Each year, the United Nations World Food Programme (WFP) provides food assistance to around 100 million people in more than 80 countries. Significant investments over the last decade have put planning and optimization at the forefront of tackling emergencies at WFP. A data-driven approach to managing operations has gradually become the norm and has culminated in the creation of a supply chain planning unit and savings of more than USD 150 million—enough to support two million food-insecure people for an entire year. In this paper, we describe three analytical solutions in detail: the Supply Chain Management Dashboard, which uses descriptive and predictive analytics to bring end-to-end visibility and anticipate operational issues; Optimus, which uses a mixed-integer programming model to simultaneously optimize food basket composition and supply chain planning; and DOTS, which is a data integration platform that helps WFP automate and synchronize complex data flows. Three impact studies for Iraq, South Sudan, and COVID-19 show how these tools have changed the way WFP manages its most complex operations. Through analytics, decision makers are now equipped with the insights they need to manage their operations in the best way, thereby saving and changing the lives of millions and bringing the world one step closer to zero hunger.

The literature on k-splittable flows, see Baier et al. (2002) [1], provides evidence on how controlling the number of used paths enables practical applications of flows optimization in many real-world contexts. Such a modeling feature has never been integrated so far in Quickest Flows, a class of optimization problems suitable to cope with situations such as emergency evacuations, transportation planning and telecommunication systems, where one aims to minimize the makespan, i.e. the overall time needed to complete all the operations, see Pascoal et al. (2006) [2]. In order to bridge this gap, a novel optimization problem, the Quickest Multicommodity k-Splittable Flow Problem (QM CkSF P) is introduced in this paper. The problem seeks to minimize the makespan of transshipment operations for given demands of multiple commodities, while imposing restrictions on the maximum number of paths for each single commodity. The computational complexity of this problem is analyzed, showing its N P-hardness in the strong sense, and an original Mixed-Integer Programming formulation is detailed. We propose a matheuristic algorithm based on a hybridized Very Large-Scale Neighborhood Search that, utilizing the presented mathematical formulation, explores multiple search spaces to solve efficiently large instances of the QM CkSF P. High quality computational results obtained on benchmark test sets are presented and discussed, showing how the proposed matheuristic largely outperforms a state-of-the-art heuristic scheme frequently adopted in path-restricted flow problems.

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