and including it explicitly in the tactical model would make it intractable. Since the goal is to foster best capacity deployment decisions, it is sufficient to anticipate the operations costs and time synchronisation constraints using scenario-based continuous approximations.

Accordingly, hereafter is proposed a tractable approximation of each period $\tau$ pickup and delivery problem with transshipment by developing deterministic continuous approximations of vehicle routing problems. The starting point of the proposed approximations is the estimation of the vehicle routing problem length when the depot (from which vehicles start their routes) is not necessarily located in the area where customers are located as proposed in [@Daganzo94]: $$\label{VRPDaganzo}
VRP(n) = 2rm + nk(\delta)^{-\frac{1}{2}}$$ where $r$ is the average distance between the depot and the customer locations, $m$ is the number of routes required to serve all customers, $n$ is the number of points to be visited, $k$ is a constant parameter that can be estimated through simulation ([@DaganzoBook]), and $\delta$ is the density of points in the area. An a priori lower bound on the number of routes required to serve all customers, $m$, is $n/Q$ where $Q$ is the capacity of one vehicle in terms of customer locations. The first term of 