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Custom Vans Background

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CASE STUDY: CUSTOM VANS, INC.

Custom Vans Background: * Specializes in converting standard vans into campers. * Shower-Rific is a small shower that could be placed in any type of van. * One Shower-Rific takes 3 hours of labor to build and use 2 gallons of fiberglass. * Most Shower-Rifics are manufactured in Gary which could produce 300 Shower-Rific in a month (but this capacity never seems to be enough). * Minneapolis is farther away from Gary than other Custom Van shops and Shower-Rifics have been delivered to other locations first. * Start another manufacturing plan at Fort Wayne, Indiana which could produce 150 Shower-Rifics per month. * Decision to open two new manufacturing plants as soon as possible because demand would grow rapidly (each plan would have the same capacity as Fort Wayne). * The two new manufacturing plants should be located in Detroit, Michigan; Rockford, Illinois; or Madison, Wisconsin.

Shop Location | Details | Chicago | Managed by Bill BurchOutperform other locationsPlant at Gary supply 200 Shower-Rifics each monthExpected demand = 300 unitsTransportation cost from Gary = $10/unitTransportation cost from Fort Wayne = $20/unitAlways request for additional 50 units from Fort WayneThe two new plants would be able to supply Chicago with the additional 100 units neededTransportation cost would be $30 from Detroit, $5 from Rockford and $10 from Madison per unit | Milwaukee | Managed by Wilma JacksonNot getting adequate supply of showersDemand = 100 units but get only 50 units from Fort WayneTransportation cost from Gary = $20/unitTransportation cost from Fort Wayne = $30/unitTransportation cost would be $40 from Detroit, $10 from Rockford and $5 from Madison per unit | Minneapolis | Managed by Tom PoanskiGet 100 units from Gary plantDemand = 150 unitsTransportation cost from Gary = $40/unitTransportation cost from Fort Wayne = $50/unitTransportation cost would be $60 from Detroit, $30 from Rockford and $25 from Madison per unit | Detroit | Managed by Dick LopezDemand = 200 unitsGet 100 units from Fort Wayne plantTransportation cost from Gary = $25/unitTransportation cost from Fort Wayne = $15/unitTransportation cost would be $5 from Detroit, $35 from Rockford and $40 from Madison per unitHoping to get 150 units from Detroit and the other 50 units from Fort Wayne |

Plant Location | Reasons for selection | Rockford | Reduce transportation cost for Minneapolis | Madison | Reduce transportation cost for MinneapolisCheaper labor force ($1 less per hour than others) | Detroit | There is a shop located in DetroitLargest suppliers of fiberglass (can get fiberglass for $2 per gallon less than others) |

Objective
To determine the best locations for the two new plants to reach minimum total costs.

CURRENT TRANSPORTATION COST: (use data given to fill in and calculate cost)

SHOP
PLANT
| CHICAGO | MILWAUKEE | MINNEAPOLIS | DETROIT | CAPACITY | GARY | 10
200 | 20 | 40
100 | 25 | 300 | FORT WAYNE | 20 | 30
50 | 50 | 15
100 | 150 | DUMMY | 0
100 | 0
50 | 0
50 | 0
100 | 300 | DEMAND | 300 | 100 | 150 | 200 | Dummy represents the needed capacity to meet the demand
750 |

Total cost = 200 (10) + 50 (30) + 100 (40) + 100 (15) = $9000

COST TABLE

Period | PLANT
SHOP
| CHICAGO | MILWAUKEE | MINNEAPOLIS | DETROIT | CAPACITY | CURRENT | GARY | 10 | 20 | 40 | 25 | 300 | | FORT WAYNE | 20 | 30 | 50 | 15 | 150 | PROPOSED | DETROIT | 26 | 36 | 56 | 1 | 150 | | MADISON | 7 | 2 | 22 | 37 | 150 | | ROCKFORD | 5 | 10 | 30 | 35 | 150 | | DEMAND | 300 | 100 | 150 | 200 | Total should be 750 as only pick 2 of 3 proposed location |

Note that $4 is deducted from the transportation cost from Detroit because a plant in Detroit could purchase a gallon of fiberglass at $2 less than other plant and Shower-Rific uses 2 gallons of fiberglass.

In addition, the Madison plant could hire labor at $1 per hour cheaper than other plants and one Shower-Rific takes 3 labor hours to build therefore, $3 is deducted from transportation cost from Madison.

OPTION ONE – DETROIT & MADISON
We use the solution from excel calculation; however it can be done using any of the 3 methods for example, Vogel’s Approximation Method as shown below.

=SUMPRODUCT(B13:E16,B5:E8)

Calculate using Excel Total cost of Option One = 300 (10) + 100 (30) + 150 (22) + 50 (15) + 150 (1) = $10,200

SHOP
PLANT
| CHICAGO | MILWAU-KEE | MINNEA-POLIS | DETROIT | CAPACITY | GARY | 10
200 | 20 | 40
100 | 25 | 300 | FORT WAYNE | 20
100 | 30 | 50 | 15
50 | 150 | DETROIT | 26 | 36 | 56 | 1
150 | 150 | MADISON | 7 | 2
100 | 22
50 | 37 | 150 | DEMAND | 300 | 100 | 150 | 200 | 750 |

Calculate using VAM Total cost of Option One = 200 (10) + 100 (20) + 100 (2) + 100 (40) + 50 (22) + 50 (15) + 150 (1) = $10,200

OPTION TWO – MADISON & ROCKFORD

=SUMPRODUCT(B13:E16,B5:E8)

PLANT
SHOP
| CHICAGO | MILWAU-KEE | MINNEA-POLIS | DETROIT | CAPACITY | GARY | 10
250 | 20 | 40 | 25
50 | 300 | FORT WAYNE | 20 | 30 | 50 | 15
150 | 150 | MADISON | 7 | 2
100 | 22
50 | 37 | 150 | ROCKFORD | 5
50 | 10 | 30
100 | 35 | 150 | DEMAND | 300 | 100 | 150 | 200 | 750 |

Both EXCEL and VAM Total cost of Option Two = 250 (10) + 50 (5) + 100 (2) + 50 (22) + 100 (30) + 50 (25) + 150 (15) = $10,550

OPTION THREE – DETROIT & ROCKFORD

=SUMPRODUCT(B13:E16,B5:E8)

Calculate using Excel Total cost of Option Three = 300 (10) + 100 (30) + 150 (30) + 50 (15) + 150 (1) = $11,400

SHOP
PLANT
| CHICAGO | MILWAU-KEE | MINNEA-POLIS | DETROIT | CAPACITY | GARY | 10
200 | 20 | 40
100 | 25 | 300 | FORT WAYNE | 20
100 | 30 | 50 | 15
50 | 150 | DETROIT | 26 | 36 | 56 | 1
150 | 150 | ROCKFORD | 5 | 10
100 | 30
50 | 35 | 150 | DEMAND | 300 | 100 | 150 | 200 | 750 |

Total cost of Option Three = 200 (10) + 100 (20) + 100 (20) + 150 (30) + 50 (15) + 150 (1) = $11,400

In this case we use EXCEL to find the total cost of each option, however, if we use methods such as Northwest Corner, Minimum Cost or VAM to develop the initial solution; we then need to apply the Stepping Stone Method to obtain improved solution!

FOR EXAMPLE: OPTION ONE – DETROIT & MADISON

Check empty cells
1-2 +20-40+22-2 = 0
1-4 +25-15+20-10= 20
2-2 +30-20+10-40+22-2 = 0
2-3 +50-40+10-20 = 0
3-1 +26-1+15-20 = 20
3-2 +36-1+15-20+10-40+22-2 = 20
3-3 +56-40+10-20+15-1 = 20
4-1 +7-10+40-22 = 15
OPTIMAL SOLUTION!

OPTION TWO – MADISON & ROCKFORD

1-2 +20-10+5-30+22-2 = 5
1-3 +40-30+5-10 = 5
2-1 +20-15+25-10 = 20
2-2 +30-15+25-10+5-32+22-2 = 23
2-3 +50-15+25-10+5-30 = 25
3-1 +7-5+30-22 = 10
3-4 +37-22+30-5+10-25 = 25
There are alternative solutions to each option as can see from the different solutions that we get from excel calculation and VAM method and also you can tell from the empty cell using stepping stone method that getting a zero mean there is other optimal solution
4-2 +10-2+22-30 = 0
4-4 +35-5+10-25 = 15
OPTIMAL SOLUTION!

OPTION THREE – DETROIT & ROCKFORD

1-2 +20-10+30-40 = 0
1-4 +25-15+20-10 = 20
2-2 +30-20+10-40+50-10 = 20
2-3 +50-20+10-40 = 0
3-1 +26-20+15-1 = 20
3-2 +36-10+30-40+10-20+15-1 = 20
3-3 +56-40+10-20+15-1 = 20
4-1 +5-30+40-10 = 5
4-4 +35-30+40-10+20-15 = 40
OPTIMAL SOLUTION!

As the three options illustrated, the first option leads to the minimum total cost of $10,200 which means that it is best to open the two new plants at Detroit and Madison.

When looking at the overall unit cost of transportation:
Total transportation cost ÷ production unit (capacity)
Current $9000 ÷ 450 unit = $20/unit
Proposed $10200 ÷ 750 unit = $13.60/unit

With the two new plants, Custom Vans is able to meet the customers’ demand and reduce the cost per of transportation per unit as well!

APPENDIX
Other possible solutions
OPTION 1 SHOP
PLANT
| CHICAGO | MILWAU-KEE | MINNEA-POLIS | DETROIT | CAPACITY | GARY | 10
300 | 20 | 40 | 25 | 300 | FORT WAYNE | 20 | 30 | 50
100 | 15
50 | 150 | DETROIT | 26 | 36 | 56 | 1
150 | 150 | MADISON | 7 | 2
100 | 22
50 | 37 | 150 | DEMAND | 300 | 100 | 150 | 200 | 750 |

SHOP
PLANT
| CHICAGO | MILWAU-KEE | MINNEA-POLIS | DETROIT | CAPACITY | GARY | 10
300 | 20 | 40 | 25 | 300 | FORT WAYNE | 20 | 30
100 | 50 | 15
50 | 150 | DETROIT | 26 | 36 | 56 | 1
150 | 150 | MADISON | 7 | 2 | 22
150 | 37 | 150 | DEMAND | 300 | 100 | 150 | 200 | 750 |

SHOP
PLANT
| CHICAGO | MILWAU-KEE | MINNEA-POLIS | DETROIT | CAPACITY | GARY | 10
200 | 20
100 | 40 | 25 | 300 | FORT WAYNE | 20
100 | 30 | 50 | 15
50 | 150 | DETROIT | 26 | 36 | 56 | 1
150 | 150 | MADISON | 7 | 2 | 22
150 | 37 | 150 | DEMAND | 300 | 100 | 150 | 200 | 750 |

OPTION 2 PLANT
SHOP
| CHICAGO | MILWAU-KEE | MINNEA-POLIS | DETROIT | CAPACITY | GARY | 10
250 | 20 | 40 | 25
50 | 300 | FORT WAYNE | 20 | 30 | 50 | 15
150 | 150 | MADISON | 7 | 2 | 22
150 | 37 | 150 | ROCKFORD | 5
50 | 10
100 | 30 | 35 | 150 | DEMAND | 300 | 100 | 150 | 200 | 750 |

OPTION 3 SHOP
PLANT
| CHICAGO | MILWAU-KEE | MINNEA-POLIS | DETROIT | CAPACITY | GARY | 10
300 | 20 | 40 | 25 | 300 | FORT WAYNE | 20 | 30 | 50
100 | 15
50 | 150 | DETROIT | 26 | 36 | 56 | 1
150 | 150 | ROCKFORD | 5 | 10
100 | 30
50 | 35 | 150 | DEMAND | 300 | 100 | 150 | 200 | 750 |

SHOP
PLANT
| CHICAGO | MILWAU-KEE | MINNEA-POLIS | DETROIT | CAPACITY | GARY | 10
200 | 20
100 | 40 | 25 | 300 | FORT WAYNE | 20
100 | 30 | 50 | 15
50 | 150 | DETROIT | 26 | 36 | 56 | 1
150 | 150 | ROCKFORD | 5 | 10 | 30
150 | 35 | 150 | DEMAND | 300 | 100 | 150 | 200 | 750 |

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