Multi-period collection and distribution problems and their application to humanitarian gleaning operations

We focus on a multi-period logistic setting, in which a given fleet of vehicles is used to collect products from suppliers, transfer them to a depot where they undergo certain time-consuming processing procedures, only at the end of which can they be distributed to customers. The problem is to schedule visits to the suppliers, as well as vehicle routes that distribute the processed products to the customers, such that each vehicle can perform at most one of these activity types every day. The processed inventory at the depot creates an additional dependence between these activities. Non-profit gleaning operations performed by food banks provide a real-life motivation for the analysis of this setting. It is also applicable for the collection and distribution of blood donations. In the solution method we propose, the problem is decomposed into its collection and distribution aspects, both of which constitute non-trivial sub-problems that have not been previously studied. We show how to tackle each of them individually, while considering information obtained from their counterpart, with the inventory storage as their linkage. We further present a rolling horizon framework for the problem. We demonstrate the implementation of this approach based on the activity of an Israeli food bank that manages gleaning operations, and test it with real-life data, as well as with randomly generated instances. The numerical experiments establish the advantage of the proposed method, compared to naïve methods currently being used in practice.