We address the Clarke and Wright (CW) savings algorithm proposed for the Capacitated Vehicle Routing Problem (CVRP). We first consider a recent enhancement which uses the put first larger items idea originally proposed for the bin packing problem and show that the conflicting idea of putting smaller items first has a comparable performance. Next, we propose a robust enhancement to the CW saving...

In this article we introduce the Quadratic Capacitated Vehicle Routing Problem (QCVRP), a combinatorial optimization problem that arises in practical applications in logistics and transportation. The QCVRP extends two other known problems, the Capacitated Vehicle Routing Problem (CVRP) and the Quadratic Symmetric Traveling Salesman Problem (QSTSP), the former by considering a modified cost matr...

Abstract. The best exact algorithms for the Capacitated Vehicle Routing Problem (CVRP) have been based on either branch-and-cut or Lagrangean relaxation/column generation. This paper presents an algorithm that combines both approaches: it works over the intersection of two polytopes, one associated with a traditional Lagrangean relaxation over q-routes, the other defined by bound, degree and ca...

ABSTRACT-This experiment was carried out as factorial based on a randomized complete block design with three replications at the research station of the Islamic Azad University-Arak Branch, Iran, in 2011 and 2012. Experimental factors consisted of three levels of salicylic acid (SA); seed priming with distilled water (hydro priming), seed priming with 0.5 mM SA, and 0.5 mM SA  seed priming 1 mM...

Selenium (Se) is considered as an essential element for human body. Selenized probiotic fermented milk drink (DOOGH) as a functional beverage to increase Se available in body. The predominate sugar, protein and mineral ion of Iranian yoghurt drink (DOOGH) are lactose, casein and calcium, respectively. Different levels of  Selenium (2.5 – 3- 3,5-  4 and 4.5) is prepared and its suitability based...

The Vehicle Routing Problem (VRP) deals with the assignment of a set of transportation orders to a fleet of vehicles and the sequencing of stops for each vehicle to minimize transportation costs. This paper presents two different genetic algorithm models (panmitic and cellular models) for providing solutions for the Capacitated VRP (CVRP), which is mainly characterized by using vehicles of the ...

We present a new branch-and-cut algorithm for the capacitated vehicle routing problem (CVRP). The algorithm uses a variety of cutting planes, including capacity, framed capacity, generalized capacity, strengthened comb, multistar, partial multistar, extended hypotour inequalities, and classical Gomory mixed-integer cuts. For each of these classes of inequalities we describe our separation algor...