Integrating shift planning and pick-up and delivery problems under limited courier availability

Delivery couriers increasingly demand working in a flexible arrangement. Flexible contracts can be cost-effective from the perspective of a delivery company, but may also cripple its ability to serve all customers in time as couriers are not always available. To alleviate the complexities caused by courier-related constraints, delivery companies usually operate with a work schedule consisting of multiple shifts—allowing couriers to choose the shifts they prefer working in. Inspired by this trend and a real-world case, we propose a variant of pick-up and delivery problem with time windows considering multiple shifts and courier availability. We present a mixed-integer linear programming model and a set partitioning model that maximize the total profit by deciding on the shift allocation and the couriers’ delivery routes, taking courier shift preferences and vehicle availability into account. The model is solved exactly using a branch-price-and-cut algorithm. We generate a set of practically relevant instances to conduct computational experiments. Our results highlight the benefits of bundling customer requests and the challenges posed by limited courier availability in terms of the number of requests served. Bundling mitigates the negative impact of limited courier availability, while having more couriers can serve as an alternative. • We extend pick-up and delivery problem with shifts, flexible couriers, and profits. • To solve larger instances to optimality, we implement a branch-and- price algorithm. • We test the algorithm using a set of instances representing practical settings. • Bundling reduces the negative effect of limited courier availability. • More couriers offer an alternative in managing courier availability challenges.