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Nowadays, the distribution centres aim to reduce costs by reducing inventory and timely shipment. Cross docking is a logistics strategy in which products delivered to a distribution centre by inbound trucks are directly unloaded and transferred to outbound trucks with minimum warehouse storage. Moreover, on-time delivery in a distribution network becomes very crucial especially when several distribution centres and customers are involved. Therefore, an efficient truck scheduling is needed to synchronize the delivery throughout the network in order to satisfy all stakeholders. This paper presents a mathematical model of a mixed integer programming for door assignment and truck scheduling in a multiple inbound and outbound doors cross docking problem according to Just-In-Time concept. The objective is to find the schedule of transhipment operations to simultaneously minimize the total earliness and total tardiness of trucks. Then, a multi-objective differential evolution (MODE) is proposed with an encoding scheme and four decoding strategies, called ITSH, ITDD, OTSH and OTDD, to find a Pareto frontier for the multi-door cross docking problems. The performances of MODE are evaluated using 15 generated instances. The numerical experiments demonstrate that the proposed algorithm is capable of finding a set of diverse and high quality non-dominated solutions.

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