upplcs goous t8 three customers, who each required 30 units. The company has two
ID: 419716 • Letter: U
Question
upplcs goous t8 three customers, who each required 30 units. The company has two warehouses. Warehouse 1 has 40 units available ad warehouse 2 has 30 units available. The cost of shipping 1 units from warehouse to customer are shown in Table 2. There is penalty for each un customer 1 a penalty cost of $95 incured; with customer 2,$80, and with customer 3, met customer units of demand: with $150 Table 2 From Warehouse 1 Warehouse 2 To Customer3 26 41 Customer2 Customerl 15 10 36 56 Formulate a balanced transportation problem to minimize the sum of shortage and shipping costsExplanation / Answer
C1
C2
C3
SUPPLY
W1
15
36
26
40
W2
10
56
41
30
DUMMY/ PENALTY
95
80
150
20
DEMAND
30
30
30
90
X11, X12, X13, X21 X22, X23 indicates warehouse ( 1,2 ) to customer ( 1,2,3 ) respectively
X31, X32, X33 indicates unmated demand of customer ( 1,2,3 ) respectively
Objective function:
MINIMIZE Z = 15*X11 + 36*X12 + 26*X13 + 10*X21 + 56*X22 + 41*X23 + 95*X31 + 80*X32 + 150*X33
Supply constraints:
X11 + X12 + X13 <= 40
X21 + X22 + X23 <= 30
X31 + X32 + X33 >= 20 ( Dummy constraint )
Demand constraints:
X11 + X21 + X31 >= 30
X12 + X22 + X32 >= 30
X13 + X23 + X33 >= 30
C1
C2
C3
SUPPLY
W1
15
36
26
40
W2
10
56
41
30
DUMMY/ PENALTY
95
80
150
20
DEMAND
30
30
30
90
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