An example of the matching process involving three students and three firms is shown below. The Rank Order Lists submitted by firms and students in this example are as follows:

Firm Rank Order Lists

Student Rank Order Lists

Match Process

The actual matching is done on a computer. However, the matching process itself could be completed as effectively by hand; the computer serves only to expedite the process. The computer is set up to process the lists in the following manner.

It first attempts to place Able into his first choice, Firm B. Since Firm B has an available position, Able is tentatively matched to Firm B. Next an attempt is made to place Baker into Firm A. Since Firm A has an available position, Baker is tentatively matched to Firm A.

The computer then attempts to place Charles into Firm B. Firm B's position is currently filled, but Firm B prefers Charles to its current match with Able. Able is therefore removed from Firm B, and Charles is tentatively matched into Firm B.

Since Able has just been removed from a tentative match with Firm B, an attempt is made to re-match Able. The computer first tries to place Able into Firm B; however, this is unsuccessful because Firm B's position is now filled with Charles, who is preferred by Firm B. Next an attempt is made to place Able into his second choice, Firm A. Since Firm A still has an available position, Able is tentatively matched to Firm A.

The matching process is now complete as each student's list has been processed, and each student is tentatively matched to the most preferred choice possible. Tentative matches now become final.

Note that in the matching process, no student or firm can be forced into a final match until all student Rank Order Lists have been considered for the best possible tentative matches.

© 2008 NMS