Exam 20: Transportation Models

Given the following feasible solution determine if the problem is degenerate and then find the optimal solution and its cost. Assume that capacity for source A is 10 and 30 for source B. Destination A demands 10 units while destination B demands 30 units. Cost of shipping per unit is given as AA ($4), AB ($1), BA ($3), and BB ($2). Destination A Destination B Source A 10 Source B 30

The transportation model is an excellent tool for minimizing shipping costs among existing facilities, but it is not useful when firms consider new facility locations.

What purpose does the northwest-corner rule serve?

A transportation model uses at least 10 sources and 100 destinations. If the ratio of sources to destinations remains constant, does the maximum % of cells used by the optimum solution remain constant? Why or why not?

How many cells are filled when there are ten origins and eight destinations? How many possible routes are there?

Degeneracy occurs when the number of occupied squares is less than the number of rows plus the number of columns minus one.

The information needs of a transportation problem include

The total cost of the optimal solution to a transportation problem

When using the stepping stone method, the closed path sometimes has the shape of a triangle as diagonal moves are permitted.

The ________ is an iterative technique for moving from an initial feasible solution to an optimal solution in the transportation method.

The northwest-corner rule is best used

________ is an occurrence in transportation problems when too few shipping routes are being used to allow calculation of improvement indices.

Total demand for a transportation model is 15 while total supply is 20. Which of the following should be included?

Find the minimum cost solution for the transportation problem detailed in the table below. COSTS Dest 1 Dest 2 Dest 3 Supply Source 1 18 12 5 20 Source 2 10 14 12 30 Source 3 9 11 15 75 Demand 40 30 55 125\backslash125 Before your solution can be implemented, you discover that the combination Source 3 - Destination 1 is unavailable, due to political turmoil in the country where Source 3 is located. Solve the revised problem. How much is cost increased by this complication?

The larger a transportation problem (that is, as the problem has more rows and more columns), the smaller the fraction of all possible routes that will be filled in a solved problem. Explain. Using four origins and five destinations, compared to eight origins and ten destinations.

A manufacturer of semiconductor "wafers" has been attempting to convert its operations to practices more in keeping with JIT principles. The firm is now paying much more attention to the transit time between one processing stage and the next. The plant has a somewhat haphazard pattern of machine locations, partly because the machines were purchased and installed at different times, partly from a shortage of floor space, and partly from previous experiments with work cells. The bottom line is this: there are four machines that perform a certain processing phase, and three machines that perform the next phase. All units of a large class of wafers go through these two phases. The table below displays the transit time, in minutes, from each machine of the first phase to each machine of the second. Machine 3 is not really 100 minutes away from machine B; the company has prohibited that combination because of quality problems associated with that specific pairing. Supply and demand quantities are in wafers processed per week. Develop a transit time minimizing solution for this firm. What is the total transit time of this solution? Which machines are fully utilized? Which machines have some capacity unused or requirements unfilled? Was the prohibition on the 3-B combination honored? COSTS Phase 2, Phase 2, Phase 2, Supply machine A machine B machine C Phase 1, machine 1 7.5 2.5 4.0 700 Phase 1, machine 2 3.0 6.0 6.5 600 Phase 1, machine 3 2.5 100.0 8.0 1000 Phase 1, machine 4 5.0 8.5 7.0 700 Demand 1200 800 1500 3500\backslash3000

The transportation model is a special class of linear programming models.

What does the stepping-stone method do?

Neither the northwest corner rule nor the intuitive method considers shipping cost in making initial allocations.

A transportation problem has 10 origins and 32 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?