Question

Widgetco manufactures widgets at two factories, one in Memphis and one in Denver. The Memphis factory can produce as many as 150 widgets per day, and the Denver factory can produce as many as 110 widgets per day.

Widgets are shipped by air to customers in Los Angeles and Boston. The customers in each city require 130 widgets per day.

Because of the deregulation of airfares, Widgetco believes that it may be cheaper to first fly some widgets to New York or Chicago and then fly them to their final destinations. The costs of flying a widget are shown below. Widgetco wants to minimize the total cost of shipping the required widgets to its customers.

	Shipping Costs for Transshipments ($)
From \ To	Memphis	Denver	N.Y.	Chicago	L.A.	Boston
Memphis	0	-	8	13	25	28
Denver	-	0	15	12	26	25
N.Y.	-	-	0	6	16	17
Chicago	-	-	6	0	14	16
L.A.	-	-	-	-	0	-
Boston	-	-	-	-	-	0

Widgetco wants to minimize the total cost of shipping the required widgets to its customers.

a. Identify the supply nodes, demand nodes and transshipment nodes for this problem.

Develop a spreadsheet model and solve this problem.

b. What is the optimum distribution through the network?

c. What is the optimum shipping cost?

Answer 1

a.Total supply = 150+110 =260

  Total demand = 130+130 =260

Memphis to Los Angeles =130

Memphis to Denver =20

Denver to Boston (110+20) =130

b.

Memphis to Los Angeles =130

Memphis to Denver =20

Denver to Boston (110+20) =130

c. Cost of shipping

Option 1

Memphis to Los Angeles =25

Memphis to NY to Los Angeles =8+16=24 (cheapest)

Memphis to Chicago to Los Angeles =13+14=27

Denver to Boston =25  (cheapest)

Denver to NY Boston =15+17=32

Denver to Chicago to Boston =12+16=28

Total = 24+25 =49

Option 2

Memphis to Boston =28

Memphis to NY to Boston =8+17 =25  (cheapest)

Memphis to Chicago to Boston =13+16 =29

Denver to Los Angeles =26  (cheapest)

Denver to NY Los Angeles =15+16=31

Denver to Chicago Los Angeles =12+14=26

Total = 25+26 =51

OPTION 1 IS THE CHEAPEST WHICH IS $49.