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We develop an asymptotic approximation and bounds for the traveling salesmanproblem with time slots, i.e. when the time windows of points to visit are apartition of a given time horizon. Although this problem is relevant in severaldelivery applications, operational research researchers did not pay closeattention to it, contrary to the extensively studied general formulation withtime windows. Exploiting the specificity of this problem allows to solve moreefficiently instances which may be hard to solve by specifically designedalgorithms for the traveling salesman problem with time windows. The asymptoticanalysis of the traveling salesman problem with time slots is a step towarddeveloping new approximations for the general problem with time windows.Wediscuss this case. We equally provide a formulation of the asymptoticapproximation under a worst-case demand distribution of the points to visit,based on the principle of the maximum entropy. Computational results are givenfor the benchmarks of the literature for which the time slots are randomlygenerated.

Traveling salesman problem with time slots: Asymptotic analysis and resolution algorithm