Singularly perturbed nonlinear ODEs and interior point optimizationalgorithms

This paper explores the continuous realizations of iterative processes emanating from interior point optimization algorithms, and their connection with nonlinear singularly-perturbed ordinary differential equations. This mathematical connection provides a theoretical framework for the analysis of the dynamical properties long known and exploited in interior point-based optimization techniques. In addition, this connection is used to show that the logarithmic barrier function is indeed, in some sense, optimu

Characteristics and Enablers of Transparency in Product Development Organizations

Risks in product development lead to schedule and cost overruns and poor product quality. While many risk management frameworks have been published and research on specific practices has been conducted, little is understood of key characteristics of successful risk management in product development and how they manifest in real development projects. This research consists of two phases. The first phase is a survey on 171 best practices in risk management. Analysis of over 200 responses from industry practitioners identified transparency as a key characteristic of successful risk management in product development. Due to the limited exploration of the concept of transparency in the literature, the second phase of this work consisted of a qualitative investigation of transparency through interviews with 15 industry practitioners. Analysis of the interview results suggests a hierarchical structure which decomposes transparency into several characteristics and identifies enablers for each of these characteristics. We propose that transparency can be a valuable lever for product developers and managers. Future work is needed to validate the generalizability of the observations provided

An Integrated Inventory Production System In A Three-Layer Supply Chain

With growing focus on supply chain management, firms realise that inventories across the entire supply chain can be more efficiently managed through greater co-operation and better co-ordination. This paper deals with inventory and production coordination in a three-layer supply chain involving suppliers, manufacturers and retailers. Each stage may have more than one firm. It is assumed that the cycle time at each stage is an integer multiple of the cycle time of the adjacent downstream stage. In addition, the produced lot at each stage is sent to the adjacent downstream stage in equal shipments. Shipments are sent as soon as they are produced and there is no need to wait until a whole lot is produced. A cost minimisation model and its solution procedure are derived. A numerical example is presented for illustrative purposes. This policy leads to considerable savings as compared to the scheme that allows shipments only after the whole lot is produced

An Integrated Inventory Production System In A Three-Layer Supply Chain

With growing focus on supply chain management, firms realise that inventories across the entire supply chain can be more efficiently managed through greater co-operation and better co-ordination. This paper deals with inventory and production coordination in a three-layer supply chain involving suppliers, manufacturers and retailers. Each stage may have more than one firm. It is assumed that the cycle time at each stage is an integer multiple of the cycle time of the adjacent downstream stage. In addition, the produced lot at each stage is sent to the adjacent downstream stage in equal shipments. Shipments are sent as soon as they are produced and there is no need to wait until a whole lot is produced. A cost minimisation model and its solution procedure are derived. A numerical example is presented for illustrative purposes. This policy leads to considerable savings as compared to the scheme that allows shipments only after the whole lot is produced

Entropic Tightening of Vibrated Chains

We investigate experimentally the distribution of configurations of a ring with an elementary topological constraint, a ``figure-8'' twist. Using vibrated granular chains, which permit controlled preparation and direct observation of such a constraint, we show that configurations where one of the loops is tight and the second is large are strongly preferred. This agrees with recent predictions for equilibrium properties of topologically-constrained polymers. However, the dynamics of the tightening process weakly violate detailed balance, a signature of the nonequilibrium nature of this system.Comment: 4 pages, 4 figure

Knots and Random Walks in Vibrated Granular Chains

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with the theoretical values.Comment: 4 pages, 5 figure

Spontaneous spirals in vibrated granular chains

We present experimental measurements on the spontaneous formation of compact spiral structures in vertically-vibrated granular chains. Under weak vibration when the chain is quasi two-dimensional and self-avoiding, spiral structures emerge from random initial configurations. We compare the spiral geometry with that of an ideal tight spiral. Globally, the spiral undergoes a slow rotation such that to keep itself wound, while internally, fast vibrational modes are excited along the backbone with transverse oscillations dominating over longitudinal ones