A Closed Queueing Networks Approach for an Optimal Heterogeneous Fleet Size of an Inter-Facility Bulk Material Transfer System

Mohamed Amjath, Laoucine Kerbache () and James MacGregor Smith
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Mohamed Amjath: Division of Engineering Management and Decision Sciences, College of Science and Engineering, Hamad Bin Khalifa University, Qatar Foundation, Doha 34110, Qatar
Laoucine Kerbache: Division of Engineering Management and Decision Sciences, College of Science and Engineering, Hamad Bin Khalifa University, Qatar Foundation, Doha 34110, Qatar
James MacGregor Smith: Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA

Logistics, 2024, vol. 8, issue 1, 1-38

Abstract: Background: This study addresses optimising fleet size in a system with a heterogeneous truck fleet, aiming to minimise transportation costs in interfacility material transfer operations. Methods: The material transfer process is modelled using a closed queueing network (CQN) that considers heterogeneous nodes and customised service times tailored to the unique characteristics of various truck types and their transported materials. The optimisation problem is formulated as a mixed-integer nonlinear programming (MINLP), falling into the NP-Hard, making exact solution computation challenging. A numerical approximation method, a modified sequential quadratic programming (SQP) method coupled with a mean value analysis (MVA) algorithm, is employed to overcome this challenge. Validation is conducted using a discrete event simulation (DES) model. Results: The proposed analytical model tested within a steel manufacturing plant’s material transfer process. The results showed that the analytical model achieved comparable optimisation of the heterogeneous truck fleet size with significantly reduced response times compared to the simulation method. Furthermore, evaluating performance metrics, encompassing response time, utilisation rate, and cycle time, revealed minimal discrepancies between the analytical and the simulation results, approximately ±8%, ±8%, and ±7%, respectively. Conclusions: These findings affirm the presented analytical approach’s robustness in optimising interfacility material transfer operations with heterogeneous truck fleets, demonstrating real-world applications.

Keywords: fleet sizing; heterogeneous fleet; queueing networks; material handling; simulation (search for similar items in EconPapers)
JEL-codes: L8 L80 L81 L86 L87 L9 L90 L91 L92 L93 L98 L99 M1 M10 M11 M16 M19 R4 R40 R41 R49 (search for similar items in EconPapers)
Date: 2024
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