Post on 18-Jan-2016
P R O B L E M 5 ( A )
SCHOOL
DISTRICT
ADDEEN BASHIRON COBBITH DAIMMAN STUDENTPOPULATION
NORTH 250
2505,5,5,5,5,-,-
SOUTH 340340
6,6,6,-,-,-,-
EAST 110 200 310
2,2,2,2,4,4,4,4
WEST 210210
14,14,-,-,-,-,-
CENTRAL 40 60 190290
5,5,5,5,1,1,8,-
DUMMY 200200
0,-,-,-,-,-,-
CAPACITY 40012,3,3,3,3,3,3,18
40010,5,5,10,-,-,-
40021,1,1,1,1,1,1
40010,6,1,1,1,5,-
1600
15
21
0
16
10
31
27
23
35
17
20
24
10
0 0
23
35
22
12
18
26
29
15
0
Initial total traveling time:
250(12)+110(18)+40(15)+340(15)+60(10)+200(22)
+200(0)+210(10)+190(16)
=20 820 mins
Evaluate using stepping-stone method:
1) N to B: +23-12+15-10=16
2) N to C: +35-12+18-22=19
3) N to D: +17-12+15-16=4
4) S to A: +26-15+10-15=6
5) S to C: +21-15+10-15+18-22=-3
6) S to D: +27-15+10-16=6
7) ….
8) ….
9) ….
10)….
P R O B L E M 5 ( A )
SCHOOL
DISTRICT
ADDEEN BASHIRON COBBITH DAIMMAN STUDENTPOPULATION
NORTH 250
250
SOUTH 340-40 +40 340
EAST 110+40 200-40 310
WEST 210 210
CENTRAL 40-40 60+40 190 290
DUMMY 200 200
CAPACITY 400 400 400 400 1600
15
21
0
16
10
31
27
23
35
17
20
24
10
0 0
23
35
22
12
18
26
29
15
0
P R O B L E M 5 ( A )
SCHOOL
DISTRICT
ADDEEN BASHIRON COBBITH DAIMMAN STUDENTPOPULATION
NORTH 250
250
SOUTH 300 40 340
EAST 150 160 310
WEST 210 210
CENTRAL 100 190 290
DUMMY 200 200
CAPACITY 400 400 400 400 1600
15
21
0
16
10
31
27
23
35
17
20
24
10
0 0
23
35
22
12
18
26
29
15
0
Total traveling time for new solution:
250(12)+150(18)+300(15)+100(10)+40(21)+160(22)
+200(0)+210(10)+190(16)
=20 700 mins
Evaluate the new solution using stepping-stone method:
-All indices are zero and more than zero, the solution is an optimal solution at 20700 mins.
PROBLEM 5 (B)
TRANSPORTATION PROBLEMC AT E G O R I Z E D I N TO 2 T Y P E S :
1. M I N I M I Z AT I O N P R O B L E M
2. M A X I M I Z AT I O N P R O B L E M
THIS IS AN UNBALANCED MAXIMIZATION PROBLEM FOR FINDING OUT MAXIMUM INCREASE IN PRODUCT OUTPUT
TO SOLVE THIS FIRST WE WILL CONVERT THIS IN MINIMIZATION PROBLEM BY SUBTRACTING THE LARGEST ELEMENT FROM ALL ELEMENTS
NOW WE WILL BALANCE THIS PROBLEM BY ADDING DUMMY COLUMN
NOW WE CAN SOLVE THE PROBLEM BY USING VAM
ONE OF THE WORKING HOW TO SOLVE PROBLEM BY USING VAM
NOTE : FOR CALCULATING FINAL SCHEDULE, WE MUST MULTIPLY QUANTITY BY THE ORIGINAL ELEMENT VALUE
Initial Basic Feasible Solution = (45x10) + (60x8) + (25x9) + (6x5) + (35x12) + (65x0)= 1605
MODI
1.Choose maximum allocation = 02.Let U2= 03.Find the value of U1, U3, V1, V2, V3, V4, using
the formula Cij=Ui+Vj , only for those squares that are currently used or occupied.
4.Compute the improvement index for each unused square by the formula Wij =Ui+Vj-Cij
5. In minimization, if all Wij ≤ 0, optimum allocation has been made.
MODI
MODI
U1=1 W11= -4
U2=0 W13= -5
U3=3 W14= -2
V1=2 W24= -3
V2=3 W31= 0
V3=0 W33= -1
V4= -3 Wij ≤ 0 (optimum allocation has been made)
Cij=Ui+Vj Wij =Ui+Vj-Cij
MODI
Optimal Solution = (45x10) + (60x8) + (25x9) + (6x5) + (35x12) + (65x0)= 1605
SUGGESTED LINKS
http://www.bms.co.in/how-to-solve-transportation-problems/
http://www.slideshare.net/beautifulneha/transportation-problem-in-operational-research
https://www.youtube.com/watch?v=7_yPdc0mIHE
https://www.youtube.com/watch?v=il78DKRw2JU
C)1.Unbalance transportation model
Unbalance transportation model is the total supply does not equal to the total demand. The dummy supply exactly not really be able to supply but to make adjustment at the end. The costs nothing to transport from dummy because it does not really exist. So we put ‘cost coefficient ‘ is zero to each dummy location.
2.Sentitivity analysis
Sensitivity analysis is a way to predict the outcome of a decision if a situation turns out to be different compared to the key predictions. A sensitivity analysis shows how sensitive to businesses to change.
3.Modified distribution(MODI)
The modified distribution method is an improvement over the stepping stone method for testing and finding optimal solutions. This method allows us to compute indices for each unused square without drawing all the closed paths.