Assignment:
Q1. Optimal Solution for a Balanced Transportation Problem
A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:
What are the monthly transportation costs for the optimal solution?
Hint: This is a balanced transportation problem.
a) $3380 b) $3420 c) $3480 d) $4125
Destination Assembly Plant
|
|
|
1
|
2
|
3
|
Supply
|
|
Source
|
A
|
5
|
9
|
16
|
200
|
|
Factory
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B
|
1
|
2
|
6
|
400
|
|
|
C
|
2
|
8
|
7
|
200
|
|
Demand
|
|
120
|
620
|
60
|
|
Q2. Optimal Solution to a Balanced Assignment Problem
A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work, however their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does what manuscript. Estimates of editing times (in hours) for each manuscript by each editor is:
What is the total minimum editing time?
a) 42 hours b) 44 hours c) 45 hours d) 47 hours
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Manuscript
|
A
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B
|
Editor
C
|
0
|
E
|
|
1
|
12
|
8
|
10
|
16
|
13
|
|
2
|
9
|
10
|
14
|
13
|
9
|
|
3
|
17
|
14
|
9
|
18
|
12
|
|
4
|
15
|
7
|
11
|
9
|
18
|
|
5
|
12
|
18
|
22
|
11
|
27
|
Q3. Transportation Problem Constraints
The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.
The amount supplied by DC 1 is:
a) 4X1A + 6X1B + 8X1C 500
b) 4X1A + 6X1B + 8X1C = 500
c) X1A + X1B + X1C 500
d) X1A + X1B + X1C =500
e) X1A + X1B + X1C 500
|
|
|
Customer
|
|
|
|
DC
|
A
|
B
|
C
|
Supply
|
|
1
|
4
|
6
|
8
|
500
|
|
2
|
5
|
2
|
7
|
400
|
|
3
|
3
|
5
|
9
|
300
|
|
Demand
|
200
|
350
|
400
|
|
Q4. Transportation Problem Constraints 2
Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets.
Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units.
Which constraint represents transshipment through the distribution center?
a) 2X13+3X23 = 900
b) 5X34 + 4X35 + 3X36 -2X13 - 3X23 = 0
c) X34 + X35 + X36 -X13 -X23 = 0
d) X34 + X35 + X36 -X13 -X23 0
e) X34 + X35 + X36 =900
Q5. Transshipment Optimal Solution
The following diagram shows a transshipment network. Nodes 1, 2, and 3 are supply nodes. The supply values are to the left of these nodes. Nodes 6, 7, and 8 are demand (sink) nodes, and the demand values are to the right of these nodes. Transshipment routes between nodes are labeled with the transportation cost per unit.
What is the minimum transportation cost associated with this network?
a) $3180 b) $3260 c) $3300 d) $3340
