A typical real-world routing problem involves dispatching technicians, such as repair persons or equipment installers, to customer sites. This type of problem can be viewed as a type of Vehicle Routing Problem, except that technicians must be routed along with the vehicles. Customer visits can also require a quantity of goods to be picked up or delivered.

Technicians may have different skill levels, and customer visits require a particular skill set to complete a job. Therefore you need to model these skills and apply constraints and costs to them. One way to model this is with a fixed charge for each technician based on skill level, regardless of the job skill required at the actual customer site. As long as the technician has at least the appropriate level of skill, the visit can occur. However, this can lead to obvious inequities, if highly-trained technicians are performing less-demanding visits.

There is a different and often better way to model these costs that would maximize the quality of service. If a technician type is well suited to performing a certain visit, then the cost for that technician/visit pair should be low. If a technician type is not well suited to performing a visit, the cost for that technician/visit pair should be high.

In this example, five technicians with different skill levels perform customer visits with ten different skill requirements. The costs for a particular visit can vary significantly, depending on the technician skill level used.

The first step is to write a natural language description of the problem. A good way to start this process is to analyze the constraints and objectives.

What are the constraints in this problem?

The objective is to minimize the cost of supplying technicians to visit all customer sites.