Sunco Question
-
Upload
varun-hknz -
Category
Documents
-
view
37 -
download
0
Transcript of Sunco Question
5/17/2018 Sunco Question - slidepdf.com
http://slidepdf.com/reader/full/sunco-question 1/10
1
IE 416: Operations Research I Fall 2010
Source of the problem statement: W. L. Winston, " Operations Research, Application and
Algorithms"
Solution by student groups (formulation was given)
Dr. Parisay’s comments are in red.
Sunco Oil, Problem 1, pg 97
Problem Statement
Sunco Oil has three different processes that can be used to manufacture various types of gasoline.
Each process involves blending oils in the company's catalytic cracker. Running process 1 for an
hour costs $5 and requires 2 barrels of crude oil 1 and 3 barrels of crude oil 2. The output fromrunning process 1 for an hour is 2 barrels of gas 1 and 1 barrel of gas 2. Running process 2 for an
hour costs $4 and requires 1 barrel of crude 1 and 3 barrels of crude 2. The output from running
process 2 for an hour is 3 barrels of gas 2. Running process 3 for an hour costs $1 and requires 2
barrels of crude 2 and 3 barrels of gas 2. The output from running process 3 for an hour is 2
barrels of gas 3. Each week, 200 barrels of crude 1, at $2 /barrel, and 300 barrels of crude 2, at
$3/barrel, may be purchased. All gas produced can be sold at the following per-barrel prices: gas
1, $9; gas 2, $10, gas 3, $24. Formulate an LP whose solution will maximize revenues less costs.
Assume that only 100 hours of time on the catalytic cracker are available each week.
Summary Table
Input Output
Run
Time
Run
Cost
Crude
Oil 1
Crude
Oil 2
Gas 2 Gas
1
Gas
2
Gas
3
Process 1 1 hr $5 2 3 0 2 1 0
Process 2 1 hr $4 1 3 0 0 3 0
Process 3 1 hr $1 0 2 3 0 0 2
5/17/2018 Sunco Question - slidepdf.com
http://slidepdf.com/reader/full/sunco-question 2/10
2
Max 100
hrs/week
- 200 300 - - - -
Cost - - $2/barrel $3/barrel Selling
Price
$9 $10 $24
Decision Variables
These variable names could be confusing when used in formula as there is space between letters.
For example you can change “Hrs to run P1” to “HrsToRunP1”. Even more confusing in
formula is for example “# of C1 to buy”. It is better to use your constraint name rather than C1
and C2 … to assist with analysis later on.
Hrs to run P1 = Process 1 running hours
Hrs to run P2 = Process 2 running hours
Hrs to run P3 = Process 3 running hours
# of C1 to buy = Barrels of Crude Oil 1 purchased
# of C2 to buy = Barrels of Crude Oil 2 purchased
# of G2 to sold = Barrels of Gas 2 sold (not re-used)
Objective Function
The goal of the objective function is to maximize profit, and this can be done by subtracting
purchase cost and operating cost by the revenues.
Objective: maximize profit (revenue – purchase costs – operating costs)
Max Z= (9*2* Hrs to run P1 + 10*1*# of G2 to sold +24*2* Hrs to run P3) – (2*# of C1 to
buy + 3*# of C2 to buy) – (5 Hrs to run P1 + 4 Hrs to run P2 + Hrs to run P3)
5/17/2018 Sunco Question - slidepdf.com
http://slidepdf.com/reader/full/sunco-question 3/10
3
MaxZ = 13 * Hrs to run P1 – 4 * Hrs to run P2 + 47 * Hrs to run P3 – 2 * # of C1 to buy – 3 *
# of C2 to buy + 10 * # of G2 to sold
Constraints
- Crude 1 purchase: # of C1 to buy – 2 * Hrs to run P1 - Hrs to run P2 = 0 - Crude 2 purchase: # of C2 to buy – 3 * Hrs to run P1 – 3 * Hrs to run P2 – 2 * Hrs to
run P3 = 0 - Gas 3 production: Produced= sold + re-used in process 2
Hrs to run P1 + 3 * Hrs to run P2 - # of G2 to sold – 3 * Hrs to run P3 = 0 - Process time Limit: Hrs to run P1 + Hrs to run P2 + Hrs to run P3 ≤ 100
- Max Crude 1: # of C1 to buy ≤ 200 - Max Crude 2: # of C2 to buy ≤ 300
WinQSB Problem Specification
WinQSB Input
5/17/2018 Sunco Question - slidepdf.com
http://slidepdf.com/reader/full/sunco-question 4/10
4
WinQSB Output
After performing the calculations in WinQSB, we have obtained the obtimal solution of z= 1500,
hours to run process 1 = 0, hours to run process 2 = 100, hours to run process 3 = 0, number of
C1 to buy = 100, and number of C2 to buy = 300 and number of G2 sold = 300.
Sensitivity Analysis (O.F)
This sensitivity analysis is not clear and most probably has mistake. It is hard to find out what isthe mistake because of variable names. If you are selecting “# of C1 to buy” then its coefficient
is its cost and “-2”. You need to explain motivation for selecting these SA.
5/17/2018 Sunco Question - slidepdf.com
http://slidepdf.com/reader/full/sunco-question 5/10
5
We perform sensitivity analysis on the objective function, changing the values number (cost not
number) of C1 to be bought per week. Notice that you made mistake in your explanation, and I
guess it is because of how you defined your variable names!!
Sensitivity Analysis (O.F) Output Summary
Sensitivity Analysis (O.F) Graphical Summary
5/17/2018 Sunco Question - slidepdf.com
http://slidepdf.com/reader/full/sunco-question 6/10
6
Sensitivity Analysis (RHS) Problem Specification
You need to explain motivation for selecting these SA.
We also perform sensitivity analysis on the right hand side of the constraint which limit the hours
for the process to run per week.
Sensitivity Analysis (RHS) Output Summary
Sensitivity Analysis (RHS) Graphical Summary
5/17/2018 Sunco Question - slidepdf.com
http://slidepdf.com/reader/full/sunco-question 7/10
7
Objective Function Coefficient (OBJ) SA:
You need to explain motivation for selecting these SA. These decision variables do not
match the previous tables!! Be consistant. Poor job!
SA for Process 1 Running Hours (OBJ):
You need to explain motivation for selecting these SA. This is based on another solution
that was wrong!!! Be consistent!
5/17/2018 Sunco Question - slidepdf.com
http://slidepdf.com/reader/full/sunco-question 8/10
8
Right Hand Side SA:
You need to explain motivation for selecting these SA. These constraint names do not
match the previous tables!! Be consistant. Poor job!
5/17/2018 Sunco Question - slidepdf.com
http://slidepdf.com/reader/full/sunco-question 9/10
9
SA for Constraint on Maximum Amount available for Crude Oil 1:
Report to the Manager
Is this a group effort for report to the manager?!!
Dear Manager,
After performing calculations on the data, Sunco Oil should be able to maximize revenue
to $1500 per week. (What is this?!! This is an expected value, which means that the actual value
will not be exactly the same as the value that we have calculated.) In order to obtain the
maximized profit, Sunco Oil will need to spend 100 hours each week to run process 2, buy 100barrels of Crude 1, buy 300 barrels of Crude 2 and sell 300 barrels of gas 2. (What is this?!!
Again, these are only expected values, meaning that they are averages of a number of possible
values.)
5/17/2018 Sunco Question - slidepdf.com
http://slidepdf.com/reader/full/sunco-question 10/10
10
Variable Production/PurchaseAmount
Process 1 Running Hours 100 hours
Process 2 Running Hours 0
Process 3 Running Hours 0
Barrels of Crude Oil 1 200 barrels
Barrels of Crude Oil 2 300 barrels
Barrels of Gas 2 (to sell) 100 barrels
Profit: $1,000
What is the table above?!! What is the source of it? Repeat the report below.
As this table shows, we will make our maximum profit of $1,000 by using the maximum
amount of Crude Oils 1 and 2, and using all of these resources to run Process 1 only. The
analysis performed shows all of the constraints in place are binding, meaning there is no room
for flexibility to change which Process we run for how long.
We have also performed sensitivity analysis on the case, where we want to find out the
changes that the revenue will have if the amount of crude 1 purchased per week varies. From the
sensitivity analysis output summary and the graphical summary, we can see that the revenue
decreases if the number of crude 1 purchased increases per week.
We performed another sensitivity analysis on the right hand side of the constraint which
limits the number of hours that can be used per week. The result shows that when Sunco Oil
slightly increases the number of hours from 100 to 120 hours per week, they will be expected to
gain an increase in revenue to $1560 per week. However, if the number of hours allowed to be
used per week decreases, the revenue will correspond and reduce as well.
If we had the budget to invest more into materials or time, we would want to invest in
increasing the maximum amount of Crude Oil 2 available or invest in finding a way to have
more time on the catalytic cracker each week. For every additional barrel of Crude Oil 2 that is
available, we could increase our profit by $1.67. For every additional hour that we could have
and use on the catalytic cracker, we would increase our profits by $5.00 for each additional hour.
If one of these routes were chosen, the optimal solutions would change, and further analysis
would need to be performed based on these new constraints in order to find our maximum profit
again.