routes is not necessary. TSP and VRP continuous approximations have been introduced by [@Daganzo94; @DaganzoBook] to embed operations in strategic and tactical logistics problems (e.g. [@EreraThesis], [@franceschetti2017strategic]). A recent literature on variants of this approach can be found in [@ansari2018advancements]. [@SmilowitzDaganzo; @winkenbach2016enabling; @bergmann2020integrating] adapted these continuous approximations to the context of parcel express logistics to approximate distance traveled and cost. However, the aspect of synchronization using travel time continuous approximations has not yet been studied. To the best of the authors’ knowledge, this paper is the first to study a capacity relocation problem with the synchronization of two-echelon routing operations through travel time estimates.

Problem Description and Formulation {#Probdescription}
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Business Context {#biz}
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A parcel logistics company provides pickup and delivery services to customers in a region covered by a network of access hubs. The network of access hubs may be dedicated to the parcel logistics provider, or shared between several companies as suggested by the concept of open networks in the Physical Internet. Figure \[fig: Relocation\] provides a conceptual illustration of the network of access hubs and the relocation of capacity modules over two deployment periods. Once the network capacity is set, pickups from customers are dropped off 