In this paper we develop a greedy randomized adaptive search procedure (GRASP) for solving a transportation problem arising in disaster relief situations. The problem is to satisfy the demand of a given set of customers through creating some open routes by using a limited number of vehicles located at the central depot. We assume that the demand of each customer to be directly satisfied by being visited on a route or just being close to a visited customer. Two mathematical models are proposed for the mentioned problem and enriched by introducing some valid inequalities. The performance of the developed algorithm is tested on different sets of instances. The computational results indicate the effectiveness of the developed method.

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