Suppose the company has revised its plans for the processes described in part “a” to accommodate technological process changes. Determine the placement of departments that will now minimize total travel cost. Use the distances shown in part “a”, but use the following new matrix of daily trips between departments.
To determine the placement of departments that will minimize total travel cost with the new matrix of daily trips between departments, you would need to use a technique called the optimum assignment method, also known as the Hungarian algorithm. The Hungarian algorithm is an efficient algorithm that solves the assignment problem.
Here are the steps to solve the assignment problem using the Hungarian algorithm:
1. Create a matrix representing the new matrix of daily trips between departments. This matrix should have the same dimensions as the previous matrix.
2. Subtract the smallest element in each row from all the elements in that row.
3. Subtract the smallest element in each column from all the elements in that column.
4. Find the minimum number of lines needed to cover all the zeros in the resulting matrix. This step is known as the row and column reduction.
5. If the minimum number of lines is equal to the number of rows (or columns), you have found an optimal solution. If not, proceed to the next step.
6. Draw the smallest number of lines needed to cover all the zeros in the matrix, and use these lines to make additional zeros. Then, find the smallest entry not covered by any line and subtract it from all the uncovered entries. Add it to the entries that are covered twice.
7. Go back to step 4 until an optimal solution is found.
8. Once an optimal solution is found, the assignment of departments to locations that minimizes the total travel cost can be determined from the resulting matrix.
The steps mentioned above follow the basics of the Hungarian algorithm. Implementing this algorithm requires performing matrix calculations and comparisons, which can be done manually or using software tools like a spreadsheet program or programming libraries that offer implementation of the Hungarian algorithm.
Note that this explanation assumes that you have the necessary matrix data and understanding of the Hungarian algorithm. If you have the specific matrix data and need further assistance or clarification, please provide the matrix in question.
To determine the placement of departments that will minimize total travel cost with the new matrix of daily trips between departments, we need to use a mathematical optimization technique such as the transportation problem or the linear programming problem.
However, you have mentioned that the new matrix of daily trips between departments is not provided. Please provide the new matrix of daily trips between departments so that I can assist you further in determining the placement of departments that minimizes total travel cost.