A dynamic measure of order in structural glasses

Although some patterns of physical behavior are common in the glass transition and in the properties of supercooled liquids and glasses (characteristic viscoelasticity, temperature dependence of viscosity and relaxation times, property evolution through “physical aging”, difficulties in performing equilibrium measurements or simulations, etc.), it is difficult to arrive at a definition of the glass transition which distinguishes it from other phenomena exhibiting similar features. The present paper addresses this problem by defining a dynamical measure of order involving the average “shape” of particle trajectories in supercooled liquids. This dynamic order parameter should provide a measure of “closeness” to the glass transition and some indirect insights into the physical nature of supercooled liquids and glasses. Arguments are given that the proposed dynamic measure of order [“generalized capacity”, C(T)] is related to the temperature-dependent “effective hydrodynamic radius” R_H(T) measured in supercooled liquids and model numerical calculations are given to support this view. Some consequences of the intermittent particle motion at low temperatures for stress relaxation are also discussed.     

Building performance standards into data envelopment analysis structures

Data Envelopment Analysis (DEA) is a mathematical approach to measuring the relative efficiency of peer Decision-Making Units (DMUs). DEA is particularly useful where no a priori information on the trade-offs or relations among various performance measures is available. However, it is very desirable if “evaluation standards,” when they can be established, be incorporated into DEA performance evaluation. This is particularly important when service operations are under investigation, because service standards are generally difficult to establish. A number of approaches have been developed to incorporate evaluation standards into DEA as reported in the literature. These approaches tend to be rather indirect, focusing primarily on the multipliers in the DEA models. This paper introduces a new way of building performance standards directly into the DEA structure. Based upon the conventional DEA model and an activity matrix, a set of standard DMUs can be generated and incorporated directly into the DEA analysis. The proposed approach is applied to a sample of 100 branches of a major Canadian bank where time standards are used to generate a set of standard bank branches.     

DEA cross-efficiency evaluation based on satisfaction degree: an application to technology selection

Data envelopment analysis (DEA) has been extended to cross-efficiency evaluation to provide better discrimination and ranking of decision-making units (DMUs). However, the non-uniqueness of optimal weights in the traditional DEA models (CCR and BCC models) has reduced the usefulness of the DEA cross-efficiency evaluation method. To solve this problem, we introduce the concept of the satisfaction degree of a DMU towards a set of optimal weights for another DMU. Then, a new DEA cross-efficiency evaluation approach, which contains a maxmin model and two algorithms, is proposed based on the satisfaction degrees of the DMUs. Our maxmin model and algorithm 1 can obtain for each DMU an optimal set of weights that maximises the least satisfaction degrees among all the other DMUs. Further, our algorithm 2 can then be used to guarantee the uniqueness of the optimal weights for each DMU. Finally, our approach is applied to a real-world case study of technology selection.     

How to assess sustainability of countries via inverse data envelopment analysis?

In this paper, two input-oriented and output-oriented inverse semi-oriented radial measures are presented. Such models are applied to determine resource allocation and investment strategies for assessing sustainability of countries. Our proposed models can deal with both positive and negative data. In our proposed inverse input-oriented data envelopment analysis (DEA) model, optimal inputs are suggested while outputs and efficiency score of decision-making unit (DMU) under evaluation are unchanged. Similarly, in our proposed inverse output-oriented DEA model, optimal outputs are proposed while inputs and efficiency score of DMU under evaluation are kept unchanged. For the first time, we propose two new inverse DEA models to handle resource allocation and investment analysis problems given sustainable development aspects in the presence of negative data. A case study is given for assessing sustainability of countries.     

Methods and applications of DEA cross-efficiency: Review and future perspectives

The field of engineering management usually involves evaluation issues, such as program selection, team performance evaluation, technology selection, and supplier evaluation. The traditional self-evaluation data envelopment analysis (DEA) method usually exaggerates the effects of several inputs or outputs of the evaluated decision-making unit (DMU), resulting in unrealistic results. To address this problem, scholars have proposed the cross-efficiency evaluation (CREE) method. Compared with the DEA method, CREE can rank DMUs more completely by using reasonable weights. With the extensive application of this technique, several problems, such as non-unique weights and non-Pareto optimal results, have arisen in CREE methods. Therefore, the improvement of CREE has attracted the attention of many scholars. This paper reviews the theory and applications of CREE, including the non-uniqueness problem, the aggregation of cross-efficiency data, and applications in engineering management. It also discusses the directions for future research on CREE.     

On the combined influences of Young''s modulus and stress ratio on the LEFM fatigue crack growth process: A new mechanistic approach

A new mechanistic approach (NMA) was used recently to examine the physical aspects of LEFM (long) fatigue crack growth (FCG) process in crack-ductile materials in stages I and II. In this paper, NMA is extended to examine both the physical and analytical aspects of the combined effects of Young's modulus, E and stress ratio, R, in the same stages of the same materials. It is shown that, (i) with submicroscopic cleavage or reversed shear mechanism operating in the pure form, E is the most influential intrinsic “material” property controlling FCG, (ii) E-dependence of da/dN is a natural consequence of near-crack-tip displacement control proposed previously, and (iii) the demonstrated similarity of FCG curves and the existence of characteristic “pivot points” on these curves for a “class of materials” results from E-influence which continues even at a higher R. A simple analytical model based on “strain intensity factor,” K₀, which contains E-influence implicitly and controls da/dN in all materials irrespective of class, is proposed. Model-predicted K₀-based theoretical values of threshold, “Idealised Master Growth Curves (IMGCs)” and mechanism transition point, all agreed excellently with experimental data for at least three classes of materials, i.e. steels, Al-alloys and Ti-alloys at extreme R-values of 0 and ≥ 0.6. The K₀-parameter concept is used here to raise the status of the analysis of the E-effect from a simple “normalisation” to that of direct data “representation”. Using NMA existing empirical relations are given some sound theoretical base. In addition to aiding in a clearer physical understanding of the FCG process, the unique IMGCs developed for different R-values are considered useful in quick, accurate and conservative life estimations, and performing failure analyses usually required in selection and design of materials.     

Does a purchasing manager’s need for cognitive closure (NFCC) affect decision-making uncertainty and supply chain performance?

Purchasing managers have increasingly assumed a pivotal role in supply chain management. They are extensively involved in the decision-making processes for purchasing and supply decisions. Yet, the extent to which their personal traits may affect decision-making environments and supply chain performance (SCP) has not been subjected to rigorous empirical scrutiny. Extant research has remained largely anecdotal and disjointed. This paper seeks to extend the stream of research in supply chain management by systematically investigating the antecedents and performance outcomes of decision-making uncertainty (DMU). It enhances current SCP literature by incorporating two understudied constructs, namely DMU and purchasing managers’ need for cognitive closure (NFCC), to explore behavioural impacts on SCP. Using structural equation modelling, this study empirically tests a number of hypothesised relationships based on a sample of 201 purchasing firms. Analysis results provide robust support for the links between close buyer–supplier relationships, DMU, the NFCC and the SCP of the buying firm. Implications for future research and supply chain practice are also offered.     

Measuring the R&D efficiency of regions by a parallel DEA game model

This paper proposes a model that can measure the R&D efficiency of each region (DMU) or each production unit while taking the inter-DMU competition and inter-subprocesses competition into account. The game cross-efficiency concept is introduced into the parallel DEA model. Furthermore, each DMU (subprocess) tries to maximize its own efficiency without harming the cross efficiency of each of the other DMUs (subprocess). We carry out an algorithm to obtain the best game cross-efficiency scores. This score has been proved to converge to a Nash equilibrium point. We use the proposed model to measure the R&D efficiency of the 30 provinces of China. The results show that the algorithm converges to a unique cross efficiency and our model indeed takes the bargaining power of DMUs and subprocesses into account.     

The Dynamic Lot-Sizing Problem for Multiple Items Under Limited Capacity

This paper addresses the problem of scheduling the timing and quantities of production of n different products over m periods for a single production facility with a prespecified capacity. We assume that the demand is deterministic and can vary from one period to another and from one product to another. The objective is to minimize the sum of production setup and inventory holding costs. For medium-size problems, optimal solution algorithms do not yet exist and therefore heuristic solution algorithms are of interest. Most of the existing heuristics make use of the “forward-pass” concept in one way or the other. Forward pass means we begin by determining the lot sizes for earlier periods before moving to study the later periods. In this paper we study the forward-pass approach as well as a different solution approach which we call the four-step algorithm. We develop the feasibility conditions for pure forward-pass algorithms. Finally, we perform a comparative evaluation study.     

Rotation numbers for quasi-periodically forced monotone circle maps

Rotation numbers have played a central role in the study of (unforced) monotone circle maps. In such a case it is possible to obtain a priori bounds of the form „ - 1/n ≤(1/n)(y_n - y₀) ≤„ + 1/n, where (1/n)(y_n - y₀) is an estimate of the rotation number obtained from an orbit of length n with initial condition y₀, and „ is the true rotation number. This allows rotation numbers to be computed reliably and efficiently. Although Herman has proved that quasi-periodically forced circle maps also possess a well-defined rotation number, independent of initial condition, the analogous bound does not appear to hold. In particular, two of the authors have recently given numerical evidence that there exist quasi-periodically forced circle maps for which y_n - y₀ - „n is not bounded. This renders the estimation of rotation numbers for quasi-periodically forced circle maps much more problematical. In this paper, a new characterization of the rotation number is derived for quasiperiodically forced circle maps based upon integrating iterates of an arbitrary smooth curve. This satisfies analogous bounds to above and permits us to develop improved numerical techniques for computing the rotation number. Additionally, the boundedness of y_n - y₀ - „n is considered. It is shown that if this quantity is bounded (both above and below) for one orbit, then it is bounded for all orbits. Conversely, if for any orbit y_n - y₀ - „n is unbounded either above or below, then there is a residual set of orbits for which y_n - y₀ - „n is unbounded both above and below. In proving these results a min-max characterization of the rotation number is also presented. The performance of an algorithm based on this is evaluated, and on the whole it is found to be inferior to the integral based method.     

A note on “an improved MCDM DEA model for technology selection”

This paper gives a modification on the improved technology selection DEA model proposed by Amin et al. (Amin, G.R., Toloo, M. and Sohrabi, B., An improved MCDM DEA model for technology selection. Int. J. Prod. Res., 2006, 44, 2681–2686). The paper shows the problem of using the existing model and then introduces a new modified one to obtain a single efficient DMU for the technology selection alternatives.     

Considering asymmetrical manufacturing cost information in a two-echelon system that uses price-only contracts

Consider a basic “price-only” supply chain interaction in which the “players” are a manufacturer and a retailer. The manufacturer sets the wholesale price ($w/unit) of a product she supplies to a retailer, who in turn sets the retail price ($p/unit) at which he sells to the consumers. The product's demand curve is a function of p. The players select to play one of several non-cooperative games such as the manufacturer-Stackelberg game. How should the players set their prices w and p? Most existing studies assume information symmetry i.e., the cost and market parameters are known equally and perfectly to both players. In reality, the retailer's knowledge of the manufacturing cost c is often controlled by the manufacturer. This paper considers explicitly the asymmetry of knowledge in c. This approach reveals interesting and surprising deviations from earlier symmetrical-c-knowledge results. Moreover, the approach also ameliorates some of the internal inconsistencies within the symmetric-information framework. We also show how the effect of knowledge asymmetry varies with the shape of the demand curve and with the degree of relative dominance between the players. We find that under a linear demand curve a manufacturer should overstate c, which is an intuitively expected result. However, under an iso-elastic demand curve she benefits herself and the entire system by understating c, which is counter-intuitive. Also, under asymmetric c-knowledge, the simultaneous decision (or “vertical Nash”) game becomes non-viable under a linear demand curve, but the game becomes quite viable and desirable under an iso-elastic demand curve.     

我国物流企业效率与效率持续性评价的实证

通过运用超效率方法对处在前沿上的物流企业进行排序和效率对比,分析了我国上市物流企业的效率变化情况;通过计算马姆奎斯特TFP指数,评价了上市物流企业效率的持续性,分析了其效率的动态变化趋势。经实证研究,得出目前我国上市物流企业效率较低,技术进步贡献率大于规模效率贡献率,从而认为物流企业在追求规模扩张的同时要增加技术投入。     

Driver age, car mass and accident exposure— A synthesis of available data

The tendency of younger drivers to be more likely than older drivers to drive smaller cars has been an important consideration in a number of prior investigations of the relation between car size and traffic safety. The purpose of the present study is to quantify this effect on a firmer basis than hitherto by fitting data from seven independent sources to a unified general model. More specifically, when the exposure measures “per unit distance of travel” or “per registered car” are used in studies of car mass effects on traffic safety, the exposure information often does not contain the variable driver age. This work develops a general procedure for disaggregating such exposure data into three driver (or owner) age categories; A₁: 16–24; A₂: 25–34; and A₃: 35 years. Data from the seven sources are fined to the equation

f(i,m) = H_i[1 + G _i(m/900 − 1)]

where m is the ear mass in kg, and f(i,m) is the fraction of cars of mass m which are driven (owned) by persons in the A_i, (i = 1, 2, 3) age category. The form of this equation permits easy comparison of 900 and 1800 kg cars. Those particular masses that have been chosen for illustrative comparisons in earlier work. The seven sets of data are used to derive overall average values of the parameters H₁ and G₁. The data from all seven sources show consistent effects which are summarized in one analytical expression which is well suited for use in future studies of car size effects because it reflects a synthesis of much prior data and it permits sensitivity analyses to be performed conveniently.     

Analysis of Excess Stock in Multiproduct Inventory Systems

A primary function of production management is the control of inventories. The typical manner of economic inventory control calls for a “pre-stocking” approach in which the focus is on the reorder quantities which should be put into inventory. A second manner of controlling inventories is what can be called a “post-stocking” analysis. Here the focus is on how much of the present inventory already in stock should be declared as surplus and disposed of. This paper describes the development and implementation of an analytical procedure for this second, excess inventory issue. The procedure is described in the context of an application to a General Motors carburetor assembly process in which product structure interactions play a significant role.     

Coordination of quantity and shelf-retention timing in the video movie rental industry

How should a video rental chain replenish its stock of new movies over time? Any such policy should consist of two key dimensions: (i) the number of copies purchased; and (ii) when to remove a movie from the front shelves and replace it by a newly released one. We first analyze this bi-variate problem for an integrated chain. As for decentralized chains, we show that a (wholesale) price-only contract cannot coordinate such a chain. We then consider a price-and-revenue-sharing contract. Such a contract can achieve coordination, but the unique price and share which are needed may not provide one of the parties with its desired profit (i.e., it will violate individual rationality). This situation has been reported in the case of Blockbuster Video and has led to litigation between Blockbuster and Disney Studios. We thus propose adding a third lever: a license fee (or subsidy) associated with each new movie. Such a contract can coordinate the channel and satisfy the individual rationality requirements. In fact, all our results hold true irrespective of whether or not the rental store is allowed to sell surplus copies of movies. We are able to compare the optimal decision variable and coordinating lever values, as well as the optimal profits, for the “rental only” and “sales + rental” models. Our numerical examples, which utilize empirical demand data have significant managerial implications in terms of increasing the effectiveness of the video rental industry.     

A modified effective crack-length formulation in elastic-plastic fracture mechanics

In examining the performance of standard effective crack-length formulations, the authors noted quantitative accuracy up to “high” fractions of limit load under loading conditions for which the elastic T-stress was non-negative, while a pronounced deviation from the corresponding continuum elastic-plastic plane-strain finite-element solutions was seen in shallow-cracked geometries having negative T-stress. This trend can be rationalized by noting that, under modified boundary layer (K_I and T) loading, the maximum plastic zone radius strongly increases as the T-stress decreases from zero (J.R. Rice (1974), J. Mech. Phys. Solids 22, 17–26; S.G. Larsson and A.J. Carlsson (1973), J. Mech. Phys. Solids 21, 263–277; N.P. O'Dowd and C.F. Shih (1991), J. Mech. Phys. Solids 39(8), 989–1015.) Accordingly, we formulate a modified effective crack length to account for the effects of the elastic T-stress.

The new formulation consistently extends the load range for which accurate predictions of compliance, J-integral, and crack-tip constraint are obtained in several plane strain specimen geometries. The magnitude of influence of the T-stress varies with specimen type and relative crack depth. The greatest “improvement” to standard effective crack length approximations occurs in specimens of “moderately” negative T-stress.     

Parallel time scales and two-dimensional manufacturer and individual customer warranties

We deal with a system whose failures depend on several parallel effects, such as the time in use L and the mileage H. Manufacturer warranties are typically described by a two-dimensional region in the (L, H)-plane. A proper determination of the warranty limits must be based on a two-dimensional distribution of time to failure on this plane. The aim of this paper is to demonstrate the possibility of designing individual warranties for a “nontypical” customer who has a very low or very high usage rate b = H/L, and to show a simple way to calculate warranty limits by minimizing the lifetime coefficient of variation. The latter is carried out by introducing the “best” combined time scale in the form K = (1-ε)L+εH which provides the minimal lifetime coefficient of variation.