Enhancing Waste Collection: A Branch-and-Cut-and-Price approach for the Periodic Vehicle Routing Problem with Intermediate Facilities applied to a real-world case study

The paper at hand deals with a real-world waste collection problem, which is modeled as a periodic vehicle routing problem with intermediate facilities. Therein, a route plan must be defined for each day of the planning horizon such that all customers are served according to one of their visiting schemes and the total travel time is minimized. We present an enhanced compact formulation and a branch-cut-and-price approach for its resolution, incorporating a new set of valid inequalities that exploit the coprimality of the customers’ visit frequencies. We compare the solution of the new compact formulation via a MIP-solver with the branch-cut-and-price algorithm on asymmetric instances of up to 50 customers, developed with our industry partner to reflect the characteristics of the waste collection sector. While the MIP-solver cannot solve a single instance to optimality, our branch-cut-and-price algorithm solves instances with up to 40 customers considering a four-day planning horizon, and all instances with 20 customers for a six-day planning horizon. To benchmark our algorithm, we test it on instances for multi-period problems from the literature. Our results are competitive with state-of-the-art methods, yielding 5 new proven optimal solutions, 4 new best upper bounds, and 32 new best lower bounds. Moreover, in a case study regarding organic waste collection provided by our business partner, we solved a real-world instance with more than 1000 customer locations. The resulting route plan achieves significant cost savings compared to the company's current practice.