transportation leading to warehousing cost reduction via the direct transfer of cargo from input vehicles to output vehicles without storage. Hence, product storage and recycling costs are reduced by applying cross-dock systems and even by synchronizing input and output vehicle flows [1]. In a cross-dock system, the main target is to remove storage and reduce the over-transportation of goods. Therefore, the existing product in the warehouse is stored for a short time [2]. The Material Handling Industry of America defines a cross-dock as a warehouse focused on transferring goods from a vehicle to another vehicle [2]. A cross-dock acts more as an inventory coordinator than as filling a warehousing role, shifting the focus from supply chain management to demand-supply management [3]. [PERSON] et al. (2008) presented a model based on customers' perspectives for the optimal use of cross-docking and concluded that lower demand variability and higher stock costs exacerbate the effects of cross-docking. On the other hand, supply chain management can be divided into three categories of supply chain designing, planning, and control [4]. The performance level includes scheduling problems, warehouse door allocation, transportation within doors, and vehicle routing. The tactical level examines problems in cross-dock layout design and the strategic level evaluates problems related to cross-dock networks. [PERSON] (2002) [5] examines three different models based on the number of available doors, the vehicle loading pattern of doors, and the existence or absence of temporary storage. [PERSON] et al. (2005) [6] expanded a simulation method of cross-docks in order to evaluate the existing risk value in product transportation and showed the operation within a cross-dock facility in a dynamic environment and with the existence of demand growth. [PERSON] and [PERSON] (2007) [7] examined a model without a temporary warehouse and unlimited transportation systems, and for solving their minimization objective function they calculated the distance from the discharging site to the loading site. [PERSON] and [PERSON] (2008) [8] presented a mixed integer programming model with cross-docks including an entrance door and an exit door and combined it with product allocation problems. This model was more flexible than unpredictable events. [PERSON] and [PERSON] (2009) [9] considered the cross-dock scheduling problem in which an operation is performed based on a two-machine flow shop. The first machine discharges input products and the second machine loads an input vehicle. [PERSON] and [PERSON] (2010) [10] scheduled input and output vehicles in cross-docks using the imperialist competitive Algorithm. [PERSON] et al. (2010) [1] presented a mixed integer linear programming algorithm aiming at minimizing system delivery costs, taking into consideration product combinations and delivery windows. [PERSON] and [PERSON] (2015) [11] examined vehicle routing problems and presented a reciprocating method, finding a near optimum solution. [PERSON] et al. (2014) [12] considered vehicle routing and scheduling in a cross-docks customer-supplier network in which a set of homogenous vehicles transfer products from suppliers to customers using cross-docks. [PERSON] et al. (2015) [13] evaluated a model consisting of a two-vehicle routing level with cross-docks. [PERSON] et al. (2016) [14] considered one type of product and cross-dock with homogenous capacity vehicles in which vehicles start the loading operation at different points at various times. [PERSON] and [PERSON] (2016) [15] studied truck scheduling problems in cross-docks with the assumption of truck failure. The truck failure rate was modeled by Poisson distribution and used three metaheuristic algorithms to solve it. [PERSON] et al. (2015) [14] introduced a model that considers two-level vehicle routing along with cross-docking. [PERSON] et al. (2015) [16] proposed a truncated branch and price solution algorithm to take care of a sensible issue including the satisfaction of a random of transportation demands.