Question

1. a) In a transportation algorithm, explain the meaning of an improvement index that is equal to zero in the final iteration (optimal solution). (1 point)

2. b) In a minimization transportation problem, explain the meaning of an improvement index that is equal to 5. (1 point)

3. c) In a transportation algorithm, explain what happens when the solution to a transportation problem is degenerate (number of used cells < number of columns + number of rows -1). (1 point)

Answer 1

The significance of an enhancement index equivalent to null in the final iterations is that alternate shipping routes can be planned at the same overall cost of shipping.

In a transport problem of minimization the idea of an index of change which is equivalent to 5 optimal solution has not been achieved. optimal solution is not reached.

For a typical transport problem with m supply sources and n demand destinations, the optimality check of any viable solution involves allocations for m + n-1 independent cells. Degeneration happens where the number of individual assignments is less than m + n-1, where m and n equate to the number of rows and columns of the transport problem. Degeneration in question of transportation will evolve in two ways.

From the initial stage the simple feasible solution may have degenerated.
At any immediate point, they may become degenerate.

To overcome a small positive amount of degeneration, one or more unoccupied cells are allocated to one or more unoccupied cells with the lowest transport costs, making N = m + n-1 allocations. While there is some flexibility when selecting an unused square for a block, the standard practice, by following the North West Corner Principle, is to move it to a square such that it retains an unbroken chain of block squares. However, where the procedure of the Vogel is used, the allocation is performed in an isolated cell with a minimal rate. In this case, an isolated cell implies a cell which on such allocation does not lead to a closed-path.
After that, the optimality test is applied, and the solution can be modified in the usual way if necessary before optimality is reached.