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.