Ordered–Fuzzy-Numbers-Driven Approach to Out-Plant Milk-Run Dynamic Routing and Scheduling

We consider a dynamic vehicle routing problem in which a fleet of service vehicles pay preventive maintenance visits to a set of spatially distributed customers over a given time horizon. Each vehicle follows a pre-planned separate route which links points defined by customer location and service periods. Customer orders and the feasible time windows for the execution of those orders are dynamically revealed over time. The objective is to maximize the number of new urgent requests, which are inserted dynamically throughout the assumed time horizon, but not at the expense of the already accepted orders. The question that must be considered is whether the newly reported service request and the correction of the fulfillment date of the already submitted request can be accepted or not. Problems of this type arise, for example, in systems in which preventive or corrective maintenance requests are scheduled to follow periodically performed inspections or repairs. The problem under consideration is formulated as a constraint satisfaction problem using the ordered fuzzy number formalism, which allows to handle the fuzzy nature of the variables involved through an algebraic approach. The computational results show that the proposed solution outperforms the commonly used computer simulation methods.