An appointing authority may lay off a classified employee whenever he deems it necessary because of a material change in duties or organization, or a shortage or stoppage of work or lack of funds. The rules and regulations shall specify the method of determining the persons to be laid off and in every case of layoff for more than two weeks duration the appointing authority shall, not less than fifteen days before the effective date thereof, give to the employee a written statement of the reasons for such action and shall at the same time file a copy thereof with the Personnel Director. In the case of layoffs of more than two weeks duration the Personnel Board shall, upon the written request of the laid-off employee made within ten days after the effective date of such layoff, investigate such layoff. If it shall find as result of such investigation that the layoff was made for reasons other than a material change in duties or organization or a shortage or stoppage of work or a lack of funds, or was not made in accordance with the method prescribed by the rules and regulations for determining persons to be laid off, it shall so report to the appointing authority, and the person so laid off shall thereupon be entitled to resume his position. The names of all persons who have been laid off for an indefinite period shall be placed on an appropriate re-employment list in the manner provided in the personnel rules.