عنوان مقاله [English]
Transportation is an important factor in the economic, production and service systems and it has allocated a significant portion of the gross domestic product (GDP) of any country. Production routing problem is development of the traveling salesman and vehicle routing problems in which scheduling and production planning are considered too. Generally, in the above problems it is assumed that there is a monopoly and the impact of competitors has not been considered. In this paper, for creating competitive condition, it is assumed that the earliest and latest time of competitor arrival is known. After modeling problem as mixed intger programming, valid inequalities are proposed, and their effects on the model have been investigated by the CPLEX software. These inequalities are provided for production routing problem with homogeneous and heterogeneous vehicles, separately. To evaluate the performance of the proposed valid inequalities, the results of them have been compared.
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