Optimizing the number of outbound doors in the crossdock based on a new queuing system with the assumption of beta arrival time

Crossdocking is one of the supply chain strategies that can reduce transportation and inventory costs. Many studies are conducted the problem of crossdocking by considering various characteristics of crossdocks. In this paper, a queuing model is proposed in order to optimize the number of outbound doors based on minimizing the total costs including the costs of adding a new outbound door and the expected waiting time of customers. The total number of trucks arriving for service is constant. Trucks arrive to outbound doors of the crossdock within a specified time window. Arrival times of trucks follow a beta distribution and customers to be served based on first in first out policy (FIFO). Since, the total number of customers as well as the time of arrivals are finite, the steady state distribution for the long run of the system is inapplicable. Instead, based on conditional joint probabilities, order statistics along with the Bayes theorem we calculate the total expected waiting time.