linear programming transportation

i need a casestudy and answer on linnear programming transportation problem i attached a sample question in the attachment

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CMP 684 Management Decision Modeling. Fall 2017
Final Exam
Case 1
Custom Vans, Inc.
Custom Vans, Inc., specializes in converting standard vans into campers. Depending on the amount of work and
customizing to be done, the customizing could cost less than $1,000 to more than $5,000. In less than four years, Tony
Rizzo was able to expand his small operation in Gary, Indiana, to other major outlets in Chicago, Milwaukee,
Minneapolis, and Detroit.
Innovation was the major factor in Tony’s success in converting a small van shop into one of the largest and most
profitable custom van operations in the Midwest. Tony seemed to have a special ability to design and develop unique
features and devices that were always in high demand by van owners. An example was Shower-Rific, which was
developed by Tony only six months after Custom Vans, Inc., was started. These small showers were completely selfcontained, and they could be placed in almost any type of van and in a number of different locations within a van.
Shower-Rific was made of fiberglass and contained towel racks, built-in soap and shampoo holders, and a unique
plastic door. Each Shower-Rific took 2 gallons of fiberglass and 3 hours of labor to manufacture.
Most of the Shower-Rifics were manufactured in Gary in the same warehouse where Custom Vans, Inc., was founded.
The manufacturing plant in Gary could produce 300 Shower-Rifics in a month, but this capacity never seemed to be
enough. Custom Van shops in all locations were complaining about not getting enough Shower Rifics, and because
Minneapolis was farther away from Gary than the other locations, Tony was always inclined to ship Shower-Rifics to
the other locations before Minneapolis. This infuriated the manager of Custom Vans at Minneapolis, and after many
heated discussions, Tony decided to start another manufacturing plant for Shower-Rifics at Fort Wayne, Indiana. The
manufacturing plant at Fort Wayne could produce 150 Shower-Rifics per month.
The manufacturing plant at Fort Wayne was still not able to meet current demand for Shower-Rifics, and Tony knew
that the demand for his unique camper shower would grow rapidly in the next year. After consulting with his lawyer
and banker, Tony concluded that he should open two new manufacturing plants as soon as possible. Each plant would
have the same capacity as the Fort Wayne manufacturing plant. An initial investigation into possible manufacturing
locations was made, and Tony decided that the two new plants should be located in Detroit, Michigan; Rockford,
Illinois; or Madison, Wisconsin. Tony knew that selecting the best location for the two new manufacturing plants
would be difficult. Transportation costs and demands for the various locations should be important considerations.
The Chicago shop was managed by Bill Burch. This Custom Van shop was one of the first established by Tony, and
it continued to outperform the other locations. The manufacturing plant at Gary was supplying 200 Shower-Rifics
each month, although Bill knew that the demand for the showers in Chicago was 300 units. The transportation cost
per unit from Gary was $10, and although the transportation cost from Fort Wayne was double that amount, Bill was
always pleading with Tony to get an additional 50 units from the Fort Wayne manufacturer. The two additional
manufacturing plants would certainly be able to supply Bill with the additional 100 showers he needed. The
transportation costs would, of course, vary, depending on which two locations Tony picked. The transportation cost
per shower would be $30 from Detroit, $5 from Rockford, and $10 from Madison.
Wilma Jackson, manager of the Custom Van shop in Milwaukee, was the most upset about not getting an adequate
supply of showers. She had a demand for 100 units, and at the present time, she was only getting half of this demand
from the Fort Wayne manufacturing plant. She could not understand why Tony didn’t ship her all 100 units from
Gary. The transportation cost per unit from Gary was only $20, while the transportation cost from Fort Wayne was
$30. Wilma was hoping that Tony would select Madison for one of the manufacturing locations. She would be able
to get all of the showers needed, and the transportation cost per unit would only be $5. If not Madison, a new plant in
Rockford would be able to supply her total needs, but the transportation cost per unit would be twice as much as it
would be from Madison. Because the transportation cost per unit from Detroit would be $40, Wilma speculated that
even if Detroit became one of the new plants, she would not be getting any units from Detroit.
Custom Vans, Inc., of Minneapolis was managed by Tom Poanski. He was getting 100 showers from the Gary plant.
Demand was 150 units. Tom faced the highest transportation costs of all locations. The transportation cost from Gary
Page 1 of 3
CMP 684 Management Decision Modeling. Fall 2017
Final Exam
was $40 per unit. It would cost $10 more if showers were sent from the Fort Wayne location. Tom was hoping that
Detroit would not be one of the new plants, as the transportation cost would be $60 per unit. Rockford and Madison
would have a cost of $30 and $25, respectively, to ship one shower to Minneapolis.
The Detroit shop’s position was similar to Milwaukee’s—only getting half of the demand each month. The 100 units
that Detroit did receive came directly from the Fort Wayne plant. The transportation cost was only $15 per unit from
Fort Wayne, whereas it was $25 from Gary. Dick Lopez, manager of Custom Vans, Inc., of Detroit, placed the
probability of having one of the new plants in Detroit fairly high. The factory would be located across town, and the
transportation cost would be only $5 per unit. He could get 150 showers from the new plant in Detroit and the other
50 showers from Fort Wayne. Even if Detroit was not selected, the other two locations were not intolerable. Rockford
had a transportation cost per unit of $35, and Madison had a transportation cost of $40.
Tony pondered the dilemma of locating the two new plants for several weeks before deciding to call a meeting of all
the managers of the van shops. The decision was complicated, but the objective was clear—to minimize total costs.
The meeting was held in Gary, and everyone was present except Wilma.
Tony: Thank you for coming. As you know, I have decided to open up two new plants at Rockford, Madison, or
Detroit. The two locations, of course, will change our shipping practices, and I sincerely hope that they will supply
you with the Shower-Rifics that you have been wanting. I know you could have sold more units, and I want you to
know that I am sorry for this situation.
Dick: Tony, I have given this situation a lot of consideration, and I feel strongly that at least one of the new plants
should be located in Detroit. As you know, I am now only getting half of the showers that I need. My brother, Leon,
is very interested in running the plant, and I know he would do a good job.
Tom: Dick, I am sure that Leon could do a good job, and I know how difficult it has been since the recent layoffs by
the auto industry. Nevertheless, we should be considering total costs and not personalities. I believe that the new plants
should be located in Madison and Rockford. I am farther away from the other plants than any other shop, and these
locations would significantly reduce transportation costs.
Dick: That may be true, but there are other factors. Detroit has one of the largest suppliers of fiberglass, and I have
checked prices. A new plant in Detroit would be able to purchase fiberglass for $2 per gallon less than any of the other
existing or proposed plants.
Tom: At Madison, we have an excellent labor force. This is due primarily to the large number of students attending
the University of Madison. These students are hard workers, and they will work for $1 less per hour than the other
locations that we are considering.
Bill: Calm down, you two. It is obvious that we will not be able to satisfy everyone in locating the new plants.
Therefore, I would like to suggest that we vote on the two best locations.
Tony: I don’t think that voting would be a good idea. Wilma was not able to attend, and we should be looking at all
of these factors together in some type of logical fashion.
Where would you locate the two new plants?
Page 2 of 3
CMP 684 Management Decision Modeling. Fall 2017
Final Exam
Case 2
Biales Waste Disposal, GmbH
Biales Waste Disposal, GmbH, headquartered in the industrial city of Dusseldorf, Germany, operates seven speciallyconstructed semitrailers and cabs for commercial long-distance hauling of radioactive waste materials. Each truck
averages one completed load per week, picking up the radioactive containers from chemical companies and other
manufacturers in central Europe. The loads are carefully driven to a government site near Dresden, which until the
reunification was a manufacturing center in East Germany. Currently, pickups are made in eight countries: Italy,
Germany, Austria, France, Belgium, Netherlands, Denmark, and Poland.
Biales maintains an office in each country’s capitol. Staffing includes not only a manager and a secretary at each
national office, but a part-time lobbyist/attorney to assist in the many political, cross-cultural, border, and legal issues
that arise in the nuclear waste disposal industry.
Sybil Biales, owner of the firm, is seriously considering dropping Italy as source of business. Last year, only 25
truckloads of wastes were handled there. Since textile manufacturers in northern Italy are the primary source of
trucking for Biales, the size and revenues from their shipments will determine if it is profitable to retain an office and
do business in that country.
To analyze the Italian market, Biales gathers data on last year’s shipments and revenues. Each of the 25 trucks that
were loaded in Italy last year carried between 26 and 50 barrels of waste. The income generated per barrel differed
significantly (ranging from 50 to 80 German marks, or Dmarks) based on the type of radioactive material being loaded
and the weight of the barrels to be shipped. (See the accompanying table for details.) Biales decided that if she were
to simulate 25 truckloads out of Italy she could determine if it would be profitable to continue to operate there next
year. She estimates that each shipment to the Dresden dump site costs 900 Dmarks, including driver, gasoline, and
truck expenses; other cargo and loading and unloading costs average 120 Dmarks per shipment. In addition, it costs
41,000 Dmarks per year to operate the Italian office, including salaries and indirect overhead costs from the home
office in Dusseldorf.
Number of Barrels
26–30 (28)
31–35 (33)
36–40 (38)
41–45 (43)
46–50 (48)
Revenue per
Will the shipments in Italy next year generate enough revenues to cover Biales’ costs there?
Page 3 of 3

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