A matheuristic solution approach for the production routing problem with visit spacing policy

The production routing problem (PRP) is an integrated operational planning problem that combines the two well-known optimization problems, vehicle routing problem (VRP) and lot-sizing problem (LSP). The PRP especially arises in vendor managed inventory (VMI) systems. The solutions obtained in VMI systems tend to benefit both the vendor and the retailers, however, solving PRPs by aiming only cost minimization may not provide satisfactory results to both parties. To remain competitive, companies also need to consider the service quality level. Visit spacing policy (VSP) is especially important to provide higher quality service to the retailers. In the VSP implementation, visit times of the retailers are regulated by imposing a minimum and a maximum time interval between two consecutive visits to the same retailer to ensure smoother operations. In this study, we extend the basic version of the PRP by taking into consideration the VSP. For its solution, an iterative matheuristic algorithm (MA) is proposed. The proposed MA is tested on a set of randomly generated problem instances with VSP as well as on standard PRP and the inventory routing problem (IRP) with VSP benchmark instances. The results indicate the effectiveness of the algorithm. Although not designed especially for the standard PRP and the IRP with VSP, the developed MA has also managed to improve the best known solutions for 388 out of 1174 standard PRP and the 1RP with VSP test instances. Moreover, an extensive computational study is performed to reveal the effect of the VSP on the PRP. (C) 2019 Elsevier B.V. All rights reserved.