We define a pickup and delivery routing problem with time windows that arises in last-mile delivery. A customer can be served either directly at home, by one of the available capacitated trucks, or via lockers, that allow a self-service option. On the same route, the couriers must deliver the parcels and collect the packages that the customers intend to return. The returned parcels can be picked up directly at the customers’ homes or at a locker. Customers can select home service, self-service at one of the nearby lockers with a discount, or let the logistics company decide. All services must be performed within a given time window.

We propose three formulations, two branch-and-cut algorithms, and some valid inequalities. We also investigate the case with a single vehicle, with different types of time windows, including no time windows. Moreover, we show how to accommodate simultaneous pickup and delivery and multiple requests from a customer.

我们使用最后一英里交付中出现的时间窗定义取货和交付路由问题。可以直接在家中使用可用的容量卡车之一或通过允许自助服务选项的储物柜为客户提供服务。在同一路线上，快递员必须递送包裹并收集客户打算退回的包裹。退回的包裹可以直接到客户家中或储物柜领取。客户可以选择上门服务、附近有优惠的储物柜自助服务，或让物流公司决定。所有服务都必须在给定的时间窗口内执行。

我们提出了三个公式、两个分支切割算法和一些有效的不等式。我们还调查了单个车辆的情况，具有不同类型的时间窗口，包括没有时间窗口。此外，我们还展示了如何适应同时取货和送货以及来自客户的多个请求。