When a city undertakes any improvement authorized by this chapter and the expenditures required exceed the sum of five hundred dollars, it shall be done by contract and shall be let to the lowest responsible bidder, after due notice, under such regulation as may be prescribed by ordinance: PROVIDED, That the city council or commission may reject all bids presented and readvertise, or, if in the judgment of the city council or commission the work can be performed, or supplies or materials furnished by the city independent of contract, cheaper than under the bid submitted, it may after having so advertised and examined the bids, cause the work to be performed or supplies or materials to be furnished independent of contract. This section shall be construed as a concurrent and cumulative power conferred on cities and shall not be construed as in any wise repealing or affecting any law now in force relating to the performing, execution and construction of public works.