A business executive must make four roundtrips as listed in

A business executive must make four round-trips as listed in The following table between Boston and a branch office in Atlanta: The price of a round-trip ticket from Boston is $400. A 25% discount is granted if The date of arrival and departure span a weekend (Saturday and Sunday). If The stay in Atlanta lasts more than 21 days, The discount price is increased to 30%. A one-way ticket between Boston and Atlanta (either direction) costs $250. Formulate an assignment/matching problem for how The executive should purchase The tickets. What are The sets (pairings) in The problem? How should The executive purchase The ticlets?

Solution

Ans: Use the city & date to define row & column; B3 means leaving Boston & A7 means returning from Atlanta.

Step 1: First requirement is that, matrix should be balanced i.e. number of row should be equal to number of column. Second Requirement is that each row and each column must have least one zero. So Select, least number from first row i.e. 1 and subtract that number from remaining numbers of that row. Follow similar procedure for rest of the rows. Then follow the similar procedure for column as wee, select least number from that column and subtract it from remaining numbers of that column, if zero is already present in that column , no need to perform the operation.

Step 2: Perform Row & column operation.

To perform row operation, the particular row should have only one zero, then only you can perform row operation, otherwise proceed to next row.

In the first row, there is only one zero, so roe operation can be performed. Row operation is performed by assigning the zero, by making square on it and canceling the column.

Step 3 : For optimal solution, Number of squared zero= number of row/column.

Here, Number of squared zero=4 & number of row=4, so optimal solution.

D3-A28=280, D10-A21=300, D17-A12=300, D25-A21=300

solving this you will get answer zmin= 1180$

	A7	A12	A21	A28
D3	400	300	300	280
D10	300	400	300	300
D17	300	300	400	300
D25	300	300	300	400