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The impact of stochastic lead times on the bullwhip effect – an empirical insight

Nielsen P., Michna Z.

Management and Production Engineering Review

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2018

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Vol. 9, No. 1

65--70

EN

In this article, we review the research state of the bullwhip effect in supply chains with stochastic lead times. We analyze problems arising in a supply chain when lead times are not deterministic. Using real data from a supply chain, we confirm that lead times are stochastic and can be modeled by a sequence of independent identically distributed random variables. This underlines the need to further study supply chains with stochastic lead times and model the behavior of such chains.

2

Remarks on Pickands’ theorem

Michna Z.

Probability and Mathematical Statistics

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2017

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Vol. 37, Fasc. 2

373--393

EN

In this article we present the Pickands theorem and his double sum method. We follow Piterbarg’s proof of this theorem. Since his proof relies on general lemmas, we present a complete proof of Pickands’ theorem using the Borell inequality and Slepian lemma. The original Pickands’ proof is rather complicated and is mixed with upcrossing probabilities for stationary Gaussian processes. We give a lower bound for Pickands constant. Moreover, we review equivalent definitions, simulations and bounds of Pickands constant.

3

Lead times - their behavior and the impact on planning and control in supply chains

Nielsen P., Michna Z., Sørensen B. B., Dung N. D. A.

Management and Production Engineering Review

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2017

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Vol. 8, No. 2

30--40

EN

Lead times and their nature have received limited interest in literature despite their large impact on the performance and the management of supply chains. This paper presents a method and a case implementation of the same, to establish the behavior of real lead times in supply chains. The paper explores the behavior of lead times and illustrates how in one particular case they can and should be considered to be independent and identically distributed (i.i.d.). The conclusion is also that the stochastic nature of the lead times contributes more to lead time demand variance than demand variance.

4

Simulation of Pickands constants

Burnecki K., Michna Z.

Probability and Mathematical Statistics

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2002

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Vol. 22, Fasc. 1

193--199

EN

Pickands constants appear in the asymptotic formulas for extremes of Gaussian processes. The explicit formula of Pickands constants does not exist. Moreover, in the literature there is no numerical approximation. In this paper we compute numerically Pickands constants by the use of change of measure technique. To this end we apply two different algorithms to simulate fractional Brownian motion. Finally, we compare the approximations with a theoretical hypothesis and a recently obtained lower bound on the constants. The results justify the hypothesis.