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

• Published in: Scientia Iranica. Transaction E, Industrial engineering Vol. 25; no. 4; pp. 2282 - 2296
• Main Authors: Motaghedi-Larijani, A, Aminnayeri, M
• Format: Journal Article
• Language: English
• Published: Tehran Sharif University of Technology 01.08.2018
• Subjects: Bayes Theorem; Bayesian analysis; Costs; Customers; Doors; Logistics; Optimization; Probability; Probability distribution functions; Queues; Queuing; Queuing theory; Statistics; Supply chains; Transportation; Trucks; Windows (intervals)
• DOI: 10.24200/sci.2017.4452

Crossdocking is one of the supply chain strategies that can reduce costs of transportation and inventory. Many studies on the problem of crossdocking have been conducted with respect to 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 at outbound doors of the crossdock within a specified time window. Arrival times of trucks follow a beta distribution, and customers are 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 is inapplicable to the long run of the system. Instead, the total expected waiting time is calculated based on conditional joint probabilities, order statistics along with the Bayes theorem.