H. Edwin Romeijn, Dolores Romero Morales
Asymptotic analysis of a greedy heuristic for the multi-period single-sourcing problem: the acyclic case

The multi-period single-sourcing problem that we address in this paper can be used as a tactical tool for evaluating logistics network designs in a dynamic environment. In particular, the objective will be to find an assignment of customers to facilities, as well as the location, timing and size of inventories, that minimizes total assignment and inventory costs. We propose a greedy heuristic, and prove that this heuristic is asymptotically optimal in a probabilistic sense for the subclass of problems where the assignment of customers to facilities is allowed to vary over time. In addition, we prove a similar result for the subclass of problems where each customer needs to be assigned to the same facility over the planning horizon, and where the demand for each customer exhibits the same seasonality pattern. We illustrate the behaviour of the heuristic, as well as some improvements where the heuristic is used as the starting point of a local interchange procedure, on a set of randomly generated test problems.