This paper transposes the classic frequency-based transit assignment method of Spiess and Florian to containersdemonstrating its promise as the basis for a global maritime container assignment model. In this model,containers are carried by shipping lines operating strings (or port rotations) with given service frequencies. Anorigin-destination matrix of full containers is assigned to these strings to minimize sailing time plus containerdwell time at the origin port and any intermediate transhipment ports. This necessitated two significant modelextensions. The first involves the repositioning of empty containers so that a net outflow of full containers fromany port is balanced by a net inflow of empty containers, and vice versa. As with full containers, emptycontainers are repositioned to minimize the sum of sailing and dwell time, with a facility to discount the dwelltime of empty containers in recognition of the absence of inventory. The second involves the inclusion of anupper limit to the maximum number of container moves per unit time at any port. The dual variable for thisconstraint provides a shadow price, or surcharge, for loading or unloading a container at a congested port.Insight into the interpretation of the dual variables is given by proposition and proof. Model behaviour isillustrated by a numerical example applied to the Asia-Europe schedules of a major liner company. The paperconcludes by considering the next steps toward realising a container assignment model that can, amongst otherthings, support the assessment of supply chain vulnerability to maritime disruptions.
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