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



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



# 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)



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



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

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



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



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!



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!



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.)



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.

sunco question

Documents