25 May Question 10.1 Transportation and assignment problems are really linear progra
Question
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 Flood’s 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
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