Zbigniew Michna

Simulation of the asymptotic constant in some fluid models

Let Z(t) be a stationary centered Gaussian process with a Markovian structure. In some fluid models, the stationary buffer content V can be expressed as and P(V>u)=Ce −γu (1+o(1)). The asymptotic constant C can be expressed by the so called generalized Pickands constants H. In most cases no formula or approximation for C are known. In this paper we show a method of simulation of C by the use of change of measure technique. The method is applicable when Z(t) is a stationary Ornstein-Uhlenbeck process or where (X 1(t),…,X n (t)) is a Gauss-Markov process. Two examples of simulations are included. Moreover we give a formula for a lower bound for generalized Pickands constants.

An Empirical Investigation of Lead Time Distributions

This paper proposes a methodology for analyzing lead time behavior. The method focuses on identifying whether lead times are in fact identically independently distributed (i.i.d.). The method uses a combination of time series analysis, Kolmogorov-Smirnov’s test for similar distributions and data sampling to arrive at its result. The method is applied to data obtained from a manufacturing company. The conclusions are that while the lead time to customers can for some products be assumed to be i.i.d. this is not uniformly true. Some products’ lead times are in fact neither independently nor identically distributed.

Quantifying the Bullwhip Effect of Multi-echelon System with Stochastic Dependent Lead Time

Considering a multi-echelon system, the bullwhip effect is recognized as a significant factor with regards to the inventory management. This paper focuses on the effect of stochastic dependent lead time on the bullwhip effect. Simulation based approach is used to quantify the bullwhip effect with different demand and lead time distributions. The experiment results show that the dependent lead time has much effect on the 2nd echelon (from the downstream to the upstream) and bullwhip effect decrease significantly if the variance of this echelon decreases.

An Approach for Designing Order Size Dependent Lead Time Models for Use in Inventory and Supply Chain Management

This paper addresses the issue of lead time behavior in supply chains. In supply chains without information sharing a supply chain member can only use the information they observe; orders/demand and their lead times. Using this information four different scenarios of lead time behavior are suggested and discussed. Based on this discussion an analytical approach is proposed that investigates the link between order quantities and lead times. This approach is then demonstrated on data from a company. In the particular case it is determined that there seems to be a link between order quantities and lead times, indicating that a complex lead time model may be necessary. It is also concluded that current state of supply chain management does not offer any methods to address this link between order quantities and lead times and that therefore further research is warranted.

Lead Times and Order Sizes—A not so Simple Relationship

Order quantity and lead time are two critical aspects of inventory management. In literature, lead time is considered as a constant or an uncontrollable stochastic variable. Theoretically, the order size has linear relationship with lead time meaning that order size increases when lead time increases. A data analysis from a Danish company reveals that the relationship between lead time and order size are not so simple. This paper focuses on analyzing the relationship between lead time and order size in order to answer two questions: (1) whether lead time is affected by order size or not; and (2) whether lead time and order size has linear relationship or not.

Reducing Truck Emissions in Import Operations at Container Terminal—A Case Study in a Singaporean Port

Emissions from idle truck engines are a main source of pollution from transportation, and emission reduction from idle truck engines at container terminal has for this reason become a priority. At the import yard of a container terminal, an incoming truck has to wait for its turn to be loaded with containers which are then to be delivered to a customer. Reducing waiting time of trucks means that truck emissions are decreased as well as the competition of port increases. In this study, the emission from idle truck engines at the import yard is considered. The goal of this study is to develop a methodology for reducing emissions generated by trucks idling at import yards. The proposed method includes a mathematical model for minimizing truck emissions. In the model, total truck waiting time in the yard is estimated using discrete event simulation. To solve this model, a genetic algorithm is proposed. A case study in a Singaporean port is used for conducting experiments. The experiment result shows that the manager of a container terminal should control truck arrivals based on the stacking of import containers in order to reduce the truck idling time and thereby the truck emissions in the import yard.

On the Mean of a Stochastic Integral with Non-Gaussian α-Stable Noise

Abstract In this article, we consider a Lévy process under condition Γ1 = x where {Γ k } is a sequence of arrivals of a Poisson process with unit arrival rate. We show that under condition Γ1 = x Lévy process can be decomposed into a simple process and a Lévy process. These two processes are independent. As an application of this decomposition we consider α-stable Lévy processes. We give a closed form of the process and evaluate its expected value where Z is an α-stable Lévy process with 0 < α < 2. We show that 𝔼X(t) = 0 for 1 < α < 2 and this expectation is equal infinity for α ≤ 1.

Approximation of Sojourn Times of Gaussian Processes

We investigate the tail asymptotic behavior of the sojourn time for a large class of centered Gaussian processes X, in both continuous- and discrete-time framework. All results obtained here are new for the discrete-time case. In the continuous-time case, we complement the investigations of Berman (Commun Pure Appl Math 38(5):519–528, 1985a and Probab Theory Relat Fields 20(1):113–124, 1987) for non-stationary X. A by-product of our investigation is a new representation of Pickands constant which is important for Monte-Carlo simulations and yields a sharp lower bound for Pickands constant.

An Experimental Investigation of Lead Time and the Effect of Order Crossover

This paper presents results from an experimental investigation of lead time distributions. The focus is on the order crossover phenomenon where slower orders are overtaken by faster orders and the impact of this on the structure of the observed lead time distribution. The natural conclusion is that the likelihood of order crossover occurring strongly depends on the skewness and variance of the lead time distribution. Furthermore, the conclusion is that while lead times may be i.i.d. random variables, when crossover occurs lead times observed in the sequence orders are received are in fact mutually dependent. This has a significant impact on how supply chain members should estimate lead times and lead time distributions. That lead times are in fact mutually dependent is a major finding and has implications for both practice and academia.

The actual nature of lead times in supply chains following a strict reorder point based approach

The aim of this research is to demonstrate that supply chains by their very nature will experience stochastic rather than deterministic lead times. The presented study focuses on simulating delivery lead times in supply chains, where each echelon is servicing the next downstream member from inventory. The aim is to highlight the need for increased research focus on supply chains with stochastic lead times. Through a simple numerical example we conclusively show that lead times in any real supply chain following a re-order point method must be stochastic even in the case where lead times between individual echelons are in fact deterministic.