A toy manufacturer currently has two warehouses (1 and 2) that are operational a
ID: 457941 • Letter: A
Question
A toy manufacturer currently has two warehouses (1 and 2) that are operational and meet the demand of backyard play sets at three retail outlets A, B and C. The supply of the play sets at warehouse 1 and 2 are 500 and 400 units respectively. The demand of play sets at warehouses A, B and C are 400, 600, and 350 units respectively. The unit cost of transportation from warehouse 1 and 2 to retail outlets A, B and C are shown in the table below. The toy manufacturer wants to open a third warehouse which will have a supply of 500 units of backyard play sets per week. Two locations, N1 and N2, are being considered for the new warehouse. Transportation costs from location N1 to stores A, B, and C are $6, $8, and $7 per unit, respectively; from location N2, the costs are $10, $6, and $4, respectively. Which of the two locations is the preferred location for the new warehouse? Hint: You will have to model and solve two LP transportation problems. Retail Outlet A Retail Outlet B Retail Outlet C Warehouse 1 8 3 7 Warehouse 2 5 10 9
Explanation / Answer
We consider two locations N1 and N2 separately and calculate to total transportation cost for N1 location and Total transportation cost N2 using LP transport model.
Decision Variables are in Option1 (N1):
X1a, X1b, X1c
X2a, X2b, X2c
X3a, X3b, X3c
Cost Table:
A
B
C
Supply
W1
8
3
7
500
W2
5
10
7
400
W3
6
8
7
500
Demand
400
600
350
Constraints:
Warehouse related
X1a+X1b+X1c = 500
X2a+X2b+X2c = 400
X3a+X3b+X3c = 500
Retail related
X1a+X2a+X3a = 400
X1b+X2b+X3b = 600
X1c+X2c+X3c = 350
Non –ve constraint
X1a, X1b, X1c
X2a, X2b, X2c
X3a, X3b, X3c
Objective Function:
Min. total transport cost (8*X1a +3*X1b+7*x1c+5*X2a+10*X2b+7*X2c+6*X3a+8*X3b+7*X3c)
Option 1 : Location N1
Cost table
A
B
C
Supply
W1
8
3
7
500
W2
5
10
7
400
N1
6
8
7
500
Demand
400
600
350
Changing Cells
A
B
C
W1
0
500
0
W2
400
0
0
W3
0
100
350
Constraints
LHS
RHS
W1 Supply
500
<=
500
W2 supply
400
<-
400
N1 Supply
450
<=
500
Store A
400
=
400
Store B
600
=
600
Store C
350
=
350
Obj. function
6750
Total cost of transportation for Location 1, N1 = $ 6750
Decision Variables are in Option2(N2):
X1a, X1b, X1c
X2a, X2b, X2c
X3a, X3b, X3c
Cost Table:
A
B
C
Supply
W1
8
3
7
500
W2
5
10
7
400
N2
10
6
4
500
Demand
400
600
350
Constraints:
Warehouse related
X1a+X1b+X1c = 500
X2a+X2b+X2c = 400
X3a+X3b+X3c = 500
Retail related
X1a+X2a+X3a = 400
X1b+X2b+X3b = 600
X1c+X2c+X3c = 350
Non –ve constraint
X1a, X1b, X1c
X2a, X2b, X2c
X3a, X3b, X3c
Objective Function:
Min. total transport cost (8*X1a +3*X1b+7*x1c+5*X2a+10*X2b+7*X2c+10*X3a+6*X3b+4*X3c)
Option 2 : Location N2
Cost table
A
B
C
Supply
W1
8
3
7
500
W2
5
10
7
400
N2
10
6
4
500
Demand
400
600
350
Changing Cells
A
B
C
W1
0
500
0
W2
400
0
0
W3
0
100
350
Constraints
LHS
RHS
W1 Supply
500
<=
500
W2 supply
400
<-
400
N2 Supply
450
<=
500
Store A
400
=
400
Store B
600
=
600
Store C
350
=
350
Obj. Function
5500
Total cost of transportation for Location 2, N2 = $ 5500
Solution: Location N2 is best option because low transport cost.
A
B
C
Supply
W1
8
3
7
500
W2
5
10
7
400
W3
6
8
7
500
Demand
400
600
350
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