We present a methodology for long-term mine planning based on a general capacitated multicommodity network flow formulation. It considers underground and open-pit ore deposits sharing multiple downstream processing plants over a long horizon. The purpose of the model is to optimize several mines in an integrated fashion, but real size instances are hard to solve due to the combinatorial nature of the problem. We tackle this by solving the relaxation of a tight linear formulation, and we round the resulting near-integer solution with a customized procedure. The model has been implemented at Codelco, the largest copper producer in the world. Since 2001, the system has been used on a regular basis and has increased the net present value of the production plan for a single mine by 5%. Moreover, integrating multiple mines provided an additional increase of 3%. The system has allowed planners to evaluate more scenarios. In particular, the model was used to study the option of delaying by four years the conversion of Chiquicamata, Codelco's largest open-pit mine, to underground operations.

The Chilean State delivers essential meal services at schools for low-income students. Junta Nacional de Auxilio Escolar y Becas, the institution in charge of covering 1,300,000 children, leases the meal service to private enterprises. We developed an integer linear programming model to assign the meal contracts, in a process known as combinatorial auctions. The resulting model, which is NP-hard, led to significant improvements in efficiency and also contributed to making the process more transparent. The results are apparent in substantial improvements in quality and coverage of the service, and important savings to the country, which are equivalent to feeding 300,000 children in addition. We developed techniques to solve the combinatorial models and also to analyze and compare multiple scenarios to find robust solutions. For the objective function of this problem, we analyzed several options to consider different kinds of social benefits. In this paper, we describe the problem, the methodology and the results. We also present empirical results based on 6 years of experience. Finally, we discuss the relevance and impact of using operations research in these central issues in developing countries.

Chile's school system is using mathematical modeling to assign catering contracts in a singleround sealed-bid combinational auction. The Chilean state spends around US$180 million a year to feed 1,300,000 students from low income families, making this one of the largest state auctions. To improve the quality of the assignment in the auction process, we constructed an integer linear programming model to decide contract awards optimally among different concession holders. The model completely changed the nature of the process in three crucial aspects. First, it gave transparency and objectivity to the complete process, generating competition among firms. Second, it allowed the companies to build flexible territorial bids to include their scale economies, leading to efficient resource allocation. Finally, the model indeed found an optimal solution, which is not easy because the assignment problem was NPcomplete with more than 10,000 binary variables. This new methodology improved the pricequality ratio of the meals with yearly savings of around US$40 million-equivalent to the cost of feeding 300,000 children during one year. (Games/group decisions: bidding/auctions. Government: agencies.

Posterior dislocation of the elbow joint with fracture of both the radial head and coronoid process, the so-called 'terrible triad', is a complex and difficult-to-treat injury. We report a case of a 34-year-old man with terrible triad of the elbow and associated injuries secondary to a fall. The patient was treated with radial head osteosynthesis, resection of the coronoid process fragments, and stabilisation of the ulnohumeral joint by Kirschner wire transfixation. The sequence of treatment steps is provided. The priority for treating multiple injuries should be established. The integrity of the coronoid process is essential for providing the elbow with maximum functionality.

In this paper, we present a system that Compañía Sud Americana de Vapores (CSAV), one of the world's largest shipping companies, developed to support its decisions for repositioning and stocking empty containers. CSAV's main business is shipping cargo in containers to clients worldwide. It uses a fleet of about 700,000 TEU containers of different types, which are carried by both CSAV-owned and third-party ships. Managing the container fleet is complex; CSAV must make thousands of decisions each day. In particular, imbalances exist among the regions. For example, China often has a deficit of empty containers and is a net importer; Saudi Arabia often has a surplus and is a net exporter. CSAV and researchers from the University of Chile developed the Empty Container Logistics Optimization System (ECO) to manage this imbalance. ECO's multicommodity, multiperiod model manages the repositioning problem, whereas an inventory model determines the safety stock required at each location. CSAV uses safety stock to ensure high service levels despite uncertainties, particularly in the demand for containers. A hybrid forecasting system supports both the inventory and the multicommodity network flow model. Major improvements in data gathering, real-time communications, and automation of data handling were needed as input to the models. A collaborative Web-based optimization framework allows agents from different zones to interact in decision making. The use of ECO led to direct savings of $81 million for CSAV, a reduction in inventory stock of 50 percent, and an increase in container turnover of 60 percent. Moreover, the system helped CSAV to become more efficient and to overcome the 2008 economic crisis.