CAn someone please help? Solutions Plus is an industrial chemicals company that

Question

CAn someone please help?
Solutions Plus is an industrial chemicals company that produces specialized cleaning fluids and solvents for a wide variety of applications. Solutions Plus just received an invitation to submit a bid to supply Great North American railroad with a cleaning ?uid for Locomotives. Great North American needs the cleaning fluid at 11 locations (railway stations); it provided the following information to Solutions Plus regarding the number of gallons of cleaning ?uid required at each location (see Table 6.8): Solutions Plus can produce the cleaning fluid at its Cincinnati plant for $1.20 per gallon. Even though the Cincinnati location is its only plant, Solutions Plus has negotiated with an industrial chemicals company located in Oakland, California, to produce and ship up to 500,000 gallons of the locomotive cleaning fluid to selected Solutions Plus customer locations. The Oakland company will charge Solutions Plus $1.65 per gallon to produce the cleaning ?uid, but Solutions Plus thinks that the lower shipping costs from Oakland to some customer locations may offset the added cost to produce the product. Table 6.8 Location Gallons Required Location Gallons Required Santa Ana 22,418 Glendale 33,689 El Paso 6,800 Jacksonville 68,486 Pendelton 80,290 Little Rock 148,586 Houston 100,447 Bridgeport 111,475 Kansas City 24,570 Sacramento 112,000 Los Angeles 64, 761 Table 6.9 Cincinnati Oakland Santa Ana - 0.22 El Paso 0.84 0.74 Pendelton 0.83 0.74 Houston 0.45 - Kansas City 0.36 - Los Angeles - 0.22 Glendale - 0.22 Jacksonville 0.34 - Little Rock 0.34 - Bridgeport 0.34 - Sacramento - 0.15 The president of Solutions Plus, Charlie Weaver, contacted several trucking companies to negotiate shipping rates between the two production facilities (Cincinnati and Oakland) and the locations where the railroad locomotives are cleaned. Table 6.9 shows the quotes received in terms of dollars per gallon. The CAn someone please help?
Solutions Plus is an industrial chemicals company that produces specialized cleaning fluids and solvents for a wide variety of applications. Solutions Plus just received an invitation to submit a bid to supply Great North American railroad with a cleaning ?uid for Locomotives. Great North American needs the cleaning fluid at 11 locations (railway stations); it provided the following information to Solutions Plus regarding the number of gallons of cleaning ?uid required at each location (see Table 6.8): Solutions Plus can produce the cleaning fluid at its Cincinnati plant for $1.20 per gallon. Even though the Cincinnati location is its only plant, Solutions Plus has negotiated with an industrial chemicals company located in Oakland, California, to produce and ship up to 500,000 gallons of the locomotive cleaning fluid to selected Solutions Plus customer locations. The Oakland company will charge Solutions Plus $1.65 per gallon to produce the cleaning ?uid, but Solutions Plus thinks that the lower shipping costs from Oakland to some customer locations may offset the added cost to produce the product. Table 6.8 Location Gallons Required Location Gallons Required Santa Ana 22,418 Glendale 33,689 El Paso 6,800 Jacksonville 68,486 Pendelton 80,290 Little Rock 148,586 Houston 100,447 Bridgeport 111,475 Kansas City 24,570 Sacramento 112,000 Los Angeles 64, 761 Table 6.9 Cincinnati Oakland Santa Ana - 0.22 El Paso 0.84 0.74 Pendelton 0.83 0.74 Houston 0.45 - Kansas City 0.36 - Los Angeles - 0.22 Glendale - 0.22 Jacksonville 0.34 - Little Rock 0.34 - Bridgeport 0.34 - Sacramento - 0.15 The president of Solutions Plus, Charlie Weaver, contacted several trucking companies to negotiate shipping rates between the two production facilities (Cincinnati and Oakland) and the locations where the railroad locomotives are cleaned. Table 6.9 shows the quotes received in terms of dollars per gallon. The Location Gallons Required Location Gallons Required Santa Ana 22,418 Glendale 33,689 El Paso 6,800 Jacksonville 68,486 Pendelton 80,290 Little Rock 148,586 Houston 100,447 Bridgeport 111,475 Kansas City 24,570 Sacramento 112,000 Los Angeles 64, 761

Explanation / Answer

Transportation assignment problem
Decision variables
Supply to cities from which location
Cincinnati
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11

Sanat Ana
El Paso
Pendleton
Houston
Kansas City
Los Angeles
Glendale
Jacksonville
Little Rock
Bridgeport
Sacramento

Oakland
y1
y2
y3
y4
y5
y6
y7
y8
y9
y10
y11

Constrains
Demand at each point
Supply capacity of each station
Pay off table
Production cost
$ per gallon
Cincinnati
Oakland
$1.20
$1.65
$1.20
$1.65
$1.20
$1.65
$1.20
$1.65
$1.20
$1.65
$1.20
$1.65
$1.20
$1.65
$1.20
$1.65
$1.20
$1.65
$1.20
$1.65
$1.20
$1.65

Sanat Ana
El Paso
Pendleton
Houston
Kansas City
Los Angeles
Glendale
Jacksonville
Little Rock
Bridgeport
Sacramento
Transportation cost

Feight Cost ($ per gallon)
Cincinnati
Oakland
Sanat Ana
$9,999.00
$0.22
El Paso
$0.84
$0.74
Pendleton
$0.83
$0.49
Houston
$0.45
$9,999.00
Kansas City
$0.36
$9,999.00
Los Angeles
$9,999.00
$0.22
Glendale
$9,999.00
$0.22
Jacksonville
$0.34
$9,999.00
Little Rock
$0.34
$9,999.00
Bridgeport
$0.34
$9,999.00
Sacramento
$9,999.00
$0.15
Note : high values are indicated to prevent solver from assigning on these routes
Solver Model
Total
Constraint
Cincinnati
Oakland
gallons
Demand
Sanat Ana
0
22418
22418
=
22418
El Paso
6800
0
6800
=
6800
Pendleton
39636
40654
80290
=
80290
Houston
100447
0
100447
=
100447
Kansas City
24570
0
24570
=
24570
Los Angeles
0
64761
64761
=
64761
Glendale
0
33689
33689
=
33689
Jacksonville
68486
0
68486
=
68486
Little Rock
148586
0
148586
=
148586
Bridgeport
111475
0
111475
=
111475
Sacramento
0
112000
112000
=
112000
Total supply
Supply constraint

500000
500000

273522
500000

Objective function
Total cost should be minimum
Total cost =
=

x1*(Production + transportation cost) +y11(production and transportation cost)
$1,051,311.30
Transportation cost =
267673.63

Total cost

$1,318,984.93

Cost for 2 years =
Cost with 15 % markup
With Risk Mark-up

$2,637,969.86
$3,033,665.34
$3,073,816.38

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