Exam 18: Transportation and Assignment Solution Methods

Given the following transportation tableau where the numbers in each cell represent transportation costs from the specific source to the specific destination with supply figures corresponding to each source and demand figures corresponding to each destination: Source A B C Demand 1 \ 2.2 2.4 2.1 350 Destination 2 3.4 3.2 3.6 400 3 1.9 1.8 2.1 200 Supply 200 300 450 -According to the Northwest Corner method, the initial solution would have a total transportation cost of ________.

The supply and demand values along the outside rim of a tableau are called rim requirements.

Transportation problems are solved manually within a tableau format.

There are 4 jobs in a 4 person office that must be done as quickly as possible. The supervisor has used the assignment method to assign people to jobs, and has completed the first step. She had to rush off to a meeting and has asked to assign the jobs to the people before she returns. The original matrix which shows the expected completion time for each person for each job, and the one she just completed are both shown below. Job Ruth Steve Valerie Wayne A 8 26 17 11 B 13 28 4 26 C 38 19 18 15 D 19 26 24 10 Job Ruth Steve Valerie Wayne A 0 18 9 3 B 9 24 0 22 C 23 4 3 0 D 9 16 14 0 Which person should be assigned to which job? How long will the jobs take?

An opportunity cost table is developed by first subtracting the minimum value in each row from all other row values and then repeating this process for each column.

Use the following table and the information to answer the questions below. In the following transportation matrix, all cells except 2C have been evaluated and show no improvement. Evaluate that cell. -How many units would be allocated to cell 2C?

A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work; however, their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does which manuscript. Estimates of editing times (in hours) for each manuscript by each editor are: Editor Manuscript 1 12 8 10 16 13 2 9 10 14 13 9 3 17 14 9 18 12 4 15 7 11 9 18 5 12 18 22 11 27 How many variables are involved in this assignment method?

SS 1 2 1 100 5 6 2 200 4 2 3 150 3 6 4 50 9 7 DD 250 250 What are the demand-side constraints?

In a balanced transportation model where supply equals demand, all constraints are equalities.

Assignments are made to locations with 1 in the opportunity cost table.

In a transportation problem, items are allocated from sources to destinations at a minimum cost.

In the ________ method, the largest possible allocation is made to the cell in the upper-left-hand corner of the tableau, followed by allocations to adjacent feasible cells.

An opportunity cost table is developed by first subtracting the minimum value in each row from all other row values and then repeating this process for each row.

The two solution methods for transportation problems that do not require the use of a computer are ________ and ________.

If the number of unique assignments is less than the number of rows, then a ________ test must be used.

A company that repairs and maintains HVAC systems for businesses wants to assign three service teams to three geographical zones, one team to each zone. Because of the familiarity with each team to the companies located in a zone, there are differences in the efficiencies of each team, reflected in the service costs. The matrix below shows the service costs (in thousands of dollars) for each team in each zone. Assign each team to a zone that minimizes cost.

In using the minimum cell cost method, as much as possible is allocated to the cell with the ________ cost.

Canning Transport wants to move goods from three (3) factories to three (3) distribution centers. Information about the move is given below: Supply at Source 50 100 150 Demand at Destination 50 \nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace I 125 \nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace II 125 \nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace III Shipping costs are (in $): I II III A 3 2 5 B 9 10 12 C 5 6 4 -According to the Northwest Corner method, the initial solution would give to cell CIII a loading of ________.

In a transportation tableau to rectify a degenerate tableau, an empty cell must artificially be treated as an ________ cell.

A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work; however, their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does which manuscript. Estimates of editing times (in hours) for each manuscript by each editor are: Editor Manuscript 1 12 8 10 16 13 2 9 10 14 13 9 3 17 14 9 18 12 4 15 7 11 9 18 5 12 18 22 11 27 How many constraints are needed?