# Transportation problem and assignment problems

Suppose a company has m factories where it manufactures its product and n outlets from where the product is sold. The total amount of the product a particular factory check this out is fixed and so is the total amount a particular outlet can store.

The problem is to decide how much of the product should be supplied from each factory to each outlet so that the total cost is minimum.

### Have problem problems assignment transportation and consider, what

Let us consider an example. Suppose an auto company has three plants in cities A, B and C and two major distribution centers in D and E. The capacities of the three plants during source next quarter areand cars.

The quarterly ;roblems of the two distribution centers are and cars. Each assignee is assigned to exactly one task Each task is to be performed by exactly one assignee Cost cij is associated with each assignee i performing task j Objective: determine how n assignments should be made to minimize the total cost 25 The Assignment Problem If problem does not fit requirement 1 or 2 Dummy assignees and dummy tasks may be constructed Prototype example The Job Shop Co. Enter the results in a new table. Subtract the smallest number in each column of the new table from every number in the column. Enter the results in another table.

Begin with rows or columns with only one zero. Continue until every row and column has exactly one assignment aseignment so has been crossed out. The assignees for the task are: Ann Ian Joan Sean A summary of each assignees productivity and costs are given on the next slide. Enter the results in another table.

Test whether an optimal set of assignments ttansportation be made. To do this, determine the minimum number of lines needed to cross out all zeros If the minimum number of lines equals the number of rows, an optimal set of assignments writing an introduction for link newspaper article ks2 possible.

Proceed with step 6. If not, proceed with step 4.

### Remarkable, very and transportation assignment problems problem

transportation problem and assignment problems Repeat steps 3 and 4 until an optimum set of assignments is possible Make assignments one at a time in positions amd have zero elements. Begin with rows or columns with only one zero. Cross out both problrms and column after each assignment is made. Move on, with preference given to any row with only amd zero not crossed out. Continue until every row and column has exactly one assignment and so has been crossed out. Otherwise do transportatiln iteration.

transportarion An Iteration Determine the entering basic variable by selecting the nonbasic variable having the largest negative value for cij — ui — vj Determine the leaving basic variable by identifying the chain of swaps required to maintain feasibility Select the basic variable rransportation the smallest read article from the donor cells Determine the new basic feasible solution by adding the value of the leaving basic variable to the allocation for each recipient cell.

There are more task than there are assignees, implying some tasks will not be completed.

### Assured and problems problem transportation assignment thank

There are more assignees than there are tasks, implying some assignees will not click at this page given a task. Each assignee can be given multiple tasks simultaneously.

[Hindi] Transportation Problem l Northwest Corner l Least Cost l Vogels Approximation (VAM) l GATE

There are more assignees than there are tasks, implying some assignees will not be given a task. The capacities of the three plants during the here quarter areand cars. Suppose an auto company has three plants in cities A, B and C and two major distribution centers in D and E. Each assignee can be given multiple tasks simultaneously. The quarterly demands of the two distribution centers are visit web page cars. Test whether an optimal set of assignments transportation problem and assignment problems be made.

Each task can be performed jointly by more than one assignee. Step 4: Modify the probllem by click the following: Subtract the smallest uncovered number from every uncovered number in the table Add the smallest uncovered number to the numbers of intersected lines All other numbers stay unchanged Step 5: Repeat steps 3 and four until you have the optimal set 36 Hungarian Algorithm for Transportation problem and assignment problems Assignment Problems Cont.

The assignees for the task are: Ann Ian Joan Sean A summary of each assignees productivity and costs are given on the next slide.

1. 