B10
=C5*D11-B5*B11
=C6*D12-B6*B12
=SUM(B16:B18)
(a) What formula should they enter in cell F10? Be sure your answer will also yield
correct results if copied to cells F11 and F12.
(b) Explain all the Solver settings you would use to have Excel find an optimal solution to
this problem. What is the “target cell”? Should you maximize or minimize it? What are
the changing cells? What are all the constraints? Should you “assume linear model”?
7: Shipping Explosives
Creative Destruction, Inc. (CDI) produces a specialty explosive called Semrok, which is used in
the excavation, construction, and demolition industries. CDI can produce Semrok at three plants,
East, Central, and West. The production unit costs and monthly capacities of these plants,
measured in kilograms (Kg), are as follows:
Unit Cost ($/Kg) Capacity (Kg)
$ 13.20
1050
East Plant
$ 15.25
1250
Central Plant
$ 18.20
850
West Plant
CDI must ship the explosive to four customers, Tristate, Prairie, Bayou, and Southcoast, who act
as regional distributors for the product. For the coming month, these customers have ordered
900, 710, 500, and 650 kilograms of Semrok, respectively. Unit shipping costs (per kilogram)
between the plants and customers are as follows:
To
East Plant
From Central Plant
West Plant
Practice Questions for Midterm Exam 2
Tristate
$ 5.40
$ 9.10
$ 11.75
-- 7 --
Prairie
$ 7.95
$ 4.25
$ 9.00
Bayou
$ 8.15
$ 7.60
$ 8.25
Southcoast
$ 12.20
$ 9.75
$ 4.95
Fall 2001
Because the federal government considers Semrok to be a hazardous, controlled substance, CDI
must also purchase special licenses in order to transport it. Each license costs $1,000, lasts one
month, and only permits shipments between one specific plant and one specific customer. For
example, suppose temporarily that CDI were to decide on the following pattern of shipments:
Amount Shipped (Kg)
From
East Plant
Central Plant
West Plant
To
Tristate
900
0
0
Prairie
0
510
200
Bayou
150
350
0
Southcoast
0
0
650
Then CDI would have to buy six licenses, because it is using six distinct shipping routes.
CDI would like to find a production and shipping plan that meets next month's orders at the
lowest possible cost. To this end, it is using the spreadsheet model on the last page of this exam.
There are two sets of changing cells: C20:F22 and C26:F28. Cells C20:F22 are meant to have a 1
in positions corresponding to purchased licenses, and otherwise 0. Cells C26:F28 hold the
shipment plan. All the formulas in the model are obscured by “????”.
(a) What formula should be in cell G26, to compute total shipments from the East plant?
Make sure your answer will compute the correct total shipments for the Central and
West plants, respectively, if copied to cells G27 and G28.
(b) What formula should be in cell C29, to compute total shipments to Tristate? Make
sure the formula will yield the correct total shipments to the other customers if copied
to cells D29:F29.
(c) Cells C34:F36 hold “logical upper bounds” on the shipment amounts between each
plant and customer. Write a formula for cell C34 that will compute a valid logical
upper bound on the amount shipped between the East plant and Tristate. Make sure
the formula will compute valid logical bounds on all the other shipping routes if it is
copied to the rest of the cells in C34:F36.
(d) What formula should be in cell B39, to compute the total cost of licenses purchased?
(e) What formula should be in cell B40, to compute the total cost of production?
(f) What formula should be in cell B41, to compute the total shipping cost? The cost of the
licenses is in cell B39, and shouldn’t be included in B41.
(g) What formula should be in cell B42, to compute total overall cost?
(h) What target cell would you use in the Solver? Would you maximize or minimize?
What are all the constraints you would specify?
Practice Questions for Midterm Exam 2
-- 8 --
Fall 2001
(i) The firm is willing to accept any solution that is with a quarter of a percent of the
absolute optimum cost. Indicate how you should set the following Solver Options:
Precision, Tolerance, Assume Linear Model, Assume Nonnegative.
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
B
C
D
Unit Cost ($/Kg) Capacity (Kg)
East Plant
$
13.20
1050
Central Plant $
15.25
1250
West Plant
$
18.20
850
E
F
Tristate
900
Bayou
500
Southcoast
650
Demand (Kg)
Unit Shipping Costs ($/Kg)
From
East Plant
Central Plant
West Plant
$
$
$
Tristate
5.40
9.10
11.75
Prairie
710
To
Prairie
$
7.95
$
4.25
$
9.00
$
$
$
G
Bayou Southcoast
8.15 $
12.20
7.60 $
9.75
8.25 $
4.95
License Cost
$
1,000.00
Licenses Purchased
From
East Plant
Central Plant
West Plant
Tristate
1
0
0
To
Prairie
0
1
0
Bayou
0
1
0
Southcoast
0
0
1
Tristate
900
0
0
????
To
Prairie
0
710
0
????
Bayou
0
500
0
????
Southcoast
0
0
650
????
Tristate
????
????
????
To
Prairie
????
????
????
Bayou
????
????
????
Southcoast
????
????
????
Amount Shipped (Kg)
From
East Plant
Central Plant
West Plant
Total
Shipment Quantity
Logical Upper Bounds (Kg)
From
East Plant
Central Plant
West Plant
Licenses
Production
Shipping
Total
Total
????
????
????
Cost
????
????
????
????
8: An Online Auction with Group Bids
E-Gulf, Inc., operates an auction website. The firm has acquired a set of rare antique Alice in
Wonderland figurines: Alice, the Cheshire Cat, the March Hare, and the Mad Hatter, and has
just finished collecting bids on these items. Some bidders placed bids on individual items,
another placed a bid for the entire set, and still others placed bids on subsets of the items. The
bids are as follows:
Practice Questions for Midterm Exam 2
-- 9 --
Fall 2001
Bid Number
1
2
3
4
5
6
7
8
9
10
Items
Alice only
Cheshire Cat only
March Hare only
Mad Hatter only
Entire Set
Alice and Cheshire Cat
Cheshire Cat and March Hare
March Hare and Mad Hatter
Alice, Cheshire Cat, and Mad Hatter
Alice and Mad Hatter
Bid Price
$ 50.00
$ 75.00
$ 80.00
$ 65.00
$ 300.00
$ 145.00
$ 160.00
$ 190.00
$ 240.00
$ 175.00
E-Gulf would like to know which bids it should accept in order to bring in the most revenue. For
example, they could accept just bid 5 for $300, or a combination of bids 3 and 9 for a total
revenue of $80 + $240 = $320. They could not accept the combination of bids 7 and 9, since that
would involve selling the Cheshire Cat twice. Each bid can be accepted at most once.
(a) Algebraically formulate a linear programming model to give E-Gulf the highest
possible revenue. Give clear, numeric definitions of your decision variables. You are
allowed to skip algebraic simplifications (if any arise).
Now suppose that a private antique dealer, who has been observing the auction over the web,
contacts E-Gulf. The dealer has four Mad Hatter figurines identical to the one E-Gulf has. He
offers to sell any number of them to E-Gulf for $75 per figurine plus, a “flat” $25 handling
charge, independent of the number of figurines ordered. If E-Gulf decides not to buy any
figurines from the dealer, there is no handling charge. E-Gulf can then immediately resell the
additional Mad Hatter figurines to its bidders as part of the current auction. Each bid can still be
accepted at most once; however, more different combinations of bids can be accepted, since
there may be more than one Mad Hatter to sell.
(b) Modify your linear programming model to tell E-Gulf what course of action will give it
the maximum profit from the figurines in this new situation. Rewrite your entire
model, adding new variables if necessary. Give clear, numeric definitions of your
decision variables. You are allowed to skip algebraic simplifications (if any arise).
9: Configuring Intranet Servers
An information systems manager has been asked to configure an internal network server facility
for her firm. The facility must fit in an equipment rack that has slots for up to four server
computers. Each slot may be empty, contain a basic server, or contain a super server. A basic
server has a computation capacity of 32 SpecMarks and costs $7,000, while a super server has a
computation capacity of 50 SpecMarks and costs $10,000. Each server may be fitted with up to
four hard disks. Each hard disk has a capacity of 18 gigabytes and costs $650.
There are six applications that need to be run on the server facility. An application must run on
only one server, but a server can run more than one application. The computation and disk space
requirements of the six applications are as follows:
Practice Questions for Midterm Exam 2
-- 10 --
Fall 2001
Peak
Computation
Application
(SpecMarks)
ERP Accounting
19
Human Resources Intranet
10
Intranet Search Engine
18
Online Case Library
8
Transportation Planning
26
Customer Service Database
12
Disk
Storage
(GB)
50
15
1
60
5
25
The disk storage needed by an application may be spread over multiple disks (but all on the same
server). The MIS manager must make the following decisions: how many of each server to buy,
how many disks to put on each server, and which applications should go on each server. She
would like to do this as cheaply as possible, so long as each server has sufficient disk space and
computational power for the applications assigned to it.
She has devised the spreadsheet model on the next page to help her with the decision. The
decision variables are in cells B24:E26 and B33:E38. Cells B24:E25 indicate what kind of server
(if any) is installed in each equipment rack slot. In the solution shown, there are basic servers in
slots 1 and 2, slot 3 is empty, and there is a super server in slot 4. Cells B26:E26 indicate how
many disk are installed in each server; for example, the “4” in cell E26 indicates the server in
slot 4 has 4 disks. Finally, B33:E38 indicate which applications are assigned to which servers.
For example, in the solution shown, the server in slot 1 handles the ERP Accounting and Human
Resources Intranet applications, the server in slot 2 handles the Intranet Search Engine and
Customer Service Database applications, and the server in slot 4 handles the Online Case
Library and Transportation Planning applications.
All cells that contain formulas either have their contents shown, or are shaded like
.
(a) What formula should you put in cell B28, which should contain the computation
capacity of the server in slot 1? Make sure your answer will yield correct results for the
other slots when copied to cells C28:E28.
(b) What formula should you put in cell B29, which should hold the disk capacity of the
server in slot 1? Make sure your answer will yield correct results for the other slots
when copied to cells C29:E29.
(c) What formula should you put in cell B39, which should contain the total computation
capacity required by the applications assigned to the server in slot 1? Make sure your
answer will yield correct results for the other slots when copied to cells C39:E39.
(d) What formula should you put in cell B40, to compute the total disk space required by
the applications assigned to the server in slot 1? Make sure your answer will yield
correct results for the other server slots when copied to cells C40:E40.
Practice Questions for Midterm Exam 2
-- 11 --
Fall 2001
(e) What formula should you put in cell E19, to compute the total cost of the configuration?
(f) What target cell should you use in the Solver? Should you maximize or minimize it?
What are all the changing cells?
(g) What are all the constraints you should use in the Solver? Should you check “assume
nonnegative”?
(h) Suppose you want a solution within 1% of the best possible. Should you check “assume
linear model”? How would you set the “tolerance” Solver parameter?
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
A
Server Configuration Problem
Application
ERP Accounting
Human Resources Intranet
Intranet Search Engine
Online Case Library
Transportation Planning
Customer Service Database
B
C
Peak
Compute
(SpecMarks)
19
10
18
8
26
12
Disk
Storage
(GB)
50
15
1
60
5
25
Compute
Capacity
32
50
Server Types
Basic
Super
Maximum Disks/Server
Cost/Disk
Disk Capacity (GB)
Server Installations
Basic
Super
Disks
Basic+Super
Compute Capacity
Disk Capacity
E
F
Cost
7,000
10,000
4
$
650
$
Cost
30,500
18
Server Rack Slot
1
2
3
4
1
1
0
0
0
0
0
1
4
2
0
4
=SUM(B24:B25) =SUM(C24:C25) =SUM(D24:D25) =SUM(E24:E25)
32
32
0
50
72
36
0
72
Application Assignments
ERP Accounting
Human Resources Intranet
Intranet Search Engine
Online Case Library
Transportation Planning
Customer Service Database
Needed compute Capacity
Needed Disk Capacity
$
$
D
1
1
1
0
0
0
0
29.0
65
Server Rack Slot
2
3
0
0
0
0
1
0
0
0
0
0
1
0
30.0
0.0
26
0
4
0
0
0
1
1
0
34.0
65
Sum
=SUM(B33:E33)
=SUM(B34:E34)
=SUM(B35:E35)
=SUM(B36:E36)
=SUM(B37:E37)
=SUM(B38:E38)
10: A More Complicated Kind of Project Scheduling
Your market research firm is working on a project for one of its clients. The project consists of
the following activities:
Length Fixed Charge Cost/Day Max Days
Practice Questions for Midterm Exam 2
-- 12 --
Fall 2001
Code
A
B
C
D
E
F
Activity
Requires (Days)
s
Product 1 Focus Group
-10
Product 2 Focus Group
-7
Product 1 Analysis
A
6
Product 1/2 Comparison
A, B
5
Analysis1 Final Report
Product
C, D
6
Product 2 Final Report
D
7
to Crash
to Crash
$
1,000 $ 200
$
1,000 $ 150
$
500 $ 400
$
500 $ 450
$
200 $ 300
$
200 $ 300
Crash
4
3
3
2
4
4
Activity A, for example, is scheduled to take 10 days. However, it may be “crashed” (reduced in
length) by up to 4 days, at a fixed cost of $1,000 plus $200 per day. For instance, if you spend
nothing on activity A, it will take 10 days; if you spend $1,200, you can shorten it to 9 days; if
you spend $1,400, you can shorten it to 8 days, and so forth down to 6 days. The other activities
are similar. All the activities must be completed in order to consider the project to be done.
You may shorten up to four of the activies. The official due date for the project is 12 days from
now. However, if you reduce the fee charged to your client by $3,000, you may complete the
project up to three days late. For an additional $5,000 fee reduction, the client will grant a
further extension of four days, for a total of 12 + 3 + 4 = 19 days. This second extension cannot
be taken unless the first one is also taken. Under no circumstances should you take more than 19
days to complete the project.
You would like to know which activities to crash, and by how much, so that your firm’s total
costs (crashing costs plus fee reductions) are as small as possible.
Algebraically formulate an integer programming model to determine the best course of
action. Give clear, numeric definitions of your decision variables. You are allowed to skip
algebraic and numeric simplifications (if any arise).
11: Planning an Advertising Campaign
Your firm makes a product that costs $15.50 per unit to produce, and sells for $23.00. You have
up to $30,000 to spend on an advertising campaign for the product, and you have identified six
possible magazines in which to place your advertisements: Motor Sport, Off-Road, Trout Caster,
DotComWorld, Mad Hacker, and Downhill Ski. You classify these magazines as “automotive”,
“computer”, and “outdoor”. Motor Sport is considered “automotive”. Off-Road is considered to
be both “automotive” and “outdoor”. Trout Caster and Downhill Ski are both “outdoor”, while
DotComWorld and Mad Hacker are classified as “computer”.
You can run up to five ads in each magazine, and you want to run at least one ad in a publication
in each of the three categories. That is, there should be at least one ad in an “automotive”
magazine, at least one ad in an “outdoor” magazine, and at least one ad in a “computer”
magazine. Note that a single ad in Off-Road would take care of both the “automotive” and
“outdoor” categories.
Practice Questions for Midterm Exam 2
-- 13 --
Fall 2001
If you decide to place any ads in a particular magazine, the magazine charges a “setup” fee to
prepare the ad for publication. There is then an additional fee each time the ad appears. The
current cost structure is as follows:
Setup Cost
Cost per Ad
Motor
Sport
$ 8,000
$ 1,000
Off-Road
$ 6,000
$ 800
Magazine
Trout
Caster DotComWorld
$ 5,500
$ 4,300
$ 700
$ 700
Mad
Hacker
$ 2,700
$ 600
Downhill
Ski
$ 7,000
$ 750
So, for example, running two ads in Off-Road would cost $6,000 + 2  $800 = $7,600. Your
marketing department has estimated the number of sales that would result from placing one, two,
three, four, or five ads in each magazine, as follows:
Number
of Ads
1
2
3
4
5
Motor
Sport
4,000
6,000
7,200
8,000
8,200
Off-Road
2,000
3,000
3,500
3,700
3,900
Sales Generated
Trout
Caster DotComWorld
4,500
2,300
5,500
3,100
6,000
3,900
6,200
4,700
6,250
5,000
Mad
Hacker
2,000
2,500
3,000
3,100
3,200
Downhill
Ski
3,500
5,000
5,200
5,400
5,600
For instance, placing one ad in Motor Sport would yield 4,000 sales of the product, while placing
two ads in Motor Sport would produce a further 2,000 sales, for a total of 6,000. A third ad
would generate another 1,200 sales, for a total of 7,200, and so forth.
If any ads are placed in Off-Road, then at least one ad must be placed in Motor Sport (this rule is
imposed by the company that owns both of these magazines).
You would like to plan the advertising campaign so that you generate the greatest possible net
profit for the company, given that your ad expenditures stay within the budget. To do so, you are
using the spreadsheet shown on the next page. The shaded cells contain formulas. The only
changing cells are B24:G28, and are interpreted as follows: in the column corresponding to a
given magazine, a one appears in the row corresponding to the number of ads to be placed, and
the rest of the changing cells in the column contain zeroes. If a magazine is not used, all the
changing cells in its column should be zero.
In the (optimal) solution shown, there are four ads in Motor Sport, two ads in Trout Caster, four
in DotComWorld, and two in Mad Hacker.
Practice Questions for Midterm Exam 2
-- 14 --
Fall 2001
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Setup Cost
Cost per Ad
Automotive
Outdoor
Computer
Number of Ads
1
2
3
4
5
B
Motor Sport
$
8,000
$
1,000
1
0
0
$
$
Motor Sport
4,000
6,000
7,200
8,000
8,200
E
F
Magazine
Trout Caster DotComWorld Mad Hacker
$
5,500 $
4,300 $
2,700
$
700 $
700 $
600
0
0
0
1
0
0
0
1
1
Downhill Ski
$
7,000
$
750
0
1
0
Number of Sales Expected as a Result of Placing Ads
Off-Road
Trout Caster DotComWorld Mad Hacker
2,000
4,500
2,300
2,000
3,000
5,500
3,100
2,500
3,500
6,000
3,900
3,000
3,700
6,200
4,700
3,100
3,900
6,250
5,000
3,200
Downhill Ski
3,500
5,000
5,200
5,400
5,600
Off-Road
6,000
800
1
1
0
Product
Unit Cost
$
15.50
Advertising Budget
$
30,000.00
Number of Ads
1
2
3
4
5
Is Magazine Used?
C
Motor Sport
0
0
0
1
0
1
Total Ad Cost
Unit Sales Generated
Motor Sport
$
12,000
8,000
Revenue
Advertising Cost
Production Cost
Profit
$
$
$
$
476,100
29,900
320,850
125,350
$
D
Product
Sales Price
$
23.00
G
Number of Magazines Required in Category
Automotive
1
Outdoor
1
Computer
1
Off-Road
0
0
0
0
0
0
Placement Decisions
Trout Caster DotComWorld
0
0
1
0
0
0
0
1
0
0
1
1
Off-Road
-
Trout Caster DotComWorld Mad Hacker
$
6,900 $
7,100 $
3,900
5,500
4,700
2,500
Mad Hacker
0
1
0
0
0
1
Downhill Ski
0
0
0
0
0
0
Downhill Ski
$
-
Magazines Used in Category
Automotive
1
Outdoor
1
Computer
2
(a) Cell B29 should contain a one if any ads are placed in Motor Sport, and otherwise it
should contain a zero. It is not itself a changing cell, but is computed via a formula.
What should that formula be? Make sure your answer will yield correct results for the
other magazines when copied to cells C29:G29.
(b) What formula should you put in cell B32, the total amount spent to place ads in Motor
Sport? Make sure your answer will yield correct results for the other magazines when
copied to cells C32:G32.
(c) What formula should you put in cell B33, the number of products sold as the result of
ads placed in Motor Sport? Make sure your answer will yield correct results for the
other magazines when copied to cells C33:G33.
(d) What formula should you put in cells B36:B39? These cells should contain,
respectively, the total revenue from sales resulting from the ad campaign, the total cost
Practice Questions for Midterm Exam 2
-- 15 --
Fall 2001
of placing the ads, the cost of making the products sold as a result of the campaign, and
the total “bottom line” effect of the campaign.
(e) What formula should be in cell E36, the number of magazines in the “automotive”
category in which ads were placed? Make sure your answer will yield correct results
for the other categories when copied to cells E37 and E38.
(f) What target cell should you use in the Solver? Should you maximize or minimize it?
What are all the constraints you should use in the Solver? Should you check “assume
nonnegative”? Should you check “assume linear model”? Suppose you want a solution
within 0.5% of the best possible. How would you set the “tolerance” Solver parameter?
12: Selling Dresses by Catalog
Madelaine, Inc. is a catalog retailer of fashion clothes for women. They are considering
purchasing some new “petite” size summer dresses at the unit cost of $10. Historical data
indicate that they have 70,000 customers who both receive their catalog and buy clothes of this
size and style.
First, Madelaine will try to sell the dresses at a regular price of $60. Some of the dresses sold at
this price may be returned for a full refund. Next, they will offer the remaining dresses,
including any that were returned, at a clearance price of $40. Clearance-price dresses may also
be returned for a full refund. Madelaine’s marketing research provides, for the customer group
in question, the following data on the probability of placing an order and returning a dress:
Probability of Order
Probability of Return
Regular Price
1%
20%
Clearance Price
2%
10%
If a customer orders a dress at the regular price, she will not order one for the clearance price,
whether or not she decides to return it.
If there are any items left after the clearance, they can be sold to the discount retailer E. X. Minn
for a price which will be determined later. This price is equally likely to be any value between
zero and a maximum value of $15. E. X. Minn will not take more than 200 dresses of this size.
Any remaining dresses must be disposed of through donation to charity. Such a donation would
involve no revenue or cost, but Madelaine would still like to know how likely it would be.
To determine the optimal number of dresses to buy from the producer, Madelaine is using the
simulation spreadsheet below. Cell E7 contains the formula =D12. Cell H9 contains =H7*H8.
Cell D15 contains =D13+D14+H9, cell D16 contains =A15*D7, and D17 contains =D15  D16.
Cells A5:A12 contain possible purchase quantities for the dresses.
Practice Questions for Midterm Exam 2
-- 16 --
Fall 2001
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A
B
C
Customer Pool Size
70000
Price
Probability of Order
Dresses Purchased
Probability of Return
1600
1700
1800
Items Available
1900
Orders Placed
2000
Items Delivered
2100
Returns
2200
Items Sold
2300
Items Left
Revenue
Unit Purchase Price
$
10
Total Revenue
Total Cost
Profit
D
E
F
Regular Clearance
$
60 $
1%
20%
40
2%
10%
Regular Clearance
1600
1045
681
1347
681
1045
126
107
555
938
1045
107
$ 33,300 $ 37,520
$ 71,756
$ 16,000
$ 55,756
G
H
Salvage
$
15
Maximum Price
200
Maximum Quantity
Salvage
$ 8.75
107
$ 936
Price
Quantity
Value
Are There Items Left?
0
(a)
What formula should be in cell D7, to set the number of dresses available for the
regular price?
(b)
What formulas should be in cells D8 and E8, to simulate the number of orders at the
regular and clearance prices, respectively?
Parts (c)-(g) below ask about cells D9:D13, which concern regular-price dresses. In each
case, make sure your answer will yield correct result for clearance-price dresses when
copied to the corresponding cell in column E.
(c)
What formula should be in cell D9, to calculate the number of dresses sent to
customers?
(d)
What formula should be in cell D10, to calculate the number of dresses returned?
(e)
What formula should be in cell D11, to calculate the number of dresses sold? A
dress is considered “sold” if it is sent to a customer and is not returned.
(f)
What formula should be in cell D12, to calculate the number of dresses left after
deliveries and returns?
(g)
What formula should be in cell D13, to calculate the revenue from sales?
(h)
What formula should be in cell H7, to simulate the salvage price offered by E. X.
Minn?
(i)
What formula should be in cell H8, to calculate the salvage quantity?
(j)
What formula should be in cell G16, which should contain 1 if there are dresses to
be disposed of via charity, and 0 otherwise?
Practice Questions for Midterm Exam 2
-- 17 --
Fall 2001
Note: the output below was produced by the commercial product @Risk, which is similar to
YASAI, but more complicated. The “Mean” column is similar to YASAI’s “Mean” column.
“Sim #1” means “scenario 1” etc. You may ignore the “minimum” and “maximum” columns.
Cell
D17 (Sim#1)
D17 (Sim#2)
D17 (Sim#3)
D17 (Sim#4)
D17 (Sim#5)
D17 (Sim#6)
D17 (Sim#7)
D17 (Sim#8)
G16 (Sim#1)
G16 (Sim#2)
G16 (Sim#3)
G16 (Sim#4)
G16 (Sim#5)
G16 (Sim#6)
G16 (Sim#7)
G16 (Sim#8)
Name
Minimum Mean
Maximum
Profit / Regular
53,724
55,819
58,526
Profit / Regular
56,340
58,494
61,276
Profit / Regular
58,956
61,168
64,026
Profit / Regular
58,785
63,738
66,749
Profit / Regular
57,785
64,758
69,499
Profit / Regular
56,785
63,992
70,333
Profit / Regular
55,785
62,994
69,573
Profit / Regular
54,785
61,994
68,573
Total Cost / Are There Items Left?
0.000
0.000
0.000
Total Cost / Are There Items Left?
0.000
0.000
0.000
Total Cost / Are There Items Left?
0.000
0.000
0.000
Total Cost / Are There Items Left?
0.000
0.007
1.000
Total Cost / Are There Items Left?
0.000
0.433
1.000
Total Cost / Are There Items Left?
0.000
0.990
1.000
Total Cost / Are There Items Left?
1.000
1.000
1.000
Total Cost / Are There Items Left?
1.000
1.000
1.000
(k)
What is the optimal number of dresses to order from the producer? At this order
level, what is the probability that any dresses will eventually have to be donated to
charity?
(l)
Suppose that, because of some problems in its tax filing procedure, Madelaine wants
to be certain that it will not have to donate any dresses to charity. In this case, what
would be the best number of dresses to buy?
13: Simulating Semiconductor Fabrication
The Silicon Circuit company produces semiconductor chips on silicon wafers. Each wafer has 20
slots for chips. The firm wants to produce two new chip types, SCA and SCB, on the same
wafers. The production process is subject to random disturbances, and new chips frequently fail
quality testing. Each SCA chip passes its quality test with probability 80%, and each SCB chip
passes with probability 60%.
Silicon Circuit manufactures SMM modules by combining two good SCA chips and one good
SCB chip. The firm wants to maximize the expected number of SMM modules that can be
assembled from the chips manufactured on one wafer. They are also interested in the question
whether the number of SMM modules assembled from chips on one wafer is greater than three.
They are considering assigning between 10 to 14 slots on each wafer to SCA chips, and the
remaining slots to SCB chips.
To assist in their planning process, the firm is using the simulation spreadsheet shown below. In
this spreadsheet, cell B8 contains the number of slots assigned to SCA chips, cell D14 contains
Practice Questions for Midterm Exam 2
-- 18 --
Fall 2001
the (random) number of SMM modules that can be built from the chips passing the quality test,
and cell D16 contains the formula =IF(D14>3,1,0).
A
B
C
1 Number of slots on wafer
20
2
3
Yield
4
SCA
80%
5
SCB
60%
6
7
Slots on Wafer Passed Quality Test
8
SCA
10
9
9
SCB
10
7
10
11
12
13
14
Number of SMM modules
15
16
Do we have more than 3 modules ?
D
E
Slots for
SCA
10
11
12
13
14
4
1
(a) What formulas should be in cells B8:B9, for the number of slots assigned to SCA and
SCB chips, respectively?
(b) What formulas should be in cells C8:C9, to simulate the number of SCA and SCB chips
passing the quality test?
(c) What formula should be in cell D14, to compute the number of SMM modules that can
be assembled? Note that this cell should also be a simulation output.
(d) What formula shold be in cell D16, to compute a 1 if the number of SMM modules is
greater than 3, and 0 otherwise? Note that this cell should also be a simulation output.
Hint: The Excel function INT(value) returns value rounded downward to a whole number.
Using the (partial) simulation output shown on the following page, answer the following
questions: Note: this is @Risk output, not YASAI, but it should be understandable. For
example,“Sim #3” means “scenario 3”, and so forth. You may ignore the “minimum” and
“maximum” columns.
(e) What is the best assignment of slots to SCA and SCB chips?
(f) If 10 slots are assigned to SCA chips, what is the probability that the number of SMM
modules assembled from one wafer will be greater than three?
Practice Questions for Midterm Exam 2
-- 19 --
Fall 2001
Cell
D14 (Sim#1)
D14 (Sim#2)
D14 (Sim#3)
D14 (Sim#4)
D14 (Sim#5)
D16 (Sim#1)
D16 (Sim#2)
D16 (Sim#3)
D16 (Sim#4)
D16 (Sim#5)
Name
Number of SMM modules
Number of SMM modules
Number of SMM modules
Number of SMM modules
Number of SMM modules
Do we have more than 3 modules
Do we have more than 3 modules
Do we have more than 3 modules
Do we have more than 3 modules
Do we have more than 3 modules
Minimum
Mean
0
0
0
0
0
0
0
0
0
0
?
?
?
?
?
Number of
Maximum
3.6858
3.9607
4.0646
3.9385
3.5563
0.6441
0.7623
0.7709
0.693
0.5432
Number of
5
5
6
6
6
1
1
1
1
1
Number of
Number of
14:
NameProducing Miniature
Number ofLocomotives
SMM modules
SMM modules SMM modules SMM modules SMM modules
Description
Output
(Sim#1)
Output
(Sim#2) Output
(Sim#3)
Output
(Sim#4)
Output (Sim#5)
Precision Modelers, Inc. produces model railroad products
for “high
end”
hobby
enthusiasts.
Cell
D14
D14
D14
D14
D14
The
firm has identified 7 possible miniature locomotives
it
is considering
making during
the 0
Minimum =
0
0
0
0
upcoming
production
cycle:
Maximum =
5
5
6
6
6
Mean =
3.6858
3.9607
4.0646 Unit 3.9385
3.5563
Maximum
Unit
Std Deviation =
0.7063132Unit0.7786883
1.064762
Tooling
that can 0.9078694Casting
Assembly1.131738
Variance =
0.4988784
0.8242269
1.28083
Profit0.6063555
Name
Costs
be Sold Axles
Time1.133718
Time
Skewness =
-0.3988454
-0.5797799
-0.5933589
-0.4729334
-0.2977693
$ 800
600
4
0.20 3.12337
0.30 2.803695
Kurtosis = 1 Acella
3.406162$ 33 3.570745
3.549976
2
SP
Cab
Forward
$
2,400
$
56
500
12
0.70
0.80
Errors Calculated =
0
0
0
0
0
Mode = 3 Mallard
4
4
4
4
4
$ 1,300
$ 48
400
6
0.30
0.40
5% Perc =4 GG1
3
3
2
2
2
$ 900
$ 31
700
10
0.20
0.45
10% Perc =
3
3
3
3
2
5 New Haven Combo
$ 700
$ 23
400
4
0.20
0.25
15% Perc =
3
3
3
3
2
6 Crocodile
$ 1,900
450
8
0.50
20% Perc =
3$ 75
3
3 0.60
3
3
7 Deltic
$ 850
300
6
0.30
25% Perc =
3$ 44
4
4 0.35
3
3
30% Perc =
3
4
4
3
3
35% Perc =
3
4
4
4
The times in the last two columns are in hours. Tooling costs are incurred only if a product is 3
40% Perc =
4
4
4
4
3
produced,
If the firm
decides to
45% Perc = but do not depend on the number of
4 units produced.
4
4
4 have any 3
production
it must4make at least4 200 units, but
50% Perc = of a given product in the current cycle,
4
4 not more 4
55% the
Perc“maximum
=
4
than
that can be sold” quantity4 in the table.4 A total of 430
hours of 4casting time 4
60% Perc =
4
4
4
4
4
and
625 hours of assembly time will be available.
You must
finish producing
all the
locomotives
65% Perc =
4
4
4
4
4
you
making during the production cycle4— you can’t4 leave fractions
of locomotives
to be 4
70%start
Perc =
5
5
finished
75% Perc in
= the next cycle.
4
4
5
5
4
80% Perc =
4
5
5
5
5
85% Perc =
4
5
5
5
At least 3 different products must be made. In addition, the products are categorized as in the 5
90% Perc =
4
5
5
5
5
table
below,
in each
European,
95% Perc
= and you must make at least one product
5
5 category (US,
5
5 electric, 5
diesel, steam). A product can “count towards” multiple categories; for example, if you make the
Acella locomotive, that would satisfy the requirement for both the US and electric categories.
1
1
2
3
4
5
6
7
Name
Acella
SP Cab Forward
Mallard
GG1
New Haven Combo
Crocodile
Deltic
Practice Questions for Midterm Exam 2
US
X
X
2
3
European Electric
X
4
5
Diesel
Steam
X
X
X
X
X
X
X
-- 20 --
X
X
X
X
X
Fall 2001
Algebraically formulate an optimization model to give the firm the highest possible profits
for the upcoming production cycle. Give clear, numeric definitions of your decision
variables. You are allowed to skip algebraic simplifications (if any arise). If possible,
make your objective function and constraints linear.
15: Assigning Workers to Tasks
You manage three workers: Bok, Bowen, and Giamatti. You have six tasks (“task 1” through
“task 6”) to assign to these workers. The tasks are independent of one another and do not have to
be done in any particular order. For each task, there should be one worker. A worker may have
more than one task, in which case the worker performs them one after another until they are all
complete. You have estimated the number of days it would take each worker to perform each of
the tasks, as indicated in the table at the top of the spreadsheet displayed below (for example,
Bok will take 3 days to perform task 1, and Bowen 7 days to perform task 3).
Your goal is to finish all the tasks, and to be able to declare them all to be done as early as
possible. To help decide the assignment of tasks, you are using the spreadsheet model below,
which shows an optimal solution. If possible, your target cell and constraints should be linear.
(a) What formula should be in cell E12, to compute the number of workers assigned to task
1? Make sure your answer will yield correct results for tasks 2-6 when copied to cells
E13:E17.
(b) What formula should be in cell B21, to compute the total days of work assigned to Bok?
Make sure your answer will yield correct results for Bowen and Giamatti when copied
to cells C21:D21.
(c) Assume that you are using Solver to find a solution within 1% of optimal. What is the
target cell, and should it be maximized or minimized? What are the changing cells?
What are all the constraints? Should you “assume nonnegative”? Is it possible to
“assume linear model”? How should you set the “tolerance”?
(d) Do you need to supply a formula for cell B24, the days until you declare all tasks
complete? If so, what should it be?
Practice Questions for Midterm Exam 2
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Fall 2001
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
A
B
Days to do Tasks
Bok
Task 1
3
Task 2
8
Task 3
4
Task 4
12
Task 5
9
Task 6
3
C
D
Bowen
4
10
7
12
6
3
Giamatti
5
7
6
9
8
5
Bowen
1
0
0
0
1
1
Giamatti
0
1
1
0
0
0
Days Spent by Workers
Bok
Bowen
12
13
Giamatti
13
E
Assignments
Task 1
Task 2
Task 3
Task 4
Task 5
Task 6
Bok
0
0
0
1
0
0
1
1
1
1
1
1
Declare All Tasks Done
13
Days
16: Staffing an Office
You operate an office that handles requests for medical documentation from insurance
companies. The number of requests you get per day varies randomly, following a Poisson
distribution with a mean of 225. Most requests require 5 minutes to process, but each one has a
30% probability, independent of all other requests, of becoming a “level 2” request that requires
15 additional minutes of processing.
You would like to operate the center at the minimum possible average cost per day, and are
trying to decide whether to hire 3, 4, 5, or 6 workers to process the requests. Each worker
receives a $175 daily salary, for which they will work up to 7 hours. Each worker can work an
additional 2 hours of overtime for $37.50 per hour. If further labor is required to finish the day’s
requests, it must be obtained from a “temp” agency that charges $60 per hour.
To help make your decision, you are using the following simulation spreadsheet:
Practice Questions for Midterm Exam 2
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Fall 2001
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
A
Average Demand
Probability of Level 2
Minutes per Level 1 Request
Extra minutes per Level 2 Request
Hours per Worker
Worker Base Salary
Max Overtime Hours per Worker
Overtime Hourly Rate
Temp Agency Hourly Rate
Workers Hired
B
$
$
$
225
0.3
5
15
7
175.00
2
37.50
60.00
4
Number of Requests
Level 2 Requests
Total Hours of Work
223
75
37.333
Hours of Regular Work
Hours of Overtime Work
Hours of Temp Agency Work
28.000
8.000
1.333
Total Cost
$ 1,080.00
(a) What formula should be in cell B11, for the number of workers hired?
(b) What formula should be in cell B13, the number of requests received?
(c) What formula should be in cell B14, the number of requests that become “level 2”?
(d) What formula should be in cell B15, the total hours of work needed to process the day’s
requests?
(e) What formulas should be in cells B17:B19, the number of regular-time hours worked,
the number of overtime hours worked, and the number of temp agency hours,
respectively?
(f) What formula should be in cell B21, the total cost of the day’s operations?
(g) Consider the simulation output report below. How many workers should you hire?
Practice Questions for Midterm Exam 2
-- 23 --
Fall 2001
YASAI Simulation Output
Workbook
Sheet
Start Date
Start Time
Run Time (h:mm:ss)
Scenarios:
Sample Size:
staff-office.xls
Sheet1
11/15/01
10:01:58 AM
0:00:18
4
1000
Scenario
1
2
3
4
Parameter
Workers Hired
3
4
5
6
Output Name
Total Cost
Total Cost
Total Cost
Total Cost
Practice Questions for Midterm Exam 2
Scenario
1
2
3
4
-- 24 --
Observations Mean
1000 1271.586
1000 1012.104
1000 933.683
1000 1050.881
Standard
Deviation
178.463
144.385
75.169
7.883
Fall 2001