10.1 Transportation and assignment problems are really linear programming techniques called network flow problems.
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10.2 Transportation models may be used when a firm is trying to decide where to locate a new facility.
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10.3 A typical transportation problem may ask the question, How many of X should be shipped to point E from source A?
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 Floods 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.
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10.14 A balanced problem 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 tableno 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.