The scientific and industrial communities are often unaware of the work of each other. We aim to provide a service where you can find all the information you require, for a specicific specialisation, all on the same web site. We would welcome suggestions for other areas.

We are currently preparing this page to outline some of the common (and not so common) models that are used to represent Vehicle Routing Problems.

The surveys page would also be a good place to look if you are looking for a particular model, or just general information about the models that are available.

If you believe that any are missing, please let us know (email: admin@researchandpractise.com)

This model, for the Capacitated Vehicle Routing Problem, is one of the moset general models. It is based on set-partitioning and the general idea is to minimise the cost, which is represented by *c _{j}*. The cost could be, for example, the distance. We have a fixed number of customers (

The model can be formally stated as follows.

where:

*q*is the the number of feasible routes.*c*is the cost associated with route_{j}*j*.*x*is a binary variable with_{j}*x*= 1 if route_{j}*j*is used in the optimal solution; 0 otherwise.*a*is a binary variable, where_{ij}*a*= 1 if vertex (customer)_{ij}*i*is visited by route*j*; 0 otherwise.*V*is the set of vertices (customers).*K*is the number of vehicles that are available.- Constraint (2) ensures that each vertex (customer) is visited exactly once (i.e. it is included in one, and only one, route), with the exception of vertex zero which is usually defined as the depot, where every route starts and ends.
- Constraint (3) imposes the condition that
*K*circuits (vehicles) are used. - Constraint (4) limits the values of
*x*to zero or one._{j}

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