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This article has studied a full truckload transportation problem in the context of an empty return scenario, particularly an order selection and vehicle routing problem with full truckload, multiple depots and time windows (SFTMDVRPTW). The aim is to develop a solution where a set of truck routes serves a subset of selected transportation demands from a number of full truckload orders to maximize the total profit obtained from those orders. Each truck route is a chain of selected demands to serve, originating at a departure point and terminating at an arriving point of trucks in a way that respects the constraints of availability and time windows. It is not mandatory to serve all orders, and only the profitable ones are selected. In this study, we have formulated the SFTMDVRPTW as a mixed-integer linear programming (MILP) model. Finally, Computational results are conducted on a new data set that contains thirty randomly generated problem instances ranging from 16 to 30 orders using the CPLEX software. The findings prove that our model has provided good solutions in a reasonable time.

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