Supply and Demand Information Is Given Below, and the Third Page Contains Distance Information

BA 308B Dr. Campbell

FLITZERBOPS

Suppose you work for a company that builds flitzerbops. Flitzerbops are built in two separate sections, and your company has supply plants in Chicago, New Orleans, San Diego and Seattle that make flitzerbop subassemblies. The subassemblies are then shipped via rail to final assembly plants which are located in Denver, Houston, New York and St. Louis. Your task involves the transportation of the flitzerbop subassemblies from the supply plants to the final assembly plants.

Supply and demand information is given below, and the third page contains distance information.

Supplier Monthly Demand Monthly Location Supply Location Demand Chicago 1500 Denver 1000 New Orleans 500 Houston 1000 San Diego 1500 New York 2000 Seattle 2500 St. Louis 2000

A flitzerbop subassembly weighs 10 pounds and the cost of rail transportation is $0.05 per ton-mile (5 cents to transport one ton one mile). (One ton equals 2000 pounds.)

1. Solve shortest path problems to determine the shortest paths from all supply plants to the final assembly plants. Record the length of the shortest path and the path in each box in the table below. For example, in the cell for Chicago-Denver, after "Dist.=" enter the length of the shortest path in miles, and after "Path =" enter the cities in that shortest path in order (such as CHI-STL- DEN or CHI-DEN, depending on which is shorter).

TO Denver Houston New York St. Louis Chicago Dist. = Dist. = Dist. = Dist. = FRO Path = Path = Path = Path = M New Dist. = Dist. = Dist. = Dist. = Orleans Path = Path = Path = Path = San Diego Dist. = Dist. = Dist. = Dist. = Path = Path = Path = Path = Seattle Dist. = Dist. = Dist. = Dist. = Path = Path = Path = Path =

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2. Solve a transportation problem (with TRANLP) using the results from problem 1 to determine the optimal (lowest cost) shipping arrangement from the four supply plants to the four demand plants, and the optimal cost. Turn in a printout of the optimal solution.

(For the transportation problem you need the 16 unit cost values to move one flitzerbop between each of the four supply plants and four final assembly plants.)

Optimal Cost = ______

3. Suppose a major snowstorm has closed the railroad tracks between Seattle and Denver. Since Seattle-Denver rail transport is not possible, a trucking company has offered to transport flitzerbop subassemblies from Seattle to Denver for $0.06 per ton-mile. (Recall that the rate for rail transportation is $0.05 per ton-mile.) The travel distance by truck from Seattle to Denver is 1350 miles. To help determine the new optimal shipping arrangement, first determine the new shortest paths and their lengths from Seattle to the final assembly plants. Fill in the table of shortest paths below. (These may involve truck and rail transportation.)

SHORTEST PATH TO Denver Houston New York St. Louis Seattle Dist. = Dist. = Dist. = Dist. = Path = Path = Path = Path =

Now calculate the lowest cost from Seattle to the 4 destinations. This is the minimum of (a) the cost with truck transport from Seattle to Denver, then rail transport from Denver to the destination, and (b) the cost with rail transport only from Seattle to the destination. Fill in the table below with the minimum cost to send one flitzerbop from Seattle to each destination.

MINIMUM COST PER FLITZERBOP TO Denver Houston New York St. Louis

Seattle

Use these new unit costs from Seattle, with the same unit costs used in part 2 from the other three supply plants, in TRANLP to determine the new optimal shipping arrangement from supply plants to final assembly plants and the optimal cost. Turn in a printout of your solution.

Optimal Cost = ______

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Mileage Table

Mileage by TRAIN TO Chicago Denver Houston New Orleans New York St. Louis San Diego Seattle Chicago --- 1038 VIA 940 850 290 VIA 2112 Denver 1038 --- 1162 1323 VIA 851 1052 1216 FRO M Houston VIA 1162 --- 368 VIA 810 1481 VIA New Orleans 940 1323 368 --- 1319 672 VIA VIA New York 850 VIA VIA 1319 --- 939 VIA VIA St. Louis 290 851 810 672 939 --- 1901 VIA San Diego VIA 1052 1481 VIA VIA 1901 --- 1376 Seattle 2112 1216 VIA VIA VIA VIA 1376 ---

Note: VIA indicates that direct travel is not available, so travel must be via another city. For example, travel between Chicago and Houston must be via another city (such as St. Louis, New Orleans, etc.) .