The transportation and reimbursement authorized by section 453(c) of title 37 shall be available hereafter to pay a monetary allowance in place of such transportation to a member who, under regulations prescribed by the Secretary, participates in a program designated by the Secretary in which his baggage and household effects are moved by a privately owned or rental vehicle. This allowance shall not be limited to reimbursement for actual expenses and may be paid in advance of the transportation of the baggage and household effects. The allowance shall, however, be in an amount that will result in savings to the Government when the total cost of the movement of baggage and household effects is compared with the cost that otherwise would have been incurred under section 453(c) of title 37.