There are a couple of considerations regarding resumes and applications, and both are relevant for Affirmative Action/applicant tracking purposes as well as sound hiring practices.
As a general rule, I suggest that you accept resumes and/or applications for only those positions which are open. By doing so, you can consider those applicants for applicant tracking purposes related to your Affirmative Action reporting. It makes for a more efficient method for these tracking purposes, and it's only these that you need to keep on file for EEOC compliance.
Secondly, I recommend that you always have an applicant complete an employment application, even with submitting a resume. There are several reasons for this practice: 1) if this is a serious candidate, an interviewer can compare the information on both documents, and often uncover good areas of questioning, such as gaps in employment, etc.; 2) the application provides some "contractual" authority for you to check credit, criminal records, etc. and often has some legal terminology related to employment at will, etc. These contractual agreements are not on resumes, of course, so by having a signed app on file, you have the applicant and potential new employee's agreement.
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Gayla R. Sherry, SPHR, CMC
President, Gayla R. Sherry Associates, Inc.
Helping organizations improve employee morale, retention and productivity
HR Consulting and Compliance; Training, Conflict Resolution, Internal Investigations, Expert Witness