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By A. N. Kostovski

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3) forbids the vehicle to serve more customers than its capacity q allows. 6). 8) ensures that the time windows are respected. Here K is a sufficiently large constant. 4) leads to a set partitioning master problem. It contains one type of variables, namely structured route flow variables. 4). The difference lies in the D-W subproblem, since a feasible route in the VRPTW has to satisfy a larger number of constraints than a feasible route in the VRP. If the entire set of feasible routes is considered, the complete master problem becomes an alternative way of formulating the full problem.

In this chapter, we describe various routing problems and discuss the relations between them. In particular, we show that the log truck scheduling problem is a very general routing problem. For this purpose, we start by describing the most basic routing problems and proceed by adding and removing constraints until the log truck scheduling problem is derived. 1 The travelling salesman problem The most basic routing problem is the Travelling Salesman Problem (TSP), a problem that has been studied for over 50 years.

Note that the constraints concerning the feasibility of the routes are not explicit in the model. We refer to these constraints as local, while the three sets of constraints expressed in the model are global. Local constraints are associated with each column, or variable in the model, while global constraints involve a set of variables. This structure of global and local constraints gives flexibility to the model, since all rules concerning the routes do not influence the model or the solution method.

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