10.1
Transportation and assignment
problems are really linear programming techniques called network flow problems.
}
10.2
Transportation models may be
used when a firm is trying to decide where to locate a new facility.
}
10.3
A typical transportation
problem may ask the question, âHow many of X should be shipped to point E from
source A?â
10.4
The objective of a
transportation problem solution is to schedule shipments from sources to
destinations while minimizing total transportation and production costs.
10.5
In a transportation problem,
each destination must be supplied by one and only one source.
10.6
In a transportation problem, a
single source may supply something to all destinations.
Like the simplex method, the
transportation and assignment methods are fairly simple in terms of
computation.
10.7
While the transportation and
assignment algorithms have computation times that are generally 100 times
faster than the simplex algorithm, the size of problems solvable on a computer
is approximately the same as when using the simplex algorithm.
10.8
In finding the maximum quantity
that can be shipped on the least costly route using the stepping-stone method,
one examines the closed path of plus and minus signs drawn and selects the
smallest number found in those squares containing minus signs.
10.9
Another name for the MODI
method is Floodâs technique.
In using the stepping-stone method,
the path can turn at any box or cell that is unoccupied.
ANSWER: FALSE {moderate,
STEPPING-STONE METHOD: FINDING A LEAST-COST SOLUTION}
10.10
Using the stepping-stone method
to solve a maximization problem, we would choose the route with the largest
positive improvement index.
10.11
One of the advantages of the
stepping-stone method is that if, at a particular iteration, we accidentally
choose a route that is not the best, the only penalty is to perform additional
iterations.
10.12
The transportation table used
for transportation problems serves the same primary role as the simplex tableau
does for general linear programming problems.
10.13
Vogel’s approximation method
will often give a “good,” if not “optimal,” solution to a
transportation problem.
}
10.14
A âbalanced problemâ exists in
a transportation model when the optimal solution has the same amount being
shipped over all paths that have any positive shipment.
10.15
It is possible to find an
optimal solution to a transportation problem that is degenerate.
10.16
A solution to the transportation
problem can become degenerate at any iteration.
10.17
The transportation algorithm
can be used to solve both minimization problems and maximization problems.
10.18
Assignment problems involve
determining the most efficient assignment of people to projects, salesmen to
territories, contracts to bidders, and so on.
10.19
The objective of an assignment
problem solution most often is to minimize the total costs or time of
performing the assigned tasks.
10.20
In the assignment problem, the
costs for a dummy row will be equal to the lowest cost of the column
for each respective
cell in that row.
10.21
The Hungarian method is
designed to solve transportation problems efficiently.
10.22
Maximization assignment
problems can easily be converted to minimization problems by subtracting each
rating from the largest rating in the table.
10.23
Transportation and assignment
problems can never have more than one optimal solution.
10.24
In a transportation problem, a
dummy source is given a zero cost, while in an assignment problem, a
dummy source is
given a very high cost.
MULTIPLE CHOICE
Table 10-1
To==>
1
2
3
Supply
From
A
| 3
20
| 6
20
| 4
40
B
| 3
| 4
30
| 5
30
C
| 5
| 7
20
| 6
10
30
Demand
20
70
10
10.25
What is the total cost
represented by the solution shown in Table 10-1?
(a) 60
(b) 2500
(c) 2600
(d) 500
(e) none
of the above
What is the value of the improvement
index for cell B1 shown in Table 10-1?
(a) -50
(b) +3
(c) +2
(d) +1
(e) none
of the above
Table 10-2
To==>
1
2
3
Supply
From
A
| 3
20
| 6
30
| 3
50
B
| 4
| 4
40
| 3
40
C
| 5
| 7
10
| 6
15
25
Demand
20
80
15
10.26
In Table 10-2, cell A3 should
be selected to be filled in the next solution.
If this was selected as the cell to be filled, and the next solution was
found using the appropriate stepping-stone path, how many units would be
assigned to this cell?
(a) 10
(b) 15
(c) 20
(d) 30
(e) none
of the above
Table 10-3
To==>
1
2
3
Dummy
Supply
From
A
| 10
| 8
80
| 12
| 0
20
100
B
| 6
120
| 7
| 4
30
| 0
150
C
| 10
| 9
| 6
170
| 0
80
250
Demand
120
80
200
100
The following
cell improvements are provided for Table 10-3
Cell Improvement Index
A1 +2
A3 +6
B2 +1
B-Dummy +2
C1 +2
C2 +1
10.27
The cell improvement indices
for Table 10-3 suggest that the optimal solution has been found. Based on this solution, how many units would
actually be sent from source C?
(a) 10
(b) 170
(c) 180
(d) 250
(e) none
of the above
In Table 10-3, suppose shipping cost
from source C to point 2 was 8, which below would be true?
(a) There
would be multiple optimal solutions.
(b) The
minimum possible total cost would decrease.
(c) The
minimum possible total cost would increase.
(d) Another
dummy column would be needed.
(e) none
of the above
10.28
Both transportation and
assignment problems are members of a category of LP techniques called ____.
(a)
transasignment problems
(b)
Hungarian problems
(c)
source-destination problems
(d)
supply and demand problems
(e)
Network flow problems
10.29
Transportation models can be
used for which of the following decisions?
(a) facility
location
(b) production
mix
(c) media
selection
(d) portfolio
selection
(e) employee
shift scheduling
Table 10-6
Initial
tableâno allocations yet
To==>
1
2
3
Supply
From
A
| 6
| 4
| 5
200
B
| 8
| 6
| 7
300
C
| 5
| 5
| 6
300
Demand
400
200
100
Optimal
Solution by the Modi Method
To==>
1
2
3
Dummy
Supply
From
A
| 6
100
| 4
| 5
100
| 0
200
B
| 8
| 6
200
| 7
| 0
100
300
C
| 5
300
| 5
| 6
| 0
300
Demand
400
200
100
100
10.30
In Table 10-6, which presents a
MODI solution for a transportation problem, which statement is true?
(a) There
is no feasible solution to the problem.
(b) The
total cost represented by the solution is $3,700.
(c) One
hundred units of demand are not met.
(d) The
original problem was unbalanced.
(e) The
cheapest route has the highest shipment amount.
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