Within 15 days after receiving a decision under § 14-305 of this subtitle, a grievant or a grievant’s representative may appeal in writing to the Secretary of Budget and Management. The appeal shall designate whether the grievant elects the appeal to be heard by the Secretary of Budget and Management or submitted to arbitration. In a reclassification grievance proceeding, the Secretary of Budget and Management shall order an audit of the position if it has not been audited within the last year. If the grievant elects to have a hearing, the Secretary of Budget and Management shall conduct the hearing. The Secretary of Budget and Management shall issue a decision in writing within 45 days after the later of: The conclusion of the hearing; or The day when all briefs or memoranda have been submitted. If the grievant elects arbitration, the parties shall mutually select an arbitrator. If the parties are unable to agree on an arbitrator, an arbitrator shall be selected through the American Arbitration Association in accordance with its procedures. The arbitrator shall assess all fees that result from the arbitration equally between the parties. The arbitrator shall issue an advisory decision to the Secretary of Budget and Management, and additional appeals or hearings may not be considered or held. Within 15 days after the decision of the arbitrator is received, the Secretary of Budget and Management shall issue a decision in writing. A decision of the Secretary of Budget and Management is final and binding on all parties. If an initial determination is rescinded by the Secretary of Budget and Management, further action may not be taken against the grievant with respect to any charge that was considered at the hearing. The Secretary of Budget and Management may order the University to grant back pay to a classified employee in any grievance proceeding. In a reclassification grievance proceeding in which the Secretary of Budget and Management determines that the grievant is working outside of classification or in a position that is improperly classified, the Secretary of Budget and Management, in the Secretary’s discretion, may order back pay for a period not exceeding 1 year before the grievance proceeding was initiated. The University shall carry out a back pay order issued under this section.