GSB 622 Decision Support Systems LINEAR PROGRAMMING & EXCEL SOLVER PART B: LINEAR PROGRAMMING EXAMPLE -- MINIMIZATION The Electro-Wiley Corporation is the world's leading manufacturer of slip rings. A slip ring is an electrical coupling device that allows

   

GSB 622 Decision Support Systems

LINEAR PROGRAMMING & EXCEL SOLVER

PART B: LINEAR PROGRAMMING EXAMPLE -- MINIMIZATION

The Electro-Wiley Corporation is the world's leading manufacturer of slip rings. A slip ring is an electrical coupling device that allows current to pass through a spinning or rotating connection —such as a gun turret on a ship, aircraft or tank. The company recently received a $750,000 order for various quantities of three types of slip rings. Each slip ring requires a certain amount of time to wire and harness. The following table summarizes the requirements for the three models of slip rings.

  

Modell

Model 2

Model 3

 

Number ordered

3000

2000

900

 

Hours of wiring required per unit

2

1.5

3

 

Hours of harnessing required per unit

1

2

1

Unfortunately, Electro-Wiley does not have enough wiring and harnessing capacity to fill the order by its due date. The company has only 10,000 hours of wiring capacity and 5,000 hours of harnessing capacity available to devote to this order. Should the company reject the business because it cannot handle the entire job? Or should the company subcontract a portion of the order to one of its competitors? The unit costs of producing each model in-house and buying the finished products from a competitor are provided here:

  

Modell

Model 2

Model 3

 

Cost to make Cost to buy

$50

$61

$83
  $97

$130
  $145

Decision Variables:

X1 number of Model 1 slip rings to make in-house

X2 number of Model 2 slip rings to make in-house

X3 number of Model 3 slip rings to make in-house

X4 number of Model 1 slip rings to buy from a competitor

X5 number of Model 2 slip rings to buy from a competitor

X6 number of Model 3 slip rings to buy from a competitor

The linear programming model representation of this problem consists of:

Minimize: 50X1 + 83X2 + 130 X3 ÷ 61 X4 ÷ 97 X5 ÷ 145 X6 cost

Constraints: X1 + X4 = 3000 demand for Model 1

X2 ÷ X5 = 2000 demand for Model2

X3 ÷ X6 = 900 demand for Model 3

2 X1 + 1.5 X2 ÷ 3 X3 <=10000 wiring constraint

1 X1 + 2 X2 ÷ 1 X3 <= 5000harnessing constraint

All decision variables must be nonnegative

   

Use Excel Solver (as explained in subsequent pages) to determine the optimal number of each model to make and to buy in order to minimize cost.

Analyze the Answer Report that is produced and answer the following questions. Then upload the spreadsheet AND your answers to these questions as well for credit.

1. According to the Solver solution, what is the optimal number of Model 1 slip rings to make?  to buy? ____________________ 

2. According to the Solver solution, what is the optimal number of Model 2 slip rings to make?  to buy? ____________________ 

3. According to the Solver solution, what is the optimal number of Model 3 slip rings to make?  to buy? ____________________ 

4. What is the total cost?____________________________________ 

5. How much of the wiring will remain unused? ________________________________ 

6. Which slip ring Model does Solver indicate should be purchased in greatest number from a competitor?  
Why do you think that Solver is recommending a significant purchase of this particular Model over the other two? Explain your answer.

      

B

C

D

E

 

Electro-Wiley Corporation

 

 

3

 

4

Slip Ring

 

6

Number to

Model I

Model 2

Model 3

 

6

-Make

 

7

-Buy

 

8

 

9

Cost to

 

10

-Make

50

83

130

Total Cost

 

11

-Buy

61

97

145'

 

12

 

13

#Available

 

14

AiNeeded

3000

2000

9:10

 

15

 

16

Hours Re . uired

Used

Available

 

17

-Wiring

2

1.5

3

10000

 

18

-Harnessing

1

2

1

5000

 

19

 

20

 

21

Cells B6 -   D7 are Decision Ell:

Variables

-- to be determined

10* CB + D10 * D6 +B11 * B7 +

 

22

B10 *138 +

Cl 1 * C7 + Dll *D7

 

23

E l ji

E6 + B7

 

24

C13:

C6 + C7

 

25

D13:

DE + D7

 

26

E17:

B17 *$B$6 + C17 ' $C$6

+1::117
+ D18

*$D$6

*$D$6 —1

 

27

EIS:

E18 *$B$6

+ C18 *$C$6

 

28

   

       

Solver Parameters

   

   

Set Target Cell: TE$11 7,

Equal To: Max .'.. Min r Value of:

By Changing Cells:

. 

1$13$6:$D$7

-Subject to the Constraints:

       

        

   

$B$13 = $B$14 $C$13 = $C$14 $D$13 = $D$14 $E$17:$E$10   <= $F$17: $F$16

i

  

Also Click Options and check Assume Non-Negative

Be sure to select the Answer Reports

Upload the spreadsheet AND your answers to the questions as well for credit.