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Global optimization of arborescent multilevel inventory systems

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Abstract

We consider the numerical resolution of hierarchical inventory problems under global optimization. First we describe the model as well as the dynamical stochastic system and the impulse controls involved. Next we characterize the optimal cost function and we formulate the Hamilton-Jacobi-Bellman equations. We present a numerical scheme and a fast algorithm of resolution, with a result on the speed of convergence. Finally, we apply the discretization method to some examples where we show the usefulness of the proposed numerical method as well as the advantages of operating under global optimization.

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González, R., Rofman, E. & Sagastizábal, C. Global optimization of arborescent multilevel inventory systems. J Glob Optim 6, 269–292 (1995). https://doi.org/10.1007/BF01099465

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Key words

  • Global optimization
  • inventory problems
  • discrete Hamilton-Jacobi-Bellman equations
  • quasi-variational inequalities
  • subsolutions and supersolutions