[yorak]

It is true that such problems /can/ be solved via mathematical linear programming (for those coming outside math circles, please note that the term programming here has nothing to do with coding) and this is how they are usually presented in academia. However, in practice, it is not something one would be advised to do. Usually, the complexities of the real world routing and scheduling make it impossible to solve these models of practical size. Therefore, numerous heuristic and metaheuristic algorithms have been proposed and are usually used in practical applications. These usually are sound familiar to those that have some experience with "old" AI: genetic algorithms, ant colony systems, simulated annealing, and even neural networks have been succesfully applied to provide "good enough" solutions to these problems.