Fleet optimization for cyclic inventory routing problems

This paper considers the optimization of a vehicle fleet to periodically repeat a given set of routes, whose frequencies can be adjusted if necessary. The objective is to minimize the overall cost rate, consisting of fixed vehicle costs, route-specific costs and holding costs at the customers being periodically replenished, where these latter two cost components depend on the selected frequency of the routes. First, this fleet design problem is formally described in a non-linear mathematical model, and a linear model is presented for the situation where frequencies are limited to a given set of values. Then, a multi-start two-phase heuristic solution method is proposed consisting of an insertion-based construction phase and a local search-based improvement phase. The performance of the solution approach and its capability in finding the appropriate cost trade-offs are shown in a design of experiments.