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Bunker fuel oil (ifo), one of the products of petroleum refining, has a strong impact in the production process because it drives the availability of heavy residues that depend on the crude quality. A simplified stochastic model for the Administracio´n Nacional de Combustibles Alcohol y Portland refinery, based on the uncertainty of the demand for ifo, is proposed for comparison with the current approach of deterministic demand. In this model, the benefits of the production process are maximized, taking decisions on the more suitable raw material, intermediate products and final blends in order to fulfill quality and demand requirements of final products. A specific case is analyzed where the maximum benefit is achieved when the most expensive crude quality is purchased, due to a lack of incentive to produce extra amounts of heavy fuel oil that must be exported at a non-attractive price. Results are compared with the solution of a deterministic model with mean demand. In addition, the stochastic model solution depicts how the refinery should operate for each scenario of ifo demand.

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We address the problem of expected cost minimization of meeting the uncertain fuel demand during a time planning horizon, where supply is provided by selecting discrete shipments with lead times. Due to uncertainty and the passage of time, corrective actions can be taken such as cancellation and postponement on supply of shipments with associated costs and delays. This problem is modeled as a stochastic multi-stage capacitated discrete lot-sizing problem with lead times. Computational experiments were performed on the resolution of various instances of the model for four information structures of uncertainty. The experimental optimal values and stochastic rating measures obtained show the validity and interest of the stochastic model, as well as the benefits that can be obtained with respect to a deterministic variant of the model that considers average demand.

This study provides insight into the seasonality of Class I price differentials in the southeastern dairy industry. This is accomplished by analyzing monthly estimates of Class I price differentials obtained from the imputed price solution or dual solution of a generalized capacitated minimum cost network flow model of the dairy industry. A smooth seasonal pattern emerges through the monthly sequence with the lowest and highest estimated Class I price differentials occurring in April and September respectively. Miami and Jacksonville areas reach $ 5.40 and $ 4.36 per hundredweight in April and $ 6.79 and $ 5.53 per hundredweight in September.

An extension of the capacitated, fixed charge, multicommodity network flow problem with an uncertain demand of services and survivability constraints was designed and modeled as a stochastic programming problem. A polynomial algorithm based on the GRASP metaheuristic with a construction phase of a survivable topology and a local search phase based on a key-path decomposition of the graph and a feasible key-path replacement was proposed to solve it. The heuristic algorithm was tested for several problem instances, and its solutions were compared with a branch-and-cut solver. The heuristic reached good quality solutions for the tested cases.An algebraic model is defined using a node-arc formulation with a directed-arc extension of the problem. The directed-arc formulation models the network flow component of the problem. Let A P be the set of possible directed arcs of an equivalent directed graph of G where both directions of arcs are established: A P ¼ fði; jÞjði; jÞ 2 A or ð j; iÞ 2 Ag.The model with an uncertain demand depicts two types of decisions: one type, associated with the network design, with the selection of arcs, and the other type associated with its operation, A. Olivera et al. / Intl. Trans. in Op. Res. 17 (2010) 765-776 766 r