We model and solve the Rainbow Cycle Cover Problem (RCCP). Given a connected and undirected graph G = ( V , E , L ) and a coloring function ℓ that assigns a color to each edge of G from the finite color set L , a cycle whose edges have all different colors is called a rainbow cycle. The RCCP consists of finding the minimum number of disjoint rainbow cycles covering G . The RCCP on general graphs is known to be NP-complete. We model the RCCP as an integer linear program, we derive valid inequalities and we solve it by branch-and-cut. Computational results are reported on randomly generated instances

We present a collaborative prepositioning strategy to strengthen the disaster preparedness of the Caribbean countries, which are frequently hit by hurricanes. Since different subsets of countries are affected in each hurricane season, significant risk pooling benefits can be achieved through horizontal collaboration, which involves joint ownership of prepositioned stocks. We worked with the intergovernmental Caribbean Disaster and Emergency Management Agency to design a collaborative prepositioning network in order to improve regional response capacity. We propose a novel insurance‐based method to allocate the costs incurred to establish and operate the proposed collaborative prepositioning network among the partner countries. We present a stochastic programming model, which determines the locations and amounts of relief supplies to store, as well as the investment to be made by each country such that their premium is related to the cost associated with the expected value and the standard deviation of their demand. We develop a realistic data set for the network by processing real‐world data. We conduct extensive numerical analyses and present insights that support practical implementation. We show that a significant reduction in total inventory can be achieved by applying collaborative prepositioning as opposed to a decentralized policy. Our results also demonstrate that reducing the replenishment lead time during the hurricane season and improving sea connectivity are essential to increasing the benefits resulting from the network.

Given an undirected and edge-colored graph G, a rainbow component of G is a subgraph of G having all the edges with different colors. The Rainbow Spanning Forest Problem consists of finding a spanning forest of G with the minimum number of rainbow components. The problem is known to be NP-hard on general graphs and on trees. In this paper, we present an integer linear mathematical formulation and a greedy algorithm to solve it. To further improve the results, we applied a multi-start scheme to the greedy algorithm. Computational results are reported on randomly generated instances

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