Models and Techniques

Networks are a major area of research and applications in Operations Research and Management Science. They are also widely used in project management.

Notes on Networks (project management)

These notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They are written by J E Beasley and used as course notes in an introductory OR course at Imperial College.

A Tutorial on Networks, by Prof. M. Trick

Student problems in Greek

SAS/OR Software

Vehicle Routing Problem

The vehicle routing problem can be defined as the problem of designing routes for delivery vehicles and is considered to be a challenging optimization task, as an optimal solution does not exist. Hence, the problem consists in designing routes for the vehicles with the objective of minimising a variable such as the total distance travelled.

The VRP Web

This is a very useful and interesting website about Vehicle Routing. It has been made in collaboration between AUREN and the Languages and Computation Sciences department of the University of Malaga by Bernabe Dorronsoro Diaz. It provides lot of information concerning the Vehicle Routing Problem, as well as an informed bibliography with the best-so-far solutions of some well-known instances of the problem.

Vehicle Routing Today, An Overview


Vehicle Routing Software Survey, by Randolph W. Hall

A side-by-side comparison of twenty-four vehicle routing software packages from twenty-one vendors including pricing and performance information, special features and significant installations.

Data Sets

Capacitated Vehicle Routing Problem (CVRP)

This set of data files are the 14 test problems from Chapter 11 of N.Christofides, A.Mingozzi, P.Toth and C.Sandi (eds) "Combinatorial optimization", John Wiley, Chichester 1979

Capacitated Vehicle Routing Problem with Time Windows (CVRPTW)

This set of data files are the 56 test problems of Solomon M.M (1987) "Algorithms for the vehicle routing and scheduling with time windows constraints" Operations Research 35, p.45-65

Multi Compartment Commodity Heterogeneous Fixed Fleet Vehicle Routing Problem with Time Windows (MCCHFFVRPTW)

Customers and Depot Data

The customers and depot data generated using Solomon's 100 customers VRPTW benchmark instances. More specifically, each customer's demand coupled with a particular commodity, while the total number of customers along with their coordinates, demand, service time and time window intervals maintainted intact. Below the data sets with two and three different commodities are given. The .zip files contain classes R1(4), RC1(4), R2(4), RC2(4). The structure of these files is the following: the first column refers to the customer indetification No, the second and third columns refer to x and y coordinates, the forth and fifth columns refer to the demand along with the respective commodity, and finally the rest columns provide the earliest, latest and service times, respectively. Note that the customer with identification No 0 represents the depot.

Vehicle Fleet Mix Characteristics

The vehicle fleet data was generated using Liu and Shen Fleet Size and Mix VRPTW benchmark instances. To define vehicle capacities and fixed costs Liu and Shen (1999b) proposed three different subclasses of instances a, b and c, each characterized by different fixed vehicle costs. The file provided below contains the fixed costs of the vehicles for subclass a, while A, B, C, D, E, F refer to the vehicle types. Moreover, for each the number of compartments along their associated capacities are given.

Fleet Composition (Fixed Fleet)

In order to define the available fleet composition and mix of vehicles, the best fleet mix obtained in [2] is assumed to be the given fixed fleet. The latter approach followed also by [3] and [4] for solving the Heterogeneous Fixed Fleet VRP. The fixed fleet used is given below for each respective problem instance. Below, the contains for each respective problem instance the given fleet composition (Fixed Fleet).


[1] Solomon, M.M. (1987). Algorithms for the vehicle routing and scheduling with time windows contraints, Operations Research 35, 254-265.

[2] Liu, F.H. and S.Y. Shen (1999b). The Fleet Size and Mix Routing Problem with Time Windows, Journal of the Operational Research Society 50(7), 721-732.

[3] Tarantilis, C.D., Kiranoudis, C.T., Vassiliadis, V.S. (2004) A threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem. European Journal of Operations Research, 148-158.

[4] Taillard, E.D.,(1999) A heuristic column generation method for the heterogeneous fleet VRP. RAIRO 1-14.

Vehicle Routing Problem with Intermediate Replenishment Facilities (VRPIRF)

The Capacitated Vehicle Routing Problem with Three-Dimensional Loading Constraints (3L-CVRP)

The Inventory Routing Problem over a finite periodic planning horizon

Moving products between location pairs: Cross-Docking versus Direct-Shipping
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