Question

Offer one example of an IT or computer application that can be modeled as the TSP problem.

Answer 1

Consider the problem of scheduling a bunch of jobs on a single machine. Each job has a processing time, which is independent of the order in which the jobs are done. Now suppose that the machine requires a setup before each job, and the setup time depends on the preceding job. For example, if the machine is a paint sprayer, you may or may not need to change colors, which requires flushing the sprayer. Changing from a dark color to a lighter color may require a more thorough flush than changing from a light color to a darker color. So doing a yellow job after a yellow job incurs zero setup time, doing a yellow job after a white job requires a short setup, and doing a yellow job after a black job requires a long setup.

The problem of sequencing the jobs to minimize the total makespan (the time to complete all jobs), or equivalently to minimize the cost of the changeovers (flushing the paint sprayer consumes water or some other fluid, wastes some residual paint, ...), can be viewed as a TSP. In general, any problem of sequencing (permuting) a bunch of objects where the only variable costs occur during transitions and where there are no side constraints can be modeled as a TSP. Just treat each object as a node, and add a dummy node that represents both the start and end of the sequence.