Abstract
Total production costs sometimes show an S-shaped form. There are several ways in which a plant with given capacity can be adapted to a specific demand rate, one of them being adaptation of intensity per work hour. In this paper we present an application of the Hamilton-Hopf bifurcation to an inventory/production intensity splitting model with a nonconvex cost function. Our analysis provides a new proof that persistent oscillations may be optimal for arbitrary small discount rates. For zero discounting a “Hamilton Hopf bifurcation” occurs, leading to a family of periodic solutions bifurcating from a steady state. If the discount rate becomes positive, almost all periodic solutions vanish; only a unique branch of periodic solutions is obtained.
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Steindl, A., Feichtinger, G. Bifurcations to Periodic Solutions in a Production/Inventory Model. J Nonlinear Sci 14, 469–503 (2004). https://doi.org/10.1007/s00332-003-0565-x
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DOI: https://doi.org/10.1007/s00332-003-0565-x