Optimization Models for Collaborative Humanitarian Supply Chains

There are several interesting and challenging mathematical and algorithmic aspects that can be studied in Humanitarian Logistics (HL). In particular, we concentrate on the design of stochastic optimization models to support the decision-making of HOs and suppliers. Nonetheless, other components that are out of the scope of this project are also an important part of HL such as demand forecasting and reliability of relief resources delivery. More importantly, to streamline the procurement process and guarantee the availability, quick delivery, and cost-effective procurement of critical relief items after a disaster, HOs are increasingly establishing close relationships with suppliers and making contractual agreements in the disaster preparedness stage. This is part of a more general framework called collaborative humanitarian logistics [e.g., 2,3 and references therein. In this project, we propose to study optimization models in collaborative HL, where contracts between HO and the private sector occur. These contracts are generally called Framework Agreements (FAs) [2. More specifically, we focus on humanitarian reverse bid auctions [5,6,9,11 where a buyer (usually an HO) places an announcement with several requirements for supplying a number of products (relief kits) in case of a disaster, and then bidders (typically commercial suppliers) construct their bids and apply to the auction. In these cases, one or many suppliers may be assigned the FA. Although the importance of optimization models for the procurement process in collaborative HL has been well-established [2,8,10, according to Shokr & Torabi [12 the literature about procurement auctions in HL is still limited, especially in the context of auctions that consider the inherent uncertainty to disasters. Moreover, it is also necessary to include collaboration between the commercial sector and HO [3,9. Therefore, in this research project, we propose to construct two two-stage stochastic programming models [1 for the first phases of the FA: announcement construction from the perspective of HO and bid construction from the perspective of commercial suppliers. That is, in the first optimization model the objective will be to minimize the total expected operational cost of the supply chain while satisfying all the operational and humanitarian constraints. In this model we will assume that the HO possesses all the infrastructure to serve the affected area after the disaster. This will provide an estimated value of the total operations and thus an approximated cost of the relief kits. It will then be useful for the HO to establish bounds on the auction prices. In the second model, the objective is to maximize the expected utility considering penalties for withdrawing, the maximum value per kit given by the HO public call and all HO requirements. Thus, this model will provide insights for bidders on whether they should apply or not to the auction and if so, under what conditions they are profitable. In both cases we will start with a single commodity model, that is, we will assume that there is only one type of product to be delivered (e.g., a humanitarian kit). As an extension of the models, and depending on the computational difficulty to solve the single commodity version, we may also present the multi-commodity variant. Furthermore, we propose to test the applicability of these models on a case study based on a public call of the Colombian Red Cross (001-2019). In particular, we propose to use a scenario-based approach to represent the uncertainty associated with the demand, transportation cost, supplier capacity and transportation time. The scenarios will be formed using the 168 municipalities included in the call of the Red Cross and the consolidated data of disasters in Colombia since 1998. This part of the project requires an important effort on data collection, cleaning and preprocessing, possibly using classification or clustering algorithms, to better capture the information and adequately represent significant properties to validate the models.