Bullwhip Effect – Logistic Stability Examination in Serial and Arborescent Topologies with Demand Uncertainty and Delay

The paper analyzes the formation of the bullwhip effect in logistic systems as a significant threat to preserving stability in the face of non-negligible goods transport delay and uncertainty of demand and stock records. The popular order-up-to policy is selected as the method governing the goods flow. A dynamic model of entity interaction is constructed and examined, first, analytically, then in numerical tests for various scenarios of practical significance, e.g., a supply chain with external and local demand signals or real-world European goods distribution system. It has been found that the order-up-to policy does not trigger the bullwhip effect despite the delays in the goods delivery in the nominal operating conditions in supply chains. However, in networked environments, even the basic configuration triggers the bullwhip effect.

Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination

In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.

Intrafractional fiducial marker position variations in stereotactic liver radiotherapy during voluntary deep inspiration breath-hold

Objectives: To evaluate intrafractional fiducial marker position variations during stereotactic body radiotherapy (SBRT) in patients treated for liver metastases in visually guided, voluntary deep inspiration breath-hold (DIBH). Methods: 10 patients with implanted fiducial markers were studied. Respiratory coaching with visual guidance was used to ensure comfortable voluntary breath-holds for SBRT imaging and delivery. Three DIBH CTs were acquired for treatment planning. Pre- and post-treatment CBCTs were acquired for each of the three treatment fractions. Per-fraction marker position was evaluated on planar 2D kV images acquired during treatment fractions for 4 of the 10 patients. Results: The median difference in marker position was 0.3 cm (range, 0.0–0.9 cm) between the three DIBH CTs and 0.3 cm (range, 0.1 to 1.4 cm) between pre- and post-treatment CBCTs. The maximum intrafractional variation in marker position in craniocaudal (CC) direction on planar kV images was 0.7 to 1.3 cm and up to 1.0 cm during a single DIBH. Conclusion: Difference in marker position of up to 1.0 cm was observed during a single DIBH despite use of narrow external gating window and visual feedback. Stability examination on pre-treatment DIBH CTs was not sufficient to guarantee per-fraction stability. Evaluation of differences in marker position on pre- and post-treatment CBCT did not always reveal the full magnitude of the intrafractional variation. Advances in knowledge To increase treatment accuracy, it is necessary to apply real-time monitoring of the tumour or a reliable internal surrogate when delivering liver SBRT in voluntary DIBH.

Stability Analysis of a Nonlinear Epidemic Model With Generalized Piecewise Constant Argument

The authors consider a nonlinear epidemic equation by modeling it with generalized piecewise constant argument (GPCA). The authors investigate invariance region for the considered model. Sufficient conditions guaranteeing the existence and uniqueness of the solutions of the model are given by creating integral equations. An important auxiliary result giving a relation between the values of the unknown function solutions at the deviation argument and at any time t is indicated. By using Lyapunov-Razumikhin method developed by Akhmet and Aruğaslan for the differential equations with generalized piecewise constant argument (EPCAG), the stability of the trivial equilibrium is investigated in addition to the stability examination of the positive equilibrium transformed into the trivial equilibrium. Then sufficient conditions for the uniform stability and the uniform asymptotic stability of trivial equilibrium and the positive equilibrium are given.