Simple Transportation Table

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Cost Matrix

Wh1 Wh 2

P1 $1.00 $3.00

P2 $4.00 $5.00

P3 $3.00 $4.00

C1 C2 C3 C4

P1 $5.00 $20.00 $20.00 $20.00

P2 $20.00 $20.00 $20.00 $20.00

P3 $20.00 $20.00 $20.00 $6.00

C1 C2 C3 C4

Wh 1 $3.00 $2.00 $3.00 $2.00

Wh 2 $2.00 $3.00 $2.00 $3.00

Flow Matrix/Variable Matrix

From Plant to Wh

Wh1 Wh2 Total

P1 250 0 250

P2 224 76 300

P3 1 374 375

Total 475 450

Capacity 600 500

From Plant to Customer

C1 C2 C3 C4 Total

P1 0 0 0 0 0

P2 0 0 0 0 0

P3 0 0 0 0 0

Total out of P1 250 250



From Wh to Customer

C1 C2 C3 C4 Total

Wh1 0 325 0 150 475

Wh2 200 0 250 0 450

Total 200 325 250 150

Demand 200 325 250 150

Total cost $4,875

Note: A large value for the cbecause these routes are noto customer at 0 price.

PlantCapacity



ost of transportation from P1 to C2,C3,C4; P2 to C1,C2,C3,C4 and P3 to C1,C2,C3 is assumt to be considered. If this is not done so then all the products will be transported from plan



dt directly



Microsoft Excel 14.0 Answer Report

Worksheet: [Marathe_Transportation_homework.xlsx]Solver

Report Created: 10/14/2011 1:58:09 AM

Result: Solver found a solution. All Constraints and optimality condition

Solver Engine

Engine: Simplex LP

Solution Time: 0.078 Seconds.

Iterations: 20 Subproblems: 0Solver Options

Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic S

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%,

Objective Cell (Min)

Cell Name riginal Valu Final Value

$D$4 Total cost C2 $4,875 $4,875

Variable Cells

Cell Name riginal Valu Final Value Integer

$C$21P1 Wh1 250 250 Contin

$D$2 P1 Wh2 0 0 Contin

$C$22P2 Wh1 0 0 Contin

$D$22P2 Wh2 300 300 Contin

$C$23P3 Wh1 225 225 Contin

$D$2 P3 Wh2 150 150 Contin

$C$28P1 C1 0 0 Contin

$D$2 P1 C2 0 0 Contin$E$28P1 C3 0 0 Contin

$F$28P1 C4 0 0 Contin


$D$2 P2 C2 0 0 Contin

$E$29P2 C3 0 0 Contin

$F$29P2 C4 0 0 Contin


$D$3 P3 C2 0 0 Contin

$E$30P3 C3 0 0 Contin

$F$30P3 C4 0 0 Contin$C$36Wh1 C1 0 0 Contin

$D$3 Wh1 C2 325 325 Contin

$E$36Wh1 C3 0 0 Contin

$F$36Wh1 C4 150 150 Contin

$C$37Wh2 C1 200 200 Contin

$D$3 Wh2 C2 0 0 Contin

$E$37Wh2 C3 250 250 Contin

$F$37Wh2 C4 0 0 Contin



Constraints

Cell Name Cell Value Formula Status lack

$C$2 Total Wh1 475 $C$24<=$C$Not Binding 125

$D$2 Total Wh2 450 $D$24<=$D Not Binding 50

$C$2 Total Wh1 475 $C$24=$G$3 Binding 0

$D$2 Total Wh2 450 $D$24=$G$3Binding 0

$C$38Total C1 200 $C$38=$C$3 Binding 0

$D$3 Total C2 325 $D$38=$D$3Binding 0

$E$38Total C3 250 $E$38=$E$3 Binding 0

$F$38Total C4 150 $F$38=$F$3 Binding 0

$G$3 Total out of P1 Tot 250 $G$31<=$H$Binding 0

$G$32Total out of P2 Tot 300$G$32<=$H$Not Binding 200




are satisfied.

aling

Assume NonNegative





Report Created: 10/14/2011 1:05:26 PM

Result: Solver found a solution. All Constraints and optimality conditions ar

Solver Engine

Engine: GRG Nonlinear



Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scali

Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, R

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Ass



$D$42 Total cost C2 $4,875 $4,725

Variable Cells


$C$22 P1 Wh1 250 300 Integer

$D$22 P1 Wh2 0 0 Integer

$C$23 P2 Wh1 0 0 Integer

$D$23 P2 Wh2 300 250 Integer

$C$24 P3 Wh1 225 175 Integer

$D$24 P3 Wh2 150 200 Integer

$C$29 P1 C1 0 0 Integer

$D$29 P1 C2 0 0 Integer$E$29 P1 C3 0 0 Integer

$F$29 P1 C4 0 0 Integer


$D$30 P2 C2 0 0 Integer

$E$30 P2 C3 0 0 Integer





$F$31 P3 C4 0 0 Integer$C$37 Wh1 C1 0 0 Integer

$D$37 Wh1 C2 325 325 Integer

$E$37 Wh1 C3 0 0 Integer

$F$37 Wh1 C4 150 150 Integer

$C$38 Wh2 C1 200 200 Integer

$D$38 Wh2 C2 0 0 Integer

$E$38 Wh2 C3 250 250 Integer

$F$38 Wh2 C4 0 0 Integer



Constraints



$D$25 Total Wh2 450 $D$25<=$D$Not Binding 50



$C$39 Total C1 200 $C$39=$C$4 Binding 0


$E$39 Total C3 250 $E$39=$E$4 Binding 0

$F$39 Total C4 150 $F$39=$F$4 Binding 0


$G$33 Total out of P2 Tot 250 $G$33<=$H$Not Binding 250


$C$22:$D$24=Integer

$C$29:$F$31=Integer

$C$37:$F$38=Integer