With the popularity of the just-in-time system, more and more companies are operating with little or no inventories, which make them highly vulnerable to delays on supply. This paper discusses a situation when the supply of the commodity does not arrive at the depot on time, so that not enough of the commodity is available to be loaded on all vehicles at the start of the delivery period. New routing plans need to be developed in such a case to reduce the impact the delay of supply may have on the distribution company. The resulting vehicle routing problem is different from other types of vehicle routing problems as it involves waiting and multiple trips. Two approaches have been developed to solve the order release delay problem, both of which involve a Tabu Search algorithm. Computational results show the proposed approaches can largely reduce the disruption costs that are caused by the delayed supply and they are especially effective when the length of delay is long.