A Shapley value analysis to coordinate the formation of procurement

In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged. Formation of such procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions. Recent research in supply chain management has emphasized that such decisions need to take into account the fact that suppliers and buyers are intelligent and rational agents who act strategically. In this paper, we view the problem of Procurement Network Formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a fair manner. We study the implications of using the Shapley value as a solution concept for forming such procurement networks. We also present a protocol, based on the extensive form game realization of the Shapley value, for forming these networks.

The core and shapley value analysis for cooperative formation of procurement networks

Formation of high value procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions, where suppliers are intelligent and rational agents who act strategically. In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged We model the problem of Procurement Network Formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a stable and fair manner We first investigate the stability of such networks by examining the conditions under which the core of the game is non-empty. We then present a protocol, based on the extensive form game realization of the core, for forming such networks so that the resulting network is stable. We also mention a key result when the Shapley value is applied as a solution concept.

A Shapley Value Analysis to Coordinate the Formation of Procurement Networks

In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged. Formation of such procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions. Research in supply chain management has emphasized that such decisions need to take into account the fact that suppliers and buyers are intelligent and rational agents who act strategically. In this paper, we view the problem of procurement network formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a fair manner. We study the implications of using the Shapley value as a solution concept for forming such procurement networks. We also present a protocol, based on the extensive form game realization of the Shapley value, for forming these networks.

The Broad-Line Type Ic Supernoava SN 2007ru: Adding To The Diversity Of Type Ic Supernovae

Photometric and spectral evolution of the Type Ic supernova SN 2007ru until around 210 days after maximum are presented. The spectra show broad spectral features due to very high expansion velocity, normally seen in hypernovae. The photospheric velocity is higher than other normal Type Ic supernovae (SNe Ic). It is lower than SN 1998bw at similar to 8 days after the explosion, but is comparable at later epochs. The light curve (LC) evolution of SN 2007ru indicates a fast rise time of 8 +/- 3 days to B-band maximum and postmaximum decline more rapid than other broad-line SNe Ic. With an absolute V magnitude of -19.06, SN 2007ru is comparable in brightness with SN 1998bw and lies at the brighter end of the observed SNe Ic. The ejected mass of Ni-56 is estimated to be similar to 0.4 M-circle dot. The fast rise and decline of the LC and the high expansion velocity suggest that SN 2007ru is an explosion with a high kinetic energy/ejecta mass ratio (E-K/M-ej). This adds to the diversity of SNe Ic. Although the early phase spectra are most similar to those of broad-line SN 2003jd, the [O I] line profile in the nebular spectrum of SN 2007ru shows the singly peaked profile, in contrast to the doubly peaked profile in SN 2003jd. The singly peaked profile, together with the high luminosity and the high expansion velocity, may suggest that SN 2007ru could be an aspherical explosion viewed from the polar direction. Estimated oxygen abundance 12 + log(O/H) of similar to 8.8 indicates that SN 2007ru occurred in a region with nearly solar metallicity.

Construction of Stability Multipliers with Prescribed Phase Characteristics: an Improved Value for $\sigma

For a feedback system consisting of a transfer function $G(s)$ in the forward path and a time-varying gain $n(t)(0 \leqq n(t) \leqq k)$ in the feedback loop, a stability multiplier $Z(s)$ has been constructed (and used to prove stability) by Freedman [2] such that $Z(s)(G(s) + {1 / K})$ and $Z(s - \sigma )(0 < \sigma < \sigma _ * )$ are strictly positive real, where $\sigma _ * $ can be computed from a knowledge of the phase-angle characteristic of $G(i\omega ) + {1 / k}$ and the time-varying gain $n(t)$ is restricted by $\sigma _ * $ by means of an integral inequality. In this note it is shown that an improved value for $\sigma _ * $ is possible by making some modifications in his derivation. ©1973 Society for Industrial and Applied Mathematics.

Singular value decomposition based computationally efficient algorithm for rapid dynamic near-infrared diffuse optical tomography

Purpose: A computationally efficient algorithm (linear iterative type) based on singular value decomposition (SVD) of the Jacobian has been developed that can be used in rapid dynamic near-infrared (NIR) diffuse optical tomography. Methods: Numerical and experimental studies have been conducted to prove the computational efficacy of this SVD-based algorithm over conventional optical image reconstruction algorithms. Results: These studies indicate that the performance of linear iterative algorithms in terms of contrast recovery (quantitation of optical images) is better compared to nonlinear iterative (conventional) algorithms, provided the initial guess is close to the actual solution. The nonlinear algorithms can provide better quality images compared to the linear iterative type algorithms. Moreover, the analytical and numerical equivalence of the SVD-based algorithm to linear iterative algorithms was also established as a part of this work. It is also demonstrated that the SVD-based image reconstruction typically requires O(NN2) operations per iteration, as contrasted with linear and nonlinear iterative methods that, respectively, requir O(NN3) and O(NN6) operations, with ``NN'' being the number of unknown parameters in the optical image reconstruction procedure. Conclusions: This SVD-based computationally efficient algorithm can make the integration of image reconstruction procedure with the data acquisition feasible, in turn making the rapid dynamic NIR tomography viable in the clinic to continuously monitor hemodynamic changes in the tissue pathophysiology.

Sensitivity of Eigen Value to Damage and Its Identification

The reduction in natural frequencies,however small, of a civil engineering structure, is the first and the easiest method of estimating its impending damage. As a first level screening for health-monitoring, information on the frequency reduction of a few fundamentalmodes can be used to estimate the positions and the magnitude of damage in a smeared fashion. The paper presents the Eigen value sensitivity equations, derived from first-order perturbation technique, for typical infra-structural systems like a simply supported bridge girder, modelled as a beam, an endbearing pile, modelled as an axial rod and a simply supported plate as a continuum dynamic system. A discrete structure, like a building frame is solved for damage using Eigen-sensitivity derived by a computationalmodel. Lastly, neural network based damage identification is also demonstrated for a simply supported bridge beam, where the known-pairs of damage-frequency vector is used to train a neural network. The performance of these methods under the influence of measurement error is outlined. It is hoped that the developed method could be integrated in a typical infra-structural management program, such that magnitudes of damage and their positions can be obtained using acquired natural frequencies, synthesized from the excited/ambient vibration signatures.

Tendency toward crossover of the effective susceptibility exponent from its doubled Ising value to its doubled mean-field value near a double critical point

The critical behavior of osmotic susceptibility in an aqueous electrolyte mixture 1-propanol (1P)+water (W)+potassium chloride is reported. This mixture exhibits re-entrant phase transitions and has a nearly parabolic critical line with its apex representing a double critical point (DCP). The behavior of the susceptibility exponent is deduced from static light-scattering measurements, on approaching the lower critical solution temperatures (TL’s) along different experimental paths (by varying t) in the one-phase region. The light-scattering data analysis substantiates the existence of a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the TL far away from the DCP, the effective susceptibility exponent γeff as a function of t displays a nonmonotonic crossover from its single limit three-dimensional (3D)-Ising value ( ∼ 1.24) toward its mean-field value with increase in t. While for that closest to the DCP, γeff displays a sharp, nonmonotonic crossover from its nearly doubled 3D-Ising value toward its nearly doubled mean-field value with increase in t. The renormalized Ising regime extends over a relatively larger t range for the TL closest to the DCP, and a trend toward shrinkage in the renormalized Ising regime is observed as TL shifts away from the DCP. Nevertheless, the crossover to the mean-field limit extends well beyond t>10−2 for the TL’s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques. As far as the critical behavior in complex or associating mixtures with special critical points (like the DCP) is concerned, our results indicate that the influence of the DCP on the critical behavior must be taken into account not only on the renormalization of the critical exponent but also on the range of the Ising regime, which can shrink with decrease in the influence of the DCP and with the extent of structuring in the system. The utility of the field variable tUL in analyzing re-entrant phase transitions is demonstrated. The effective susceptibility exponent as a function of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value toward a value slightly lower than its nonasymptotic mean-field value of 1. This behavior in the nonasymptotic, high tUL region is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values, as foreseen earlier in micellar systems.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Solution of MDPS using simulation-based value iteration

This article proposes a three-timescale simulation based algorithm for solution of infinite horizon Markov Decision Processes (MDPs). We assume a finite state space and discounted cost criterion and adopt the value iteration approach. An approximation of the Dynamic Programming operator T is applied to the value function iterates. This 'approximate' operator is implemented using three timescales, the slowest of which updates the value function iterates. On the middle timescale we perform a gradient search over the feasible action set of each state using Simultaneous Perturbation Stochastic Approximation (SPSA) gradient estimates, thus finding the minimizing action in T. On the fastest timescale, the 'critic' estimates, over which the gradient search is performed, are obtained. A sketch of convergence explaining the dynamics of the algorithm using associated ODEs is also presented. Numerical experiments on rate based flow control on a bottleneck node using a continuous-time queueing model are performed using the proposed algorithm. The results obtained are verified against classical value iteration where the feasible set is suitably discretized. Over such a discretized setting, a variant of the algorithm of [12] is compared and the proposed algorithm is found to converge faster.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Effect of boundary condition description on convergence of solution in a boundary-value problem

It is well known that the numerical accuracy of a series solution to a boundary-value problem by the direct method depends on the technique of approximate satisfaction of the boundary conditions and on the stage of truncation of the series. On the other hand, it does not appear to be generally recognized that, when the boundary conditions can be described in alternative equivalent forms, the convergence of the solution is significantly affected by the actual form in which they are stated. The importance of the last aspect is studied for three different techniques of computing the deflections of simply supported regular polygonal plates under uniform pressure. It is also shown that it is sometimes possible to modify the technique of analysis to make the accuracy independent of the description of the boundary conditions.

Comparative study on damage identification from lso-Eigen-Value-Change contours and smeared damage model

The paper proposes two methodologies for damage identification from measured natural frequencies of a contiguously damaged reinforced concrete beam, idealised with distributed damage model. The first method identifies damage from Iso-Eigen-Value-Change contours, plotted between pairs of different frequencies. The performance of the method is checked for a wide variation of damage positions and extents. The method is also extended to a discrete structure in the form of a five-storied shear building and the simplicity of the method is demonstrated. The second method is through smeared damage model, where the damage is assumed constant for different segments of the beam and the lengths and centres of these segments are the known inputs. First-order perturbation method is used to derive the relevant expressions. Both these methods are based on distributed damage models and have been checked with experimental program on simply supported reinforced concrete beams, subjected to different stages of symmetric and un-symmetric damages. The results of the experiments are encouraging and show that both the methods can be adopted together in a damage identification scenario.