Cars-to-Dealers Logistics Inc. is the exclusive logistics provider for the Summit Motor Co. and has responsibility for transporting cars from Summit’s 3 manufacturing plants in Toledo, OH; Charlotte, NC and Savannah, GA to the 7 regional dealer locations as in the tables provided in your dataset. To do this, Cars-to-Dealers uses three transshipment facilities and all cars in the distribution network pass through these transshipment facilities. Dataset also contains the information about the capacities of each of these transshipment facilities, the demand requirement at each of the regional dealer locations and the unit cost to ship one car between the various locations. In addition to supply of cars (manufacturers) and demand for cars (dealers) there are two types of constraints for each transshipment facility: 1. Balance flow constraints: dictate that all cars flowing into a transshipment facility should also flow out of the transshipment facility – i.e. no inventory of cars should remain at any of the transshipment facilities. Inflow=Outflow or Inflow-Outflow=0. In other words, sum of what quantities going in should be equal to sum of what quantities going out for each transshipment facility. 2. Capacity constraint: Above constraint does not account for capacity of each Transshipment facility. For example, what is going can be equal to what is going out in Louisville facility, but total cars going through (sum of inflows) should not exceed the capacity of Louisville. Formulate the problem as a linear program to determine how the cars should be distributed in order to minimize the distribution costs Answer parts a through c.

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Cars-to-Dealers Logistics Inc. is the exclusive logistics provider for the Summit Motor Co. and has responsibility
for transporting cars from Summit’s 3 manufacturing plants in Toledo, OH; Charlotte, NC and Savannah, GA to
the 7 regional dealer locations as in the tables provided in your dataset. To do this, Cars-to-Dealers uses three
transshipment facilities and all cars in the distribution network pass through these transshipment facilities.
Dataset also contains the information about the capacities of each of these transshipment facilities, the demand
requirement at each of the regional dealer locations and the unit cost to ship one car between the various
locations.
In addition to supply of cars (manufacturers) and demand for cars (dealers) there are two types of constraints
for each transshipment facility:
1. Balance flow constraints: dictate that all cars flowing into a transshipment facility should also flow out of the
transshipment facility – i.e. no inventory of cars should remain at any of the transshipment facilities.
Inflow=Outflow or Inflow-Outflow=0. In other words, sum of what quantities going in should be equal
to sum of what quantities going out for each transshipment facility.
2. Capacity constraint: Above constraint does not account for capacity of each Transshipment facility. For
example, what is going can be equal to what is going out in Louisville facility, but total cars going
through (sum of inflows) should not exceed the capacity of Louisville.
Formulate the problem as a linear program to determine how the cars should be distributed in order to
minimize the distribution costs

Answer parts a through c.

Manufacturers to Transshipment facilities unit costs, Transshipment capacity & Manufacturer supply quantity
Louisville, KY
Denver, CO
Phoenix, AZ
Total Supply of cars
Transshipment facilities to Dealers unit costs & Dealer demand
Syracuse, NY
Jacksonville, FL
Los Angeles, CA
Portland, OR
Chicago, IL
Kansas City, MO
Salt Lake City, UT
Toledo, OH Charlotte, NC Savannah, GA Total Capacity for Transhipment facility
138
448
385
69492
214
494
307
53199
386
51381
241
76435
322
67366
72366
Louisville, KY| Denver, CO
200
382
286
293
237
317
261
328
264
250
219
388
187
297
Phoenix, AZ
470
502
489
500
522
421
455
Total Demand for Dealer
21603
16444
19078
21739
19139
17818
23167
Transcribed Image Text:Manufacturers to Transshipment facilities unit costs, Transshipment capacity & Manufacturer supply quantity Louisville, KY Denver, CO Phoenix, AZ Total Supply of cars Transshipment facilities to Dealers unit costs & Dealer demand Syracuse, NY Jacksonville, FL Los Angeles, CA Portland, OR Chicago, IL Kansas City, MO Salt Lake City, UT Toledo, OH Charlotte, NC Savannah, GA Total Capacity for Transhipment facility 138 448 385 69492 214 494 307 53199 386 51381 241 76435 322 67366 72366 Louisville, KY| Denver, CO 200 382 286 293 237 317 261 328 264 250 219 388 187 297 Phoenix, AZ 470 502 489 500 522 421 455 Total Demand for Dealer 21603 16444 19078 21739 19139 17818 23167
a.
Draw a network flow model to represent this problem. (Any way is OK, for example you can draw it on a piece
of paper and insert it as a picture etc., )
b. Implement your model in Excel and solve it.
a) Create a conditional formatting (Data Bars) for the all the Decision Variables
b) Generate a sensitivity report for the results
c) What is total cost under the optimal plan? Which manufacturing plant and transshipment center does
not use all its available capacity, if any?
c. Explain the shadow prices for all the transshipment facilities: both balance and capacity constraints. Hint:
this means you need to explain 6 shadow prices. If a shadow price is 0, then it means there is no impact of
that constraint.
Transcribed Image Text:a. Draw a network flow model to represent this problem. (Any way is OK, for example you can draw it on a piece of paper and insert it as a picture etc., ) b. Implement your model in Excel and solve it. a) Create a conditional formatting (Data Bars) for the all the Decision Variables b) Generate a sensitivity report for the results c) What is total cost under the optimal plan? Which manufacturing plant and transshipment center does not use all its available capacity, if any? c. Explain the shadow prices for all the transshipment facilities: both balance and capacity constraints. Hint: this means you need to explain 6 shadow prices. If a shadow price is 0, then it means there is no impact of that constraint.
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Decision variables
Man to transshipment
Louisville, KY
Denver, CO
Phoenix, AZ
Transshipment to Dealers
Syracuse, NY
Jacksonville, FL
Los Angeles, AZ
Portland, OR
Chicago, IL
Kansas City, MO
Salt Lake City, UT
Total cost
Louisville, KY
Denver, CO
Phoenix, AZ
Constraints
Balance of Transshipment facility
Incoming
Louisville, KY
Denver, CO
Phoenix, AZ
Capacity of Transshipment facility
Incoming
Toledo, OH
Supply of Manufacturer
Outgoing
Available supply
Demand
Syracuse, NY
Jacksonville, FL
Los Angeles, AZ
Louisville, KY
Portland, OR
Chicago, IL
Kansas City, MO
Salt Lake City, UT
Toledo, OH
Incoming
Charlotte, NC
Denver, CO
=
|=
=
<a
Charlotte, NC
x
X=
Savannah, GA
Phoenix, AZ
Outgoing
Capacity
Savannah, GA
<
Demand needed
Transcribed Image Text:Decision variables Man to transshipment Louisville, KY Denver, CO Phoenix, AZ Transshipment to Dealers Syracuse, NY Jacksonville, FL Los Angeles, AZ Portland, OR Chicago, IL Kansas City, MO Salt Lake City, UT Total cost Louisville, KY Denver, CO Phoenix, AZ Constraints Balance of Transshipment facility Incoming Louisville, KY Denver, CO Phoenix, AZ Capacity of Transshipment facility Incoming Toledo, OH Supply of Manufacturer Outgoing Available supply Demand Syracuse, NY Jacksonville, FL Los Angeles, AZ Louisville, KY Portland, OR Chicago, IL Kansas City, MO Salt Lake City, UT Toledo, OH Incoming Charlotte, NC Denver, CO = |= = <a Charlotte, NC x X= Savannah, GA Phoenix, AZ Outgoing Capacity Savannah, GA < Demand needed
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