Numerical modeling-based optimization of circular routes in liner container networks

This article addresses the key issue of designing and optimizing circular routes in liner container shipping. The relevance of the study is driven by the need to enhance economic efficiency, operational reliability, and environmental sustainability of global supply chains, particularly under conditions of volatile cargo flows and contemporary geopolitical challenges. The objective of the study is to develop a methodology for calculating key route operational parameters based on a deterministic analytical model. The model uses an origin-destination matrix of cargo flows between ports of call as input data, allowing for the incorporation of cargo flow structure. Primary focus is placed on determining the vessel call size the number of containers handled at each port during a single call which is a critical parameter for schedule development. The proposed model enables the sequential calculation of the required number of vessel calls, the optimal container capacity of vessels deployed on the line, the handling time at each port, the total duration of the round voyage, and, ultimately, the number of ships required to maintain the target service frequency. The limiting factor in the model is the port with the maximum cargo flow, where the port stay is constrained by the tight liner schedule. A numerical case study demonstrates the practical applicability of the method: to handle a given cargo flow, a fleet of ten vessels with a capacity of approximately 2,600 TEU is required, with less than 25 % of the total cargo on board handled at each port. The rationale for using a deterministic approach with average parameter values is justified for strategic and technological planning purposes, despite the stochastic nature of real-world operational processes. The study contributes to the development of technological design methods for liner shipping by offering a practical tool for substantiating fleet and route parameters and balancing import and export container flows.