Question

4) The Don Levine Corporation currently produces in four different cities: Decatur, Minneapolis, Carbondale, and St Louis. They send their product to three different warehouses named Ciro, Blue Earth, and Des Moines. The table below shows the transportation cost of shipping from their current plants to their warehouses.

To	Decatur	Minneapolis	Carbondale	St. Louis	Demand
Blue Earth	20	17	21	27	250
Ciro	25	27	20	28	200
Des Moines	22	25	22	31	350
Capacity	300	200	150	150

Their production cost per facility is shown in the table below.

Location	Decatur	Minneapolis	Carbondale	St. Louis
Production Cost	50	60	70	50

The variables are denoted using X## where the first number is the source and the second number is the destination. Sources: Decatur = 1, Minneapolis = 2, Carbondale = 3, and St. Louis = 4. Destinations: Blue Earth = 1, Ciro = 2 and Des Moines = 3.

a) Don Levine Corporation should ship how many goods from each production facility to each warehouse? What is the cost (including production costs) of this shipping plan?

b) The State of Illinois is trying to convince the Don Levine Corporation to move their production facility from St. Louis to East St. Louis. Management has determined that with the incentives that Illinois has provided that production costs would be lower in Illinois but shipping costs to Blue Earth and Ciro would be more expensive. The production cost in East St. Louis would be $40 but the transportation costs to Blue Earth would be $29, to Ciro would be $30, and to ship to Des Moines would be $30. Assume that the corporation shuts down its St. Louis plant and moves all of its production to East St. Louis, which has a capacity of 150 units. How many goods should be shipped from each production plant to each warehouse? What is the cost (including production cost) of this shipping plan? (Hint: the shipping plans are different)

In part b East St Louis is given the source number 5.

Answer 1

a)

Let, xij = number of units shipped to location i from distribution center j where i = {Blue Earth=1,Ciro=2,Des Moines=3} and  j = {
Decatur=1,Minneapolis=2,Carbondale=3,St. Louis=4}

objective is to minimize transportation and production cost = Min 20*x11+17*x12+21*x13+27*x14+25*x21+27*x22+20*x23+28*x24+22*x31+25*x32+22*x33+31*x34+50*x11+50*x21+50*x31+60*x12+60*x22+60*x32+70*13+70*23+70*33+50*14+50*24+50*34

subject to,

x11+x12+x13+x14 = 250 (Blue Earth)
x21+x22+x23+x24 = 200 (Ciro)
x31+x32+x33+x34 = 350 (Des Moines)

x11+x21+x31 = 300 (Decatur)
x12+x22+x32 = 200 (Minneapolis)
x13+x23+x33 = 150 (Carbondale)
x14+x24+x34 = 150 (St. Louis)

xij >= 0

Solving in solver we get,

Optimal transportation schedule

	Decatur	Minneapolis	Carbondale	St. Louis
Blue Earth	0	200	0	50
Ciro	0	0	100	100
Des Moines	300	0	50	0

Cost of this production plan = 62250

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b)

Replacing St. Louis with East St. Louis,

Optimal transportation schedule

	Decatur	Minneapolis	Carbondale	East St. Louis
Blue Earth	50	200	0	0
Ciro	0	0	150	50
Des Moines	250	0	0	100

Cost of this production plan = 60900

Clearly transportation and production cost have become lower by replacing St. Louis with East St. Louis

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