Joint tank container demurrage policy and flow optimisation using a progressive hedging algorithm with expanded time-space network

A key feature of the tank container (TC) operating industry is that customers overhold TCs to provide temporary storage equipment for their contents rather than provide their own storage facilities. TC operators charge a very profitable fee (demurrage charge) for this service making it an attractive business proposition, but it can be detrimental to holistic network flows and fleet sizing. This paper addresses the problem of jointly optimising TC demurrage policy and TC flow, in the face of uncertain TC maintenance times, to maximise profits. A progressive hedging algorithm with expanded time-space network (PHA-ETSN) is designed to tackle this tactical level optimisation problem as other established techniques struggle with this optimisation in terms of computational time and memory requirements. Experiments are performed to illustrate how the optimisation tool can be used to investigate how demurrage policy affects different operational costs and TC hire revenue and thereby profit. These experiments demonstrate how the optimisation tool can be used by managers not only to optimise demurrage policy but also to explore and to understand more deeply the costs and profits in their operations.