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.
Distribution Center
1
2
3
Plant
A
$4
$6
$4
B
$6
$5
$2
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
WAREHOUSE 3
Rapid City
CANNERY 2
Eugene
WAREHOUSE 2
Salt Lake City
WAREHOUSE 1
Sacramento
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.
De ma nds
Supplie s
Destina tions
Sourc es
464
(Be llingham) 75
S1
867
352
(E ugene) 125
S2
995
(Alber t Le a)100
S3
513
654
D1
80 (Sa cr amento)
D2
65 (Sa lt La ke City)
D3
70 (Rapid City)
D4
85 (Albuquerque )
416
690
791
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
Backstroke
Breaststroke
Butterfly
Freestyle
Carl
37.7
43.4
33.3
29.2
Chris
32.9
33.1
28.5
26.4
David
33.8
42.2
38.9
29.6
Tony
37
34.7
30.4
28.5
Ken
35.4
41.8
33.6
31.1
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.