Example (Transportation Problem) A company has two plants producing a certain product that is to be...
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Transcript of Example (Transportation Problem) A company has two plants producing a certain product that is to be...
Example (Transportation Problem)
A company has two plants producing a certain product that is to be shipped to three distribution centers. The unit production costs are the same at the two plants, and the shipping cost per unit is shown below.
1 2 3
A $4 $6 $4
B $6 $5 $2Plant
Distribution Center
Shipments are made once per week. During each week, each plant produces at most 60 units and each distribution center needs at least 40 units. How many units should be shipped from each distribution center to each distribution center, so as to minimize cost?
Spreadsheet Solution of the Transportation Problem Example
Figure 5.1: Location of the canneries and warehouses for the P & T Co. problem.
CANNERY 1 Bellingham
CANNERY 2 Eugene
WAREHOUSE 1 Sacramento
WAREHOUSE 2 Salt Lake City
WAREHOUSE 3 Rapid City
WAREHOUSE 4 Albuquerque
CANNERY 3 Albert Lea
Figure 5.2: A spreadsheet formulation of the P & T Co. problem as a transportation problem, where rows 3-9 show the parameter table and rows
12-20 display the solution table after using the Excel Solver to obtain an optimal distribution plan. Both the formulas for the output cells and the
specifications needed to set up the Solver are on the next slide.
Figure 5.2: The formulas for the output cells and the specifications needed to set up the Solver.
Figure 5.3: The network representation of the P & T Co. transportation problem shows all the data in Table 5.5 graphically.
S1
S2
S3
D4
D2
D1
D3
75
125
100
80
65
70
85
Supplies Demands
SourcesDestinations
(Bellingham)
(Eugene)
(Alber t Lea)
(Sacramento)
(Salt Lake City)
(Rapid City)
(Albuquerque)
464513
654867
352 416690
791
995 682
685
388
Example (Assignment Problem)(Problem 5.22 in the book)
The coach of a swim team needs to assign swimmers to a 200-yard medley relay team (four swimmers, each swims 50 yards of one of the four strokes). Since most of the best swimmers are very fast in more than one stroke, it is not clear which swimmer should be assigned to each of the four strokes. The five fastest swimmers and their best times (in seconds) they have achieved in each of the strokes (for 50 yards) are
Carl 37.7 43.4 33.3 29.2
Ch r is 32.9 33.1 28.5 26.4
D avid 33.8 42.2 38.9 29.6
Tony 37 34.7 30.4 28.5
K en 35.4 41.8 33.6 31.1
Backstroke Breaststroke Butterfly Freestyle
How should the swimmers be assigned to make the fastest relay team?
Spreadsheet Solution of the Assignment Problem Example
Figure 5.18: The formulas for the output cells and the specifications
needed to set up the Solver for the Sellmore Co. problem.