ABSTRACT Here, we propose a novel methodology for replenishment and control systems for inventories of two-echelon logistics networks using a two-stage stochastic programming, considering periodic review and uncertain demands. In addition, to achieve better customer services, we introduce a variable rationing rule to address quantities of the item in short. The devised models are reformulated into their deterministic equivalent, resulting in nonlinear mixed-integer programming models, which are then approximately linearized. To deal with the uncertain nature of the item demand levels, we apply a Monte Carlo simulation-based method to generate finite and discrete sets of scenarios. Moreover, the proposed approach does not require restricted assumptions to the behavior of the probabilistic phenomena, as does several existing methods in the literature. Numerical experiments with the proposed approach for randomly generated instances of the problem show results with errors around 1%.

Science and technology practitioners have been studying how to take economical, social and environmental advantage of industrial residuals and discarded products. In this sense, this paper presents a Material Requirements Planning (MRP) optimization model for a particular production system that, besides manufacturing a final product and its main assembling component, it recovers units of the component from units of the returned product as well. It is assumed that the demand for the final product is independent of the amount of the returned product available, and that the market for the final product is not segmented. Considering that all parameters of the MRP mathematical model have deterministic nature, we prove that this production planning problem is NP-hard. We also show computational experiments with the model using an optimization solver and analyze some possible industrial scenarios, as well.

The hub-and-spoke network design problem, also known as the hub location problem, aims to find the concentration points in a given network flow so that the sum of the distances of the linkages is minimized. In this work, we compare discrete solutions of this problem, given by the branch-and-cut method applied to the p-hub median model, with continuous solutions, given by the hyperbolic smoothing technique applied to a min-sum-min model. Computational experiments for particular instances of the Brazilian air transportation system, with the number of hubs varying from 2 to 8, are conducted with the support of a discretization heuristic and the Voronoi diagram.