Vehicle Routing Problem (VRP) is a key element of many logistic systems which involve routing and scheduling of vehicles from a depot to a set of customers node. This is a combinatorial optimization problem with the objective to find an optimal set of routes used by a fleet of vehicles to serve a set of customers It is required that these vehicles return to the depot after s erving customers’ d...

OBJECTIVE Non-adherence is a major problem in the treatment of schizophrenia. Depot antipsychotic drugs are thought to reduce relapse rates by improving adherence, but a systematic review of long-term studies in outpatients is not available. METHOD We searched the Cochrane Schizophrenia Group's register, ClinicalTrials.gov, Cochrane reviews on depot medication, and the reference sections of i...

The vehicle routing problem with simultaneous pickup and delivery (VRPSDP) is a common transportation problem where a fleet of vehicles deliver goods from the depot to line haul customers and pick up goods from backhaul customers to the depot. This problem variation allows vehicles to make the delivery and pickup operations on same time by visiting all clients once with the aim of minimization ...

The Vehicle Routing Problem (VRP) has been extensively studied over the last twenty years, because it is an abstraction of many real-life logistics problems. In its multiple-depot variant (MDVRP), the routes of vehicles located at various depots must be optimized to serve a number of customers. In this paper, we investigate how to protect the privacy of delivery companies, when each depot is ow...

In this paper, we propose a new routing problem to model a highly relevant planning task in small package shipping. We consider the Prize-Collecting Vehicle Routing Problem with Non-Linear cost (PCVRPNL) in its single and multi-depot version, which integrates the option of outsourcing customers to subcontractors instead of serving them with the private fleet. Thereby, a lower bound on the total...

The paper [1] has three main contributions: • Modeling VRP (Vehicle Routing Problem) into the minimum cost Ktree problem. • Dualizing the side constraints to obtain a Lagrangian problem which provides lower-bounds in B&B. • Performing the algorithm on real problems. 1. Problem Definition and Lagrangian Relaxation The vehicle routing problem has the following parameters: • K = the number of vehi...

A capacitated location-routing problem (CLRP) is one of the new areas of research in distribution management. It consists of two problems; locating of facilities and routing of the vehicle with a specific capacity. The purpose of the CLRP is to open a set of stores, allocate customers to established deposits, and then design vehicle tours in order to minimize the total cost. In this paper, a ne...

In this paper, we study the complexity and (in)approximability of the minimum label vehicle routing problem. Given a simple complete graph G = (V,E) containing a special vertex 0 called the depot and where the edges are colored (labeled), the minimum label k-vehicle routing problem consists in finding a k-vehicle routing E′, i.e. a collection of cycles of size at most k+ 1 which all contain the...

Long protocol of Gonadotropin-Releasing Hormone-analougue (GnRH-a) can result in the formation of ovarian cyst by the transient initial stimulatory effect which increases the levels of both follicle-stimulating hormone (FSH) and luteinizing hormone (LH). These cysts require surgical drainage or result in poor ovarian response. Ovarian cyst formation can be prevented by taking oral contraceptive...

This article studies the double traveling salesman problem with two stacks. A number of requests have to be served where each request consists in the pickup and delivery of an item. All the pickup operations have to be performed before any delivery can take place. A single vehicle is available that starts from a depot, performs all the pickup operations and returns to the depot. Then, it perfor...