BUS606: Operations and Supply Chain Management

Cross-docking centers deal with different types of problems, such as the location and layout of the terminals  vehicle routing, port allocation problem, and truck scheduling.

This study focuses on the problem of sizing the number of receiving doors to unload feeder trucks in a terminal that operates under the cross-docking concept. A vehicle that arrives at the cross-dock terminal to be unloaded and finds one or more unoccupied service positions is directed to one of them for immediate unloading. Often, however, all unloading positions are occupied and the vehicle must wait. For the dimensioning of the cargo receiving area in the respective dock it is necessary to determine the number of doors required for that and, concurrently, estimate the number of vehicles in the queue by adopting an adequate service level, in order to provide space for truck parking, and not keeping the vehicles waiting excessive time. The number of discharge positions operating in parallel at the receiving dock is determined by the application of a mathematical queuing model, or by simulation.

The complexity of cross-docking operations has been of great interest to researchers and practitioners in the areas of optimization, supply chain management, and operational research. The following are some published works related to the use of mathematical modeling and/or simulation for cross-docking terminals.

Based on research hypotheses that addressed cross-docking simulation problems, Rohrer explained how the simulation helps to ensure the success of cross-docking operations. For example, the problem of allocating entrance and exit truck doors in a Distribution Center (DC) has been previously studied by simulation approaches.

Gue and Kang introduce a new type of queue, called "staging queues," in the case of unitized loads, mainly on pallets, in order to compare different freight preparation protocols. The authors use the Arena Simulation package to investigate three areas.

Taylor and Noble also use simulation to analyze staging methods in various cross-docking environments. In their study, three preparation alternatives and three output demand scenarios are analyzed. After the simulations, they evaluate those scenarios with four performance criteria. The issues raised by Taylor and Noble motivated a study by Sandal that analyzes the most appropriate preparation strategies in the cross-docking operation according to the attributes of the load of trailers, in order to allow an optimized load on the trucks. Integrated to the algorithm developed in this mentioned study, a simulation model using the Arena Simulator analyzed four preparation strategies in a cross-dock environment was developed and applied.

Chen et al. study a similar problem which they call the multiple cross-dock problems. The major differences observed were that supplies and demands are not separable and that different products can be considered together (multicommodity flow problem). Also, transportation times in this approach are not taken into account. An integer programming formulation of the problem is provided, together with a proof of its NP-completeness. The authors proposed three heuristics (simulated annealing, tabu search, and a combination of both) to solve the problem. These heuristics provide better solutions than those obtained by solving the integer programming formulation with CPLEX, within only less than 10% of the time used by CPLEX. Among the three heuristics, tabu search seems to give the best results.

Arnaout et al. propose a simulation model of discrete events of cross-docking operations, revealing some of the most important parameters that should be investigated. The proposed model was generated with the aid of the Arena Simulator and uses discrete events to randomly allocate orders in three different warehouses. The stochastic nature of the system allowed us to analyze different scenarios and to reveal the importance of some model parameters.

Some papers cited here show the importance that the simulation tool has been of, both in academic and business environments, especially for applications in manufacturing systems, handling, and materials storage, especially in the aid to the use of the logistics technique involving cross-docking. However, there is a gap in the literature regarding the optimization process to determine the number of receiving doors on a DC.