An Integrated Heuristic Approach for the Period Vehicle Routing Problem with Simultaneous Delivery and Pickup

This paper introduces an integrated approach for solving the Period Vehicle Routing Problem with Simultaneous Delivery and Pickup (PVRPSDP). The problem considers a dis tribution system consisting of a warehouse and many dispersed location retailers, where each of which having two type of demands to be delivered and collected, respectively. A fleet of capacitated vehicle is employed for delivering products from the warehouse to the retailers, and collecting the reusable empty-containers in the reverse direction for all day during a given T-day period. Precisely, at each retailer’s location, a pickup operation must be established immediately after a delivery operation. The retailers are typically required to be visited once or several times over the period, and once a day at the most. The days of visits must follow one of the allowable visit-day patterns that were built based on stationary-interval inventory property. The objective of the problem is to minimize the inventory and traveling system-wide costs subject to the vehicle capacity constraint. We highlight the influent role of the visit frequency. Instead of a given parameter, the visit frequency for each retailer is treated as a decision variable, and dynamically determined. The novelty of our integrated approach is comprised in maintaining the appropriate balance between the inventory costs and the traveling costs to seek the best visit frequency for each retailer while constructing the tours. We develop heuristic algorithms for the PVRPSPD and establish some experiments to show the performance and the behaviour of our approach.