Mathematical expressions for the transit time of merchandise through a liner shipping network

Abstract

Recent publications on the design of liner shipping networks are limited in their treatment of the level of service (LoS) experienced by shippers. We propose the use of inventory holding costs-a function of merchandise transit time-as a proxy for LoS. We assume the existence of a two-tier optimization model, where fleet deployment, vessel routing, and vessel speed are determined in the higher tier. Merchandise flows and transshipment quantities are determined in the lower tier. We partition the total merchandise transit time into time spent in open waters, time spent during port calls, and time spent dwelling in the terminal yard. Using the notions of service frequency and service phase, we develop mathematical expressions for the three aforementioned quantities within the lower tier of the optimization model. We arrive at a bilinear expression for overall inventory holding costs that is suitable for liner shipping network design.

Spatial Network Analysis of Container Port Operations: The Case of Ship Turnaround Times

“…One is a corpus of studies on the ocean transit times of carriers, as time rather than cost had become a paramount selection factor for shippers (Wilmsmeier et al, 2013). Scholars compared the time performance of liner shipping firms in terms of uncertainty (Saldanha et al, 2006;Slack et al, 2018) while others applied mathematical modeling to a wide set of components such as total voyage time, voyage time at sea, voyage time in port, average port time, vessel speed, and liner shipping network design (Moon and Woo, 2014;Wang and Meng, 2012;Qi and Song, 2012;Alvarez, 2012). The other direction is more firmly rooted in the "classic port performance" school, looking, for instance, at the factors influencing time efficiency such as container loading rate, containers loaded per vessel, and waiting times (Sanchez et al, 2003), the analysis of the relationship between port characteristics (of which cargo delay during customs procedures) and maritime transport costs (Wilmsmeier et al, 2006), and the analysis of the components of vessel time in ports together with the determinants of port inefficiency, such as customs clearance, container handling charges, and cargo handling restrictions (Clark et al, 2004).…”

The time constrained multi-commodity network flow problem and its application to liner shipping network design

“…Neither exact nor heuristic solution methods are yet able to solve LSND instances with the size of a global carrier to (near) optimality, but a promising approach is to rely on a two-tier structure as in Álvarez (2011);Brouer and Desaulniers (2012);Brouer et al (2014), where route planing, fleet deployment and sailing speed is determined in the upper tier corresponding to determining the cost of the network, while the lower tier determines the revenue of the network by flowing the available cargo. In the following, we consider the cargo flow subproblem, which is one of the main challenges in LSND.…”

Time Efficiency at World Container Ports

“…Besides more general discussions on such topics (Hummels 2001;Slack 1985;Djankov et al, 2005;Nordas et al, 2006;Tongzon and Savant 2007), some authors have proposed specific studies of container flows in liner shipping looking at congestion issues in ports (Notteboom, 2006;Verminen et al, 2007;Yan et al, 2009;Jones et al, 2011;Payman, 2011, 2012) but also advanced methodological frameworks including all aspects of port and vessel operations of which total voyage time, voyage time at sea, voyage time in port, average port time, and vessel speed (Moon and Woo, 2013). The latter work is rooted in earlier studies of transit time performance of ocean carriers (Saldanha et al, 2006), notably those looking at time uncertainty in shipping and port operations (Wang and Meng, 2012;Qi and Song, 2012) and measurements of the time factor in liner shipping network design through mathematical modelling (Alvarez, 2012). Suarez-Aleman et al (2013) rightly argued that very few empirical studies have been made about time efficiency, although such aspect is known to be crucial and despite the possibility for inefficient ports to remain attractive for other reasons (Wilmsmeier et al, 2003).…”