Quantitative Management Practice Assignment

Quantitative Management Practice Assignment

Quantitative Management Practice Assignment

Part I

Introduction

AMARCO, Inc was formed in 1937 as joint venture between Standard Oil Company of California and Government of Saudi Arabia to explore, produce and market any petroleum found in the country.  Since 1950, the role of company has greatly increased by involving in exploration, drilling and refining production activities. As a result company introduce a Operation Research Department to review the firm’s operations to find other areas where costs might be decreased or profits increased by application of operation research. Now, main focus of the company is to identify the most favorable situation of how to produce the maximum aviation gasoline i.e. A, B & C which are made by blending of four feedstocks, through Operational Research Department to maximize the profits (David, 1982). Now, company is doing a operation research by using Linear Programming model to get the maximum results in the different business situations.

Quantitative Management Practice Assignment

Modeling

Linear programming is a technique which shows practical problems as a series of mathematical equations which can be manipulated to find the optimum or best solution (Adams, 1969). Blending is a graphical approach to linear programming which deals with resource allocation subject to constraints. It is a model which assists firms in deciding the best possible utilization of limited resources. Each resource constraint is represented as a mathematical linear equation. A linear expression is an equation which links two variables, and if plotted on a graph, would be represented by a straight line. By plotting all the equations, the optimal use of the business's resources can be easily identified.

Blending can be useful to firms when deciding how to make the best use of their resources. Businesses can use this method to allocate factors of production so that profits are maximized or costs minimized, depending on the business's objective. Another advantage of blending is that is allows the business to decide a combination of the two goods to produce, as compared to other invest appraisal or decision making techniques where either one or the other option must be selected, but not both (Anderson et al 2002).

In oil refining business, production is done on the basis of certain product mix (Andrade, 1990).  Standardization of product mix is complex task and which is required a lot of analysis and research.  AMARCO Inc has already developed the Linear Programming Models for their organization and getting the better results and as a result company has increased their profits and production (Dantzig, 1963). Here, blending method is used which is a part of LP model.  Mainly, blending problems are identified in gasoline operations.

Examples of blending problems:

Input             

Output

Meat, Filler, Water   

Different type of sausage

Various type of oil

Heating oil, gasolines, aviation fuels

Data Description

In the present situation, AMARCO, Inc has to produce the aviation gasoline, A, B & C which are made by blending four feedstock; Alkylate, Catalytic Cracked Gasoline, Straight Run Gasoline and Isopentane. 

Data is classified into two parts i.e. Input Data & Output Data

  • Input Data – Four Feedstock i.e. Alkylate / Catalytic Cracked Gasoline / Straight Run Gasoline / Isopentane
  • Output – Three types of Aviation Gasoline i.e Gas A, Gas B & Gas C

Results

By using the Blending model, management know about the best combination of production of resources available to get the best outcome and most profitability.  Various type of situation has been applied to get the better result in the different situation with the help of LP Models.  As a result, management get to know which situation will be the best for the company.  In the standard model of LP, the revenue of company was $ 816200.  As per the situation of Question No. 3, the revenue of company was increased from $ 816200 to $ 1632400.  In another situation, as per question 4 with the situation of Question 3, variable has been re-determined to align the requirement with availability and also because of reduction of stock level, revenue was slightly down from $1632400 to $1339523.  As per the situation of Question No. 7, the revenue of the company as drastically down and that is because of rate impact.  Stock level should be reduced while we enter in the downward market.  As per the situation of question no. 8, if there is not criteria of Octane level than company will first liquidate the stock of lower value in the downwards market and keep the stock of high value in hand so that the profit of the company will not be reduced.  As per situation of question no. 9, other factors also derive the profit / revenue of the business.  As the Reid Vapor pressure is reduced from 7 to 6, we need to change our variable mix, to achieve the desired level of result of environment.  As per question no. 10, as per market demand of the respective product lead to put your business into profit and loss.  As per this situation, if the order is for less profitable gases than simultaneously, product mix will also be changed to get the better result because market share is also a important factor and not ignorable.

Conclusions

From the above, it has been found that operational situations are not remains same for entire period of operation, situation got changed because of various reasons.  So, one formula or one technique can not be enough to take decisions (Bierman et al 1973).  But by applying various methods, it become easy to decide what is good for our business or to have the better results.  Linear Programming model is one the best technique to get the better outcome.  Here, we have found that by using the blending model of Linear Programming, management can have the better mix of production to get the best results from operations in the different situations.  As per above results, it is clear that every situation is making the impact on the research.  Every time variable of production is getting changed.  Determination of suitable product mix is a most difficult task in the business and it can be derived in the business like gasoline by only blending method of Linear Programming.  Business is done to make profits and be leader in their segment.  So, by doing such type of research, it’s become easy for management to decide the ideal way for every situation / problems (Chopra & Meindl, 2001).  In the business of gasoline, pricing fluctuation is exist in the systems and also this business is highly dependable on environmental and political situation.  Any change in these conditions certainly made impact on the business.  So, management must do such type of research, so that any unforeseen problem / situation can not harm the business.  Linear Programming model is definitely a very suitable tool for avoiding such type of problems / situations.

Part – II

Q1 data analysis answer

LP spreadsheet model:

Adjustable Cells

     

Cell

Name

Final

Reduced

Objective

Allowable

Allowable

Value

Cost

Coefficient

Increase

Decrease

$C$6

Values of Variables X11

         2,175.34

                    -  

              15.00

                0.24

                    -  

$D$6

Values of Variables X12

                    -  

              (0.00)

              16.00

                0.00

                1.00

$E$6

Values of Variables X13

         5,424.66

                    -  

              16.50

                    -  

                1.00

$F$6

Values of Variables X21

                    -  

              (0.00)

              15.00

                0.00

                1.00

$G$6

Values of Variables X22

         6,780.82

                    -  

              16.00

                    -  

                0.00

$H$6

Values of Variables X23

         6,219.18

                    -  

              16.50

                0.19

                    -  

$I$6

Values of Variables X31

         8,523.12

                    -  

              15.00

                    -  

                0.00

$J$6

Values of Variables X32

         5,476.88

                    -  

              16.00

                0.00

                    -  

$K$6

Values of Variables X33

                    -  

              (0.00)

              16.50

                0.00

                1.00

$L$6

Values of Variables X41

         2,301.54

                    -  

              15.00

                    -  

                0.00

$M$6

Values of Variables X42

            742.29

                    -  

              16.00

                0.00

                    -  

$N$6

Values of Variables X43

            356.16

                    -  

              16.50

                    -  

                3.02

$O$6

Values of Variables X1

         6,400.00

                    -  

              17.00

              34.91

                0.12

$P$6

Values of Variables X2

                    -  

              (1.90)

              14.50

                1.90

                1.00

$Q$6

Values of Variables X3

                    -  

              (3.70)

              13.50

                3.70

                1.00

$R$6

Values of Variables X4

         7,600.00

                    -  

              14.00

                3.00

                0.75

       

Constraints

     

Cell

Name

Final

Shadow

Constraint

Allowable

Allowable

Value

Price

R.H. Side

Increase

Decrease

$S$10

Gas A LHS

                0.00

                0.20

                    -  

       32,630.14

       34,523.12

$S$11

Gas B LHS

              (0.00)

                0.20

                    -  

       11,108.40

         3,255.71

$S$12

Gas C LHS

                    -  

                0.20

                    -  

       79,200.00

         5,379.31

$S$14

Alkalyte LHS

       14,000.00

              17.00

       14,000.00

                1.00

         6,400.00

$S$15

Cat Crack Gas LHS

       13,000.00

              16.40

       13,000.00

            925.70

         5,697.49

$S$16

Str Run Gas LHS

       14,000.00

              17.20

       14,000.00

            694.27

         6,000.00

$S$17

Isopentane LHS

       11,000.00

              14.00

       11,000.00

                1.00

         7,600.00

$S$19

Gas A LHS

       13,000.00

                    -  

       12,000.00

         1,000.00

                1.00

$S$20

Gas B LHS

       13,000.00

              (2.20)

       13,000.00

         3,692.31

            456.30

$S$21

Gas C LHS

       12,000.00

              (0.10)

       12,000.00

         7,384.62

         1,786.15

$S$22

Marketing LHS

              (0.00)

              (1.60)

                    -  

         7,384.62

            979.19

$S$24

Gas A LHS

       13,839.21

                    -  

                    -  

       13,839.21

                1.00

$S$25

Gas B LHS

         4,273.12

                    -  

                    -  

         4,273.12

                1.00

$S$26

Gas C LHS

              (0.00)

                    -  

                    -  

       13,515.22

       26,000.00

As per above LP spreadsheet model, maximum values of the different criteria are considered as constraints and resources is considered as Adjustment cells.  As product mix impact the profitability of the business but while allocating the mix, constraints should also be taken care as if constraints are not followed than the quality of the product will not be adequate.

Q2 data analysis answer

Particulars

Alkylate

Catalytic Cracked Gasoline

Straight Run Gasoline

Isopentane

 

 

 

 

LHS

Sign

RHS

blended in gasoline

blended in gasoline

blended in gasoline

blended in gasoline

Feedstock

A

B

C

A

B

C

A

B

C

A

B

C

not blended in gasoline

Variables

X11

X12

X13

X21

X22

X23

X31

X32

X33

X41

X42

X43

X1

X2

X3

X4

Values of Variables

2175

0

5425

0

6781

6219

8523

5477

0

2302

742

356

6400

0

0

7600

 

 

 

Objective function

15

16

17

15

16

17

15

16

17

15

16

17

17

14.5

14

14

816200

 

 

Constraints

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reid Vapor Pressure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

-2

 

 

1

 

 

-3

 

 

13

 

 

 

  

 

0

0

Gas B

 

-2

 

 

1

 

 

-3

 

 

13

 

 

  

 

0

0

Gas C

 

 

-2

 

 

1

 

 

-3

 

 

13

 

 

 

 

0

0

Availability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alkalyte

1

1

1

 

 

 

 

 

 

 

 

 

1

  

 

14000

?

14000

Cat Crack Gas

 

 

 

1

1

1

 

 

 

 

 

 

 

1

 

 

13000

?

13000

Str Run Gas

 

 

 

 

 

 

1

1

1

 

 

 

 

 

1

 

14000

?

14000

Isopentane

 

 

 

 

 

 

 

 

 

1

1

1

 

 

 

1

11000

?

11000

Demand

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

1

 

 

1

 

 

1

 

 

1

 

 

 

  

 

13000

12000

Gas B

 

1

 

 

1

 

 

1

 

 

1

 

 

  

 

13000

13000

Gas C

 

 

1

 

 

1

 

 

1

 

 

1

 

 

 

 

12000

12000

Marketing

1

-1

 

1

-1

 

1

-1

 

1

-1

 

 

 

 

 

0

0

Octane

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

Gas A

14

 

 

3

 

 

-6

 

 

15

 

 

 

  

 

13839

0

Gas B

 

17

 

 

2

 

 

-4

 

 

17

 

 

  

 

4273

0

Gas C

 

 

8

 

 

-7

 

 

-13

 

 

8

 

 

 

 

0

0

As per the above spreadsheet, total revenue of the company will be $ 816200.  This revenue is as per current mix plan.  The every constraint is as per required level.  So, by above LP spreadsheet, it is a good production mix.

Q3 data analysis answer

There are two situation of this question.

Situation No. 1-

Particulars

Alkylate

Catalytic Cracked Gasoline

Straight Run Gasoline

Isopentane

 

 

 

 

LHS

Sign

RHS

blended in gasoline

blended in gasoline

blended in gasoline

blended in gasoline

Feedstock

A

B

C

A

B

C

A

B

C

A

B

C

not blended in gasoline

Variables

X11

X12

X13

X21

X22

X23

X31

X32

X33

X41

X42

X43

X1

X2

X3

X4

Values of Variables

0

4844

9156

9750

3250

0

3250

3583

7167

0

1322

3062

0

0

0

6615

 

 

 

Objective function

30

32

33

30

32

33

30

32

33

30

32

33

17

14.5

14

14

1538308

 

 

Constraints

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reid Vapor Pressure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

-2

 

 

1

 

 

-3

 

 

13

 

 

 

  

 

0

0

Gas B

 

-2

 

 

1

 

 

-3

 

 

13

 

 

  

 

0

0

Gas C

 

 

-2

 

 

1

 

 

-3

 

 

13

 

 

 

 

0

0

Availability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alkalyte

1

1

1

 

 

 

 

 

 

 

 

 

1

  

 

14000

?

14000

Cat Crack Gas

 

 

 

1

1

1

 

 

 

 

 

 

 

1

 

 

13000

?

13000

Str Run Gas

 

 

 

 

 

 

1

1

1

 

 

 

 

 

1

 

14000

?

14000

Isopentane

 

 

 

 

 

 

 

 

 

1

1

1

 

 

 

1

11000

?

11000

Demand

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

1

 

 

1

 

 

1

 

 

1

 

 

 

  

 

13000

12000

Gas B

 

1

 

 

1

 

 

1

 

 

1

 

 

  

 

13000

13000

Gas C

 

 

1

 

 

1

 

 

1

 

 

1

 

 

 

 

19385

12000

Marketing

1

-1

 

1

-1

 

1

-1

 

1

-1

 

 

 

 

 

0

0

Octane

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

Gas A

14

 

 

3

 

 

-6

 

 

15

 

 

 

  

 

9750

0

Gas B

 

17

 

 

2

 

 

-4

 

 

17

 

 

  

 

94577

0

Gas C

 

 

8

 

 

-7

 

 

-13

 

 

8

 

 

 

 

0

0

As per above spreadsheet, a product mix has changed because of this profit has been increased from $816200 to $1538308.  So, in the demanding market, profits are always seen in the organisation because organisation got the profit on the material which was produced from stock.  In the above example also, revenue has been increased because the sold material was produced with low cost.

Situation No. 2-

Particulars

Alkylate

Catalytic Cracked Gasoline

Straight Run Gasoline

Isopentane

 

 

 

 

LHS

Sign

RHS

blended in gasoline

blended in gasoline

blended in gasoline

blended in gasoline

Feedstock

A

B

C

A

B

C

A

B

C

A

B

C

not blended in gasoline

Variables

X11

X12

X13

X21

X22

X23

X31

X32

X33

X41

X42

X43

X1

X2

X3

X4

Values of Variables

2175

0

5425

0

6781

6219

8523

5477

0

2302

742

356

6400

0

0

7600

 

 

 

Objective function

30

32

33

30

32

33

30

32

33

30

32

33

34

29.0

27

28

1632400

 

 

Constraints

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reid Vapor Pressure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

-2

 

 

1

 

 

-3

 

 

13

 

 

 

  

 

0

0

Gas B

 

-2

 

 

1

 

 

-3

 

 

13

 

 

  

 

0

0

Gas C

 

 

-2

 

 

1

 

 

-3

 

 

13

 

 

 

 

0

0

Availability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alkalyte

1

1

1

 

 

 

 

 

 

 

 

 

1

  

 

14000

?

14000

Cat Crack Gas

 

 

 

1

1

1

 

 

 

 

 

 

 

1

 

 

13000

?

13000

Str Run Gas

 

 

 

 

 

 

1

1

1

 

 

 

 

 

1

 

14000

?

14000

Isopentane

 

 

 

 

 

 

 

 

 

1

1

1

 

 

 

1

11000

?

11000

Demand

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

1

 

 

1

 

 

1

 

 

1

 

 

 

  

 

13000

12000

Gas B

 

1

 

 

1

 

 

1

 

 

1

 

 

  

 

13000

13000

Gas C

 

 

1

 

 

1

 

 

1

 

 

1

 

 

 

 

12000

12000

Marketing

1

-1

 

1

-1

 

1

-1

 

1

-1

 

 

 

 

 

0

0

Octane

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

Gas A

14

 

 

3

 

 

-6

 

 

15

 

 

 

  

 

13839

0

Gas B

 

17

 

 

2

 

 

-4

 

 

17

 

 

  

 

4273

0

Gas C

 

 

8

 

 

-7

 

 

-13

 

 

8

 

 

 

 

0

0

Total revenue is increased from will be increased $816200 to $1632400.  But profit has not been increased as per revenue increased because due to increase in price, cost of production has also been increased.  Product mix has not been changed in the above spreadsheet.

Q4 data analysis answer

Particulars

Alkylate

Catalytic Cracked Gasoline

Straight Run Gasoline

Isopentane

 

 

 

 

LHS

Sign

RHS

blended in gasoline

blended in gasoline

blended in gasoline

blended in gasoline

Feedstock

A

B

C

A

B

C

A

B

C

A

B

C

not blended in gasoline

Variables

X11

X12

X13

X21

X22

X23

X31

X32

X33

X41

X42

X43

X1

X2

X3

X4

Values of Variables

6775

0

5425

0

4781

6219

3117

5883

0

1762

990

356

0

0

0

7892

 

 

 

Objective function

30

32

33

30

32

33

30

32

33

30

32

33

34

29.0

27

28

1339523

 

 

Constraints

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reid Vapor Pressure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

-2

 

 

1

 

 

-3

 

 

13

 

 

 

  

 

0

0

Gas B

 

-2

 

 

1

 

 

-3

 

 

13

 

 

  

 

0

0

Gas C

 

 

-2

 

 

1

 

 

-3

 

 

13

 

 

 

 

0

0

Availability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alkalyte

1

1

1

 

 

 

 

 

 

 

 

 

1

  

 

12200

?

14000

Cat Crack Gas

 

 

 

1

1

1

 

 

 

 

 

 

 

1

 

 

11000

?

13000

Str Run Gas

 

 

 

 

 

 

1

1

1

 

 

 

 

 

1

 

9000

?

14000

Isopentane

 

 

 

 

 

 

 

 

 

1

1

1

 

 

 

1

11000

?

11000

Demand

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

1

 

 

1

 

 

1

 

 

1

 

 

 

  

 

11654

12000

Gas B

 

1

 

 

1

 

 

1

 

 

1

 

 

  

 

11654

13000

Gas C

 

 

1

 

 

1

 

 

1

 

 

1

 

 

 

 

12000

12000

Marketing

1

-1

 

1

-1

 

1

-1

 

1

-1

 

 

 

 

 

0

0

Octane

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

Gas A

14

 

 

3

 

 

-6

 

 

15

 

 

 

  

 

102578

0

Gas B

 

17

 

 

2

 

 

-4

 

 

17

 

 

  

 

2857

0

Gas C

 

 

8

 

 

-7

 

 

-13

 

 

8

 

 

 

 

0

0

As per question no. 4, availability of raw material has been decreased, but the prices are considered as per question no. 3, so revenue has been decreased because per day stock has been reduced.  As per above product mix revenue has been decreased from $1632400 to $1339523.

Q5 data analysis answer

As per the situation mentioned in question no. 4, the availability ration of raw material has been decreased.  Cost of processing will be increased because the availability of Straight Run Gasoline is decreased @ 35% which is almost double the rest other products.  And the cost of Straight Run Gasoline is cheaper than other products.  So, increasing the production in the present situation will lead to increase the cost of production.  So, profit will be decreased.  So, in this situation, product increase should be on the cost of increase the price of Gases also.

Q6 data analysis answer

As per current standard production mix with current demand, company is earning around 8% profit.  The declining and growing markets affect the profit of the company.  Increase in demand of one product and decline in demand of another product cal also lead to change the profit ration of the company.  The entire LP study is based on production mix. 

It is sensitive analysis that how change in market demand will impact the profit of company.  20% of increase or 20% decrease will change the profit of the company.

Q7 data analysis answer

Particulars

Alkylate

Catalytic Cracked Gasoline

Straight Run Gasoline

Isopentane

 

 

 

 

LHS

Sign

RHS

blended in gasoline

blended in gasoline

blended in gasoline

blended in gasoline

Feedstock

A

B

C

A

B

C

A

B

C

A

B

C

not blended in gasoline

Variables

X11

X12

X13

X21

X22

X23

X31

X32

X33

X41

X42

X43

X1

X2

X3

X4

Values of Variables

2175

0

5425

0

6781

6219

8523

5477

0

2302

742

356

6400

0

0

7600

 

 

 

Objective function

10

11

12

10

11

12

10

11

12

10

11

12

17

14.5

14

14

626200

 

 

Constraints

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reid Vapor Pressure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

-2

 

 

1

 

 

-3

 

 

13

 

 

 

  

 

0

0

Gas B

 

-2

 

 

1

 

 

-3

 

 

13

 

 

  

 

0

0

Gas C

 

 

-2

 

 

1

 

 

-3

 

 

13

 

 

 

 

0

0

Availability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alkalyte

1

1

1

 

 

 

 

 

 

 

 

 

1

  

 

14000

?

14000

Cat Crack Gas

 

 

 

1

1

1

 

 

 

 

 

 

 

1

 

 

13000

?

13000

Str Run Gas

 

 

 

 

 

 

1

1

1

 

 

 

 

 

1

 

14000

?

14000

Isopentane

 

 

 

 

 

 

 

 

 

1

1

1

 

 

 

1

11000

?

11000

Demand

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

1

 

 

1

 

 

1

 

 

1

 

 

 

  

 

13000

12000

Gas B

 

1

 

 

1

 

 

1

 

 

1

 

 

  

 

13000

13000

Gas C

 

 

1

 

 

1

 

 

1

 

 

1

 

 

 

 

12000

12000

Marketing

1

-1

 

1

-1

 

1

-1

 

1

-1

 

 

 

 

 

0

0

Octane

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

Gas A

14

 

 

3

 

 

-6

 

 

15

 

 

 

  

 

13839

0

Gas B

 

17

 

 

2

 

 

-4

 

 

17

 

 

  

 

4273

0

Gas C

 

 

8

 

 

-7

 

 

-13

 

 

8

 

 

 

 

0

0

As per above spreadsheet, suddenly drop in aviation gasoline price lead to loss to company because stock in hand was bought by company at the higher price.  Now, It has not been told about the prices impact Alkylate / Catalytic Cracked Gasoline / Straight Run Gasoline / Isopentane.  If the price of raw material has also been decreased than it’s a one time loss, but if the prices of raw material has not been decreased than company needs to seriously think about the continuation of business and needs to take the hard step regarding continuation of business.  Higher raw material cost could not be compensated with any method or technique.

Q8 data analysis answer

Particulars

Alkylate

Catalytic Cracked Gasoline

Straight Run Gasoline

Isopentane

 

 

 

 

LHS

Sign

RHS

blended in gasoline

blended in gasoline

blended in gasoline

blended in gasoline

Feedstock

A

B

C

A

B

C

A

B

C

A

B

C

not blended in gasoline

Variables

X11

X12

X13

X21

X22

X23

X31

X32

X33

X41

X42

X43

X1

X2

X3

X4

Values of Variables

0

0

7600

3250

9750

0

8125

3250

2625

1625

0

1775

6400

0

0

7600

 

 

 

Objective function

10

11

12

10

11

12

10

11

12

10

11

12

17

14.5

14

14

626200

 

 

Constraints

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reid Vapor Pressure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

-2

 

 

1

 

 

-3

 

 

13

 

 

 

  

 

0

0

Gas B

 

-2

 

 

1

 

 

-3

 

 

13

 

 

  

 

0

0

Gas C

 

 

-2

 

 

1

 

 

-3

 

 

13

 

 

 

 

0

0

Availability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alkalyte

1

1

1

 

 

 

 

 

 

 

 

 

1

  

 

14000

?

14000

Cat Crack Gas

 

 

 

1

1

1

 

 

 

 

 

 

 

1

 

 

13000

?

13000

Str Run Gas

 

 

 

 

 

 

1

1

1

 

 

 

 

 

1

 

14000

?

14000

Isopentane

 

 

 

 

 

 

 

 

 

1

1

1

 

 

 

1

11000

?

11000

Demand

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

1

 

 

1

 

 

1

 

 

1

 

 

 

  

 

13000

12000

Gas B

 

1

 

 

1

 

 

1

 

 

1

 

 

  

 

13000

13000

Gas C

 

 

1

 

 

1

 

 

1

 

 

1

 

 

 

 

12000

12000

Marketing

1

-1

 

1

-1

 

1

-1

 

1

-1

 

 

 

 

 

0

0

As per above spreadsheet, it is clear that there is no revenue impact because of octane constraint.  Octane level acceptance was so high in the product mix because of that we have found any revenue impact.  So, from AMARCO’s point, it is not impacting in the current production mix.

Q9 data analysis answer

Particulars

Alkylate

Catalytic Cracked Gasoline

Straight Run Gasoline

Isopentane

 

 

 

 

LHS

Sign

RHS

blended in gasoline

blended in gasoline

blended in gasoline

blended in gasoline

Feedstock

A

B

C

A

B

C

A

B

C

A

B

C

not blended in gasoline

Variables

X11

X12

X13

X21

X22

X23

X31

X32

X33

X41

X42

X43

X1

X2

X3

X4

Values of Variables

3133

684

6316

2250

6329

4421

6750

5987

1263

867

0

0

3867

0

0

10133

 

 

 

Objective function

15

16

17

15

16

17

15

16

17

15

16

17

17

14.5

14

14

808600

 

 

Constraints

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reid Vapor Pressure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

-1

 

 

2

 

 

-2

 

 

14

 

 

 

  

 

0

0

Gas B

 

-1

 

 

2

 

 

-2

 

 

14

 

 

  

 

0

0

Gas C

 

 

-1

 

 

2

 

 

-2

 

 

14

 

 

 

 

0

0

Availability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alkalyte

1

1

1

 

 

 

 

 

 

 

 

 

1

  

 

14000

?

14000

Cat Crack Gas

 

 

 

1

1

1

 

 

 

 

 

 

 

1

 

 

13000

?

13000

Str Run Gas

 

 

 

 

 

 

1

1

1

 

 

 

 

 

1

 

14000

?

14000

Isopentane

 

 

 

 

 

 

 

 

 

1

1

1

 

 

 

1

11000

?

11000

Demand

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

1

 

 

1

 

 

1

 

 

1

 

 

 

  

 

13000

12000

Gas B

 

1

 

 

1

 

 

1

 

 

1

 

 

  

 

13000

13000

Gas C

 

 

1

 

 

1

 

 

1

 

 

1

 

 

 

 

12000

12000

Marketing

1

-1

 

1

-1

 

1

-1

 

1

-1

 

 

 

 

 

0

0

Octane

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

Gas A

14

 

 

3

 

 

-6

 

 

15

 

 

 

  

 

23117

0

Gas B

 

17

 

 

2

 

 

-4

 

 

17

 

 

  

 

0

0

Gas C

 

 

8

 

 

-7

 

 

-13

 

 

8

 

 

 

 

0

0

As per above spreadsheet, it is clear because of change in Reid Vapor pressure, product mix is also required to change.  Due to change product mix, revenue is also been decreased.  It is a loss due to product mix which were changed due to change in Reid Vapor Pressure norm from 7 to 6.  Change in constraints lead to change in adjustment cell. 

Q10 data analysis answer

Particulars

Alkylate

Catalytic Cracked Gasoline

Straight Run Gasoline

Isopentane

 

 

 

 

LHS

Sign

RHS

blended in gasoline

blended in gasoline

blended in gasoline

blended in gasoline

Feedstock

A

B

C

A

B

C

A

B

C

A

B

C

not blended in gasoline

Variables

X11

X12

X13

X21

X22

X23

X31

X32

X33

X41

X42

X43

X1

X2

X3

X4

Values of Variables

2175

0

5425

0

6781

6219

8523

5477

0

2302

742

356

6400

0

0

7600

 

 

 

Objective function

15

16

17

15

16

17

15

16

17

15

16

17

17

14.5

14

14

816200

 

 

Constraints

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reid Vapor Pressure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

-2

 

 

1

 

 

-3

 

 

13

 

 

 

  

 

0

0

Gas B

 

-2

 

 

1

 

 

-3

 

 

13

 

 

  

 

0

0

Gas C

 

 

-2

 

 

1

 

 

-3

 

 

13

 

 

 

 

0

0

Availability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alkalyte

1

1

1

 

 

 

 

 

 

 

 

 

1

  

 

14000

?

14000

Cat Crack Gas

 

 

 

1

1

1

 

 

 

 

 

 

 

1

 

 

13000

?

13000

Str Run Gas

 

 

 

 

 

 

1

1

1

 

 

 

 

 

1

 

14000

?

14000

Isopentane

 

 

 

 

 

 

 

 

 

1

1

1

 

 

 

1

11000

?

11000

Demand

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gas A

1

 

 

1

 

 

1

 

 

1

 

 

 

  

 

13000

12000

Gas B

 

1

 

 

1

 

 

1

 

 

1

 

 

  

 

13000

13000

Gas C

 

 

1

 

 

1

 

 

1

 

 

1

 

 

 

 

12000

12000

Marketing

1

-1

 

1

-1

 

1

-1

 

1

-1

 

 

 

 

 

0

0

Octane

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

Gas A

14

 

 

3

 

 

-6

 

 

15

 

 

 

  

 

13839

0

Gas B

 

17

 

 

2

 

 

-4

 

 

17

 

 

  

 

4273

0

Gas C

 

 

8

 

 

-7

 

 

-13

 

 

8

 

  

 

0

0

New MKT constraint

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

1

-1

1

1

-1

1

1

-1

1

1

-1

 

 

 

 

14000

0

As per above spreadsheet, the current marketing mixgenerate around 8% of profit.  But as per the price difference between Gas A, Gas B & Gas C it is around 9%, so increase in market share with the new contract will always a burden on the company with the current product mix. Further, as per above product mix, it is not understandable about the fix and variable cost of the cost.  As per above spreadsheet, it is assumed as variable cost.  So, in my view, additional order at the cost of loss in the current product mix is not advisable.

References

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