This study considers a variant of the vehicle routing problem (VRP) called the heterogeneous VRP with simultaneous pickup and delivery (HVRPSPD). The HVRPSPD may broadly be defined as identifying the minimum cost routes and vehicle types. To solve the HVRPSPD, first, we propose a polynomial-size mixed integer programming formulation. Because the HVRPSPD is an NP-hard problem, it is difficult to determine the optimal solution in a reasonable time for moderate and large-size problem instances. Hence, we develop a hybrid metaheuristic approach based on the simulated annealing and local search algorithms called SA-LS. We conduct a computational study in three stages. First, the performance of the mathematical model and SA-LS are investigated on small and medium-size HVRPSPD instances. Second, we compare SA-LS with the constructive heuristics, nearest neighborhood and Clarke-Wright savings algorithms, adapted for the HVRPSPD. Finally, the performance of SA-LS is evaluated on the instances of the heterogeneous VRP (HVRP), which is a special case of the HVRPSPD. Computational results demonstrate that the mathematical model can solve small-size instances optimally up to 35 nodes; SA-LS provides good quality solutions for medium and large-size problems. Moreover, SA-LS is superior to simple constructive heuristics and can be a preferable solution method to solve HVRP and VRP-SPD instances successfully.2010 Mathematics Subject Classification. Primary: 90B06, 90C11, 90C59; Secondary: 90C27.
ÖZETLojistik yönetiminde en önemli operasyonel kararlardan birisi müşterilere hizmet verecek araç rotalarının belirlenmesidir. Araç Rotalama Problemi (ARP), bir depodan müşterilerin dağıtım (toplama) taleplerini karşılayacak en uygun rotaların belirlenmesi olarak tanımlanabilir. Gerçek hayat lojistik uygulamalarında, filoda bulunan araçlar farklı özelliklerde olabilirler. Ayrıca müşterilerden/taşınanlardan kaynaklı gereklilikler de farklı özellikte araç kullanımı zorunluluğunu ortaya çıkarabilir. Bunun yanısıra firmalar, mamul, yarı mamul ve hammaddelerin tersine akışının yönetimini de hem ekonomik getirisi hem de yasal ve çevresel yükümlülüklerinden dolayı daha fazla önemsemektedirler. Bu makalede, heterojen araç filosunun bulunduğu ve müşterilerin dağıtım ve toplama taleplerinin eşzamanlı gerçekleştiği durumların birlikte dikkate alındığı bir ARP türü üzerinde çalışılmıştır. Bu problem Heterojen Eşzamanlı Topla-Dağıt Araç Rotalama Problemi (HETD-ARP) olarak adlandırılmıştır. HETD-ARP, toplam maliyeti enküçükleyen araç rotalarının ve herbir rotada kullanılan araç tipinin belirlenmesi olarak tanımlanabilir. Problem için polinom sayıda kısıta sahip akış tabanlı bir matematiksel model önerilmiştir. HETD-ARP, NP-zor problemler sınıfında olduğundan dolayı makul sürelerde orta boyutlu problemlere bile en iyi çözümü bulmak zordur. Bu nedenle bu makalede orta ve büyük boyutlu HETD-ARP'nin çözümü için basit bir kurucu sezgisel algoritma önerilmiştir. Bu algoritma, kaynaklarda ARP için önerilen Clarke-Wright Tasarruf (CWT) algoritmasının HETD-ARP için uyarlanmış halidir. Önerilen matematiksel modelin ve sezgisel algoritmanın etkinliği test problemleri üzerinde incelenmiştir.Anahtar Kelimeler: Heterojen filo, eşzamanlı topla-dağıt, araç rotalama problemi, karma tamsayılı matematiksel modelleme, sezgiseller, Clarke-Wright tasarruf algoritması HETEROGENEOUS VEHICLE ROUTING PROBLEM WITH SIMULTANEOUS PICKUP AND DELIVERY: MATHEMATICAL FORMULATIONS AND A HEURISTIC ALGORITHM ABSTRACTOne of the most important operational decisions in the logistics management is to determine the vehicle routes serving the customers. The Vehicle Routing Problem (VRP) can be defined as the determination of the optimal routes which meet the delivery (or pickup) demands from the depot to the customers. In the real life applications of logistics, vehicles in a fleet may differ from each other. In addition, the requirements arising from customers/goods may reveal the necessity to use different vehicles. Besides, companies do care more about the management of reverse flow of products, semi-finished and raw materials because of their economic benefits and as well as legal and environmental liabilities. In this paper, a variant of the VRP is considered with heterogeneous fleet of vehicles and simultaneous pickup and delivery. This problem is referred to Heterogeneous Vehicle Routing Problem with Simultaneous Pickup and Delivery (HVRPSPD). The HVRPSPD can be defined as determining the routes and the vehicle types on each route while minimizing the total cos...
This paper introduces the Selective Generalized Traveling Salesman Problem (SGTSP). In SGTSP, the goal is to determine the maximum profitable tour within the given threshold of the tour's duration, which consists of a subset of clusters and a subset of nodes in each cluster visited on the tour. This problem is a combination of cluster and node selection and determining the shortest path between the selected nodes. We propose eight mixed integer programming (MIP) formulations for SGTSP. All of the given MIP formulations are completely new, which is one of the major novelties of the study. The performance of the proposed formulations is evaluated on a set of test instances by conducting 4608 experimental runs. Overall, 4138 out of 4608 (~90%) test instances were solved optimally by using all formulations.
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