BUS606: Operations and Supply Chain Management

Among many difficulties found in the construction of complex simulation models, the modeling of nonstationary stochastic processes is certainly a case. Without even entering the mathematical formalism of the definition of these applications, consider, as an example of this type of process, a call center to the public where the calls occur randomly, but with different rates of arrivals by 30-minute intervals. This randomness is simulated in software by generating random numbers in compliance with a determined probability distribution (Poisson, Exponential, normal, Weibull, etc.). The amount of calls generated in the model, for the period, should converge on average to the value defined by the arrival rate. Bear in mind, however, that this should occur despite the intrinsic randomness to the occurrences of these calls, questions, complaints, and so forth.

In the Distribution Center that operates cross-docking logistics situations, this disposal is absolutely unacceptable or impractical. Therefore, the administrator must make a schedule of receiving goods, so that the space available for their (temporary) storage is not completely filled and the amount of unloading doors is in accordance with the quantity of products received per day, since this would generate long queues in its surroundings until all the discharge could be performed, raising costs and compromising the entire logistics operation.

Thus, the arrival of goods in the Distribution Center is done through an adequate logistics programming conducted by managers, but it still depends on how well this loading center has been designed, specifically to determine the number of doors.

This study proposes an approximate theoretical mathematical queuing model to be applied to the problem of door allocation, considering the queues to be nonstationary. This theoretical model will be later confronted with a simulation model, using the Arena software, in order to validate the former. The advantage of using simulation is that it can replicate activities and congestion in a cross-dock, as well as providing accurate information that enables correct decision making to improve cross-docking performance.

It is not the object of this work to deal with the internal part of the cross-dock operations with elements such as allocation of material handling equipment and labor effort analysis, to assist in the unloading/loading of the trucks, as well as the displacement of the materials inside the terminal. To this respect, the minimization of the internal transfer distance of goods from the receiving doors to the shipping ones, which is subject of study by some authors, is not part either of the objectives of this work.

3.1. Application Example

A supermarket chain that operates a cross-docking terminal receives products from supplier companies and transfers them to vehicles that supply the company's stores. It is assumed, in a preliminary approximation, that all products arrive in uniform cartons, with the dimensions shown in Figure 1. The carton shown in Figure 1 is understood as the equivalent handling unit of product. Thus, the flows of products that arrive, are handled, and are subsequently shipped in the terminal are measured in a simplified number of equivalent boxes.

Figure 1 Standard packaging box for products.

The terminal continuously receives an average of 10,625 equivalent cartons per hour. The composition of the feeder truck fleet is shown in Table 1.

Table 1 Composition of the fleet of feeding vehicles.