A set of vertices <i>S</i> in a graph <i>G</i> is independent if no neighbor of a vertex of <i>S</i> belongs to <i>S</i>. A set of vertices <i>U</i> in a gr...

In modern transportation systems, the potential for further decreasing the costs of fulfilling customer requests is severely limited while market competitio...

The AutoGraphiX 2 system is used to compare the index of a graph <i>G</i> with a number of other graph theoretical invariants, i.e., chromatic number, maxim...

Assouad has shown that a real-valued distance <i>d</i> = (<i>d</i>_<i>ij</i>) _{1 &le; <i>i</i> &lt; <i>j</i> &le; <i>n</i>} is isome...

The <i>Dial-a-Ride Problem</i> (DARP) consists of designing vehicle routes and schedules for <i>n</i> users who specify pickup and delivery requests between...

In one-to-one <i>Pickup and Delivery Problems</i> (PDPs), the aim is to design a set of least cost vehicle routes starting and ending at a common depot in o...

We consider a marketing channel where a retailer sells, along the manufacturer’s brand, her own private label. We assume that each player invests in adverti...

A set of vertices <i>S</i> in a graph <i>G</i> is independent if no neighbor of a vertex of <i>S</i> belongs to <i>S</i>. The independence number &alpha is ...

Given a set of timetabled tasks, the multi-depot vehicle scheduling problem is a wellknown problem that consists of determining least-cost schedules for veh...

We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph (i.e., to the index of the graph). Three of them have be...

The problem retained for the ROADEF’99 international challenge was an inventory management problem for a car rental company. It consists in managing a given...

Let &nbsp;<img src="/cgi-bin/mimetex.cgi?G=(V,E)">&nbsp; be a simple graph with vertex degrees &nbsp;<img src="/cgi-bin/mimetex.cgi?d1, d2, \ldots, d_n...

This paper argues that the literature applying differential games in economics and management science has aimed to a large extent for analytical results. On...

In this survey, a classification of twenty-seven Asymmetric Traveling Salesman Problem (ATSP) formulations is presented. The strength of their LP relaxation...

The vehicle routing problem with time windows consists of delivering goods at minimum cost to a set of customers using an unlimited number of capacitated ve...

Let &nbsp;<img src="/cgi-bin/mimetex.cgi?G=(V,E)"> be a simple graph with &nbsp;<img src="/cgi-bin/mimetex.cgi?n=|V|"> vertices and &nbsp;<img src="/cgi-bin/...

Given a simple connected graph <i>G = (V,E)</i> the geodetic closure <i>I&nbsp;[S]</i> <img src="/cgi-bin/mimetex.cgi?\subset"> <i>V</i> of a subset <i>S</i...

This paper considers the swapping problem on a tree. In this problem at most one object of some type is available at each vertex, and each vertex also reque...

We consider a dynamic marketing channel involving one manufacturer and one retailer. The strategic variables of the former are the wholesale price and the a...

The AutoGraphiX research program led to a new type of application of metaheuristics in graph theory, <i>i.e.</i>, finding conjectures on graph invariants by...