Module C Transportation Models

To utilize a transportation model for shipping supplies, which of the following three pieces of information are required?

What is the primary purpose of a transportation matrix in transportation modeling?

According to the northwest-corner rule for establishing an initial feasible solution, what is the first step in the allocation process?

In the Arizona Plumbing problem, the initial solution using the northwest-corner rule involves five shipping assignments: 100 tubs from Des Moines to Albuquerque, 200 tubs from Evansville to Albuquerque, 100 tubs from Evansville to Boston, 100 tubs from Fort Lauderdale to Boston, and 200 tubs from Fort Lauderdale to Cleveland. The costs per unit are: Des Moines to Albuquerque ($5), Evansville to Albuquerque ($8), Evansville to Boston ($4), Fort Lauderdale to Boston ($7), and Fort Lauderdale to Cleveland ($5). What is the total cost of this initial shipping assignment?

What is a major drawback of using the northwest-corner rule to find an initial solution?

The intuitive lowest-cost method for finding an initial solution begins by identifying which cell in the transportation matrix?

The stepping-stone method is used in transportation modeling to achieve what objective?

When using the stepping-stone method, what does tracing a 'closed path' allow a manager to evaluate?

In the stepping-stone method, what does a calculated improvement index for an unused square represent?

When is an optimal solution reached in the stepping-stone method?

In the Arizona Plumbing problem, the initial northwest-corner solution is evaluated using the stepping-stone method. The unused route from Fort Lauderdale to Albuquerque has a closed path involving squares with costs of $9 (Fort Lauderdale-Albuquerque, +), $7 (Fort Lauderdale-Boston, -), $4 (Evansville-Boston, +), and $8 (Evansville-Albuquerque, -). What is the improvement index for this route?

If the stepping-stone method reveals an unused route with an improvement index of -2, what is the next step to improve the solution?

When reallocating units along a closed path in the stepping-stone method, how is the maximum quantity to be shipped on the new route determined?

How are unbalanced transportation problems, where total demand is not equal to total supply, handled?

If total demand is 800 units and total supply is 700 units in a transportation problem, how would you balance it?

What are the shipping cost coefficients assigned to the squares in a dummy source row or dummy destination column?

What is the definition of a degenerate solution in a transportation problem?

To apply the stepping-stone method, a non-degenerate solution must satisfy a specific rule regarding the number of occupied shipping routes. What is this rule?

How are degenerate problems handled in the stepping-stone method?

In a transportation problem with 4 factories (sources) and 5 warehouses (destinations), how many occupied routes must a non-degenerate solution have?

When resolving degeneracy, where must the artificial occupied cell be placed?

In the solved problem for Williams Auto Top Carriers, opening a plant in New Orleans has an initial total cost of $23,600. After one stepping-stone iteration, what is the new total cost?

In the Williams Auto Top Carriers problem, the total cost for one auto top carrier from Atlanta to Los Angeles is stated as $14. How is this figure derived?

After improving the solution for the Williams New Orleans plant to a total cost of $20,000, the improvement indices for the two unused routes (Atlanta-Los Angeles and New Orleans-Los Angeles) are calculated as +6 and +2, respectively. What does this signify?

The transportation model is described as a form of what other mathematical technique?

What is the primary difference in the allocation process between the northwest-corner rule and the intuitive lowest-cost method?

In a problem with 3 sources and 3 destinations, you have found an initial solution using the northwest-corner rule. You have 5 occupied cells. Can you proceed with the stepping-stone method?

The stepping-stone method is described as an iterative technique. What does 'iterative' mean in this context?

In the stepping-stone method, the closed path traced for an unused square can only make horizontal and vertical moves. At what cells is it permissible to turn a corner?

In the Arizona Plumbing problem, after one iteration, the total cost is reduced from $4,200 to $4,000. What caused this $200 reduction?

If you are solving a transportation problem and find that all possible initial solutions are degenerate, what is the most likely cause?

Which of the two methods for finding an initial solution is generally preferred because it tends to provide a better starting point?

A firm has 2 factories with supplies of 100 and 60 units. It has 3 destinations with demands of 50, 80, and 70 units. What is the first step in setting up the transportation matrix?

What is the key advantage of a transportation model when a company like Williams Auto Top Carriers is deciding on a new plant location?

In the solved problem C.1, the improvement index for the Atlanta-New York route is -6. This is calculated as +11 (Atlanta-New York) - 14 (Atlanta-Los Angeles) + 9 (Tulsa-Los Angeles) - 12 (Tulsa-New York). Where do the costs like $11 and $14 come from?

Consider a transportation problem with sources in Mexico City, Detroit, and Ottawa, and destinations in Los Angeles, Calgary, and Panama City. Supply from Mexico City is 100. Demand in Los Angeles is 50. The cost to ship from Mexico City to Los Angeles is $6. Using the northwest-corner method, what is the first allocation made?

If a transportation model is solved and the optimal solution has two routes with improvement indices of zero, what does this indicate?

In the solved problem C.2, the Williams Auto Top Carriers problem is formulated as a linear programming model. The constraint 'XAtl,LA + XAtl,NY <= 600' is created. What does this constraint represent?

In the solved problem C.2 linear programming formulation for Williams Auto, the constraint 'XAtl,LA + XTul,LA + XNO,LA >= 800' is created. What does this constraint represent?

Can the stepping-stone method be used to solve maximization problems as well as minimization problems?

An origin point or source in a transportation model can be which of the following?

The final step of the intuitive lowest-cost method is repeated until when?

If you perform a stepping-stone iteration and reallocate 100 units along a path where the smallest number in a 'minus' square was 100, what happens to the cell where that smallest number was located?

Why must the closed path in the stepping-stone method alternate plus and minus signs on its corner squares?

You are given a transportation problem where the total supply is 1,000 units and the total demand is 1,200 units. You add a dummy source with a supply of 200 units. What can be said about the units allocated from this dummy source in the final optimal solution?

What is the result of using the intuitive lowest-cost method on the Arizona Plumbing problem data? The costs are: D-A $5, D-B $4, D-C $3; E-A $8, E-B $4, E-C $3; F-A $9, F-B $7, F-C $5. Supply is D:100, E:300, F:300. Demand is A:300, B:200, C:200.

The solution from the intuitive lowest-cost method for the Arizona Plumbing problem has a total cost of $4,100. Is this solution optimal?

Consider the problem with sources X, Y, Z (supplies 100, 50, 75) and destinations A, B, C (demands 50, 80, 70). The costs are X-C: $12, Y-C: $9, Z-C: $14. Total supply is 225, total demand is 200. After adding a dummy destination D with demand 25, you apply the intuitive lowest-cost method. The cost for Y-C is the lowest in its column. How many units are allocated to Y-C?

If you are solving a transportation problem manually, and the final optimal solution has two empty cells with improvement indices of +3 and 0 respectively, what can you conclude?

When can a transportation model be useful in an aggregate planning context, as mentioned in the chapter summary?