l this month\'s pro lowing table shows what the cost would be for shipping each
ID: 3044890 • Letter: L
Question
l this month's pro lowing table shows what the cost would be for shipping each unit from each factory to each of these customers. Also shown 410 (minimum output. The fol- e are the number of units that will be produced at each factory and level) Benefit 3: Ai + the number of units ordered by each customer A2- A, t 24, 2:30 (minimum A decision now needs to be made about the shipping acceptable level) plan for how many units to ship from each factory to each a. Which category of linear programming problem E b. Formulate and solve a linear programming model customer and does this problem fit? Why? A, 20 A220 A 20 A4 2 0 Formulate and solve the spreadsheet model for this problem. for this problem on a spreadsheet. Summarize this formulation in algebraic form. c. Unit Shipping Cost To From Customer 1 Customer 2 Customer 3 Output Factory 1 Factory 2 600 400 300 units 800 900 200 units $700 600 400 units 500 units Order size 400 units Larry Edison is the director of the Computer Center for 3.18. The Fagersta Steelworks currently is working two College. He now needs to schedule the staffing of the mines to obtain its iron ore. This iron ore is shipped to either It is open from 8 AM until midnight. Larry has monitored of two storage facilities. When needed, it then is shipped on to ge of the center at various times of the day and deter- the company's steel plant. The diagram below depicts this dis- hat the following number of computer consultants are tribution network, where MI and M2 are the two mines, SI and S2 are the two storage facilities, and P is the steel plant. TheExplanation / Answer
Given data on:
Two factories with production output as 400 and 500 units.
Three customers Customer 1, Customer 2 and Customer 3 with order size 300, 200 and 400 respectively. Matrix of unit shipping cost is also given.
This is the problem of Transportation. Define a,b,c,d,e, and f as the number of units shipped from Factory to Customer as shown below.
From
To Customer
C1
C2
C3
Factory 1
a
b
c
Factory 2
d
e
f
We can write transportation cost function as follows:
Z= 600 a+ 800 b+ 700 c+ 400 d+ 900 e+ 700 f
Subject to the constraint:
a+b+c=400
d+e+f=500
a+d=300
b+e=200
c+f=400
a,b,c,d,e,f 0
C1
C2
C3
Output
F1
0 | 600
200 | 800
200 | 700
400
F2
300 | 400
0 | 900
200 | 600
500
Order
300
200
400
In the Table above format of cell is x | y where x is shipment unit (Schedule) and y is unit cost of transportation.
The above solution is Initial Basic Feasible Solution derived using Least Cost Method.
Cost of Transportation = 200X800+200X700+300X400+200X600
= 160000+140000+120000+120000 = 540000
One can proceed for optimal solution. The test for testing degeneracy is r+c-1=b
Where r: Number of rows = 2
c: Number of columns =3
b: Number of basic cells. =4
Here condition is valid and therefore the IBFS is not degenerate.
If we apply Modi method to find U and V as follows:
U
0 | 600
200 | 800
200 | 700
0
300 | 400
0 | 900
200 | 600
-100
V
500
800
700
U+V = C for basic (allocated) cell.
For non basic cell compute U+V-C
For both cells these values are -100 and -200, both are negative hence the solution itself is Optimal with minimum cost of shipping.
Hence ship from Factor 1 to customer 2 and customer 3, 200 units each respectively.
Ship from Factor 2 to customer 1 and customer 3, 300 and 200 units respectively.
From
To Customer
C1
C2
C3
Factory 1
a
b
c
Factory 2
d
e
f
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