The workforce scheduling and routing problem with park‐and‐loop

Abstract This article introduces formulations and an exact algorithm for the workforce scheduling and routing problem with park‐and‐loop. This problem extends the standard workforce scheduling and routing problem by allowing the use of walking subtours in the routes. We introduce a compact arc‐based formulation as well as a path‐based formulation with an exponential number of variables. To efficiently solve the latter, we propose a branch‐price‐and‐cut algorithm that leverages state‐of‐the‐art techniques, including a tailored version of the pulse algorithm to solve the pricing problem and the separation of subset row inequalities to strengthen the lower bound. We report on computational experiments carried out on a set of instances with up to 75 tasks adapted from the literature. The results show that our method systematically outperforms a standard MIP solver, proving optimality for 241 out of 324 instances. We also report experiments on the closely‐related service technician routing and scheduling problem, where our method delivered 12 new best solutions on a 54‐instance testbed from the literature.