different versions of the savings method for the time limited vehicle routing problem

The time limited vehicle routing problem (TLVRP) stems from the vehicle routing problem. The main difference is that the routes are paths (not cycles), i.e. vehicles do not return to the central city (or at least we do not observe their way back). Costs are given for the straight routes between each pair of the cities and represent the time necessary for going through. Each path must not exceed a given time limit. The sum of times for all routes is to be minimized.This problem is NP-hard. There are many various possibilities how to design the heuristics (approximation methods) to solve it. One of the ways of how to obtain an approximation method for the TLVRP is to modify the famous savings method by Clark and Wright (1964) for this purpose. In this paper we suggest several different versions of this method, test them in some instances, and evaluate and mutually compare the results of individual versions.