The BridgePort Company has three plants producing white boards that are to be sh
ID: 364406 • Letter: T
Question
The BridgePort Company has three plants producing white boards that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given to the right
The freight cost for each shipment is $80 plus 50 cents per mile. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost?
(a) Formulate this problem as a transportation problem by constructing the appropriate parameter table.
(b) Obtain an optimal solution.
Explanation / Answer
The Distance table is as shown:
Distance between plant and Distribution Point)
Distribution Points
Plant
1
2
3
4
1
800
1300
400
700
2
1100
1400
600
1000
3
600
1200
800
900
Cost per Shipment
$80
Cost per mile
$0.50
Total transportation cost per shipment = fixed cost per shipment + (cost per mile x miles to travel)
Cost per shipment from plant to Distribution Point
Distribution Points
Plant
1
2
3
4
1
80+(0.5*800)
= $480
$730
$280
$430
2
$630
$780
$380
$580
3
$380
$680
$480
$530
The LPP formulation of the given problem is as follows:
Let, Xij = shipments to be transported form warehouse i to distribution center j
i = 1, 2, 3 for the for three warehouses
j = 1, 2, 3, and 4 for the four centers
Objective Function:
Min. Z = $480X11 + $730X12 + $280X13 + $430X14 + $630X21 + $780X22 + $380X23 + $580X24 + $380X31 + $680X32 + $480X33 + $530X34
Subject to:
Supply Constraint:
X11 + X12 + X13 + X14 = 12
X21 + X22 + X23 + X24 = 17
X31 + X32 + X33 + X34 = 11
Demand constraint:
X11 + X21 + X31 <= 10
X12 + X22 + X32 <= 10
X13 + X23 + X33 <= 10
X14 + X24 + X34 <= 10
Xij >= 0
Excel Model:
Distance between plant and Distribution Point)
Cost per shipment from plant to Distribution Point
Distribution Points
Distribution Points
Plant
1
2
3
4
Plant
1
2
3
4
1
800
1300
400
700
1
=+$C$9*B4+$C$8
=+$C$9*C4+$C$8
=+$C$9*D4+$C$8
=+$C$9*E4+$C$8
2
1100
1400
600
1000
2
=+$C$9*B5+$C$8
=+$C$9*C5+$C$8
=+$C$9*D5+$C$8
=+$C$9*E5+$C$8
3
600
1200
800
900
3
=+$C$9*B6+$C$8
=+$C$9*C6+$C$8
=+$C$9*D6+$C$8
=+$C$9*E6+$C$8
Cost per Shipment
80
No. of Shipment Allocation Matrix
Cost per mile
0.5
Distribution Points
Shipments shipped
Shipment Capacity
Plant
1
2
3
4
1
0
0
2
10
=SUM(H11:K11)
<=
12
2
0
9
8
0
=SUM(H12:K12)
<=
17
3
10
1
0
0
=SUM(H13:K13)
<=
11
Shipments Received
=SUM(H11:H13)
=SUM(I11:I13)
=SUM(J11:J13)
=SUM(K11:K13)
=
=
=
=
Demand for shipments
10
10
10
10
Total Shipment cost
=SUMPRODUCT(H4:K6,H11:K13)
Solver Options and Solution:
Optimal Solution:
No. of Shipment Allocation Matrix
Distribution Points
Plant
1
2
3
4
1
0
0
2
10
2
0
9
8
0
3
10
1
0
0
Total transportation cost = $19,400
Distance between plant and Distribution Point)
Distribution Points
Plant
1
2
3
4
1
800
1300
400
700
2
1100
1400
600
1000
3
600
1200
800
900
Cost per Shipment
$80
Cost per mile
$0.50
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