Frontier-based performance analysis models for supply chain management: State of the art and research directions

Effective supply chain management relies on information integration and implementation of best practice techniques across the chain. Supply chains are examples of complex multi-stage systems with temporal and causal interrelations, operating multi-input and multi-output production and services under utilization of fixed and variable resources. Acknowledging the lack of system’s view, the need to identify system-wide and individual effects as well as incorporating a coherent set of performance metrics, the recent literature reports on an increasing, but yet limited, number of applications of frontier analysis models (e.g. DEA) for the performance assessment of supply chains or networks. The relevant models in this respect are multi-stage models with various assumptions on the intermediate outputs and inputs, enabling the derivation of metrics for technical and cost efficiencies for the system as well as the autonomous links. This paper reviews the state of the art in network DEA modeling, in particular two-stage models, along with a critical review of the advanced applications that are reported in terms of the consistency of the underlying assumptions and the results derived. Consolidating current work in this range using the unified notations and comparison of the properties of the presented models, the paper is closed with recommendations for future research in terms of both theory and application.     

Atmospheric transport of polybrominated diphenyl ethers and polychlorinated biphenyls to the Baltic Sea

The atmospheric transport of polybrominated diphenyl ethers (PBDEs) and polychlorinated biphenyls (PCBs) was compared by measuring concentrations in air and deposition on an island located in the central basin of the Baltic Sea. Median sigmaPBDE and sigmaPCB concentrations (gaseous + particle) were 8.6 and 7.4 pg m(-3), respectively. Airborne PCBs were mainly found in the gaseous phase, while most of the PBDEs were detected on particles, which agrees with predicted particle/gas distributions. SigmaPBDE levels were dominated by the decabrominated BDE209 followed bythe tetrabrominated BDE47 and pentabrominated BDE99. BDE209 is a marker for the environmental distribution of the commercial deca-BDE formulation (>99.5% BDE209), whereas BDE47 and BDE99 are markers for the commercial penta-BDE mixture. General correlations between PBDEs and PCBs suggested similarities in sources and transport mechanism, while more detailed examination of the data identified notable behaviors and exceptions. Differences in regression slopes among tetra-, penta-, and decabrominated PBDEs may reflect different transport processes and the change in usage pattern. Tetra- and pentabrominated PBDEs may originate from secondary sources such as air surface exchange in a manner similar to that of the PCBs, while the deca-BDE209 formulation still has primary sources. The tribrominated BDE17 was also detected and is proposed to be a breakdown product due to atmospheric debromination processes. PBDEs had higher washout ratios than PCBs, explaining their higher concentrations compared to PCBs in precipitation (median of 6.0 and 0.5 ng L(-1) for sigmaBDE and sigmaPCB concentrations ("dissolved" + particle), respectively) than in air. The calculated yearly deposition of PBDEs and PCBs indicated that the atmospheric input of PBDEs to the Baltic Proper is currently exceeding that of the PCBs by a factor of 40, while that of the PCBs is decreasing.     

Exploiting UEP in QAM-based BICM: interleaver and code design

In this paper we formally analyze the interleaver and code design for QAM-based BICM transmissions using the binary reflected Gray code. We develop analytical bounds on the bit error rate and we use them to predict the performance of BICM when unequal error protection (UEP) is introduced by the constellation labeling. Based on these bounds the optimum design of interleaver and code is found, and numerical results for representative configurations are presented. When the new design is used, the improvements may reach 2 dB, and they are obtained without any increase on the transceiver?s complexity. We also introduce the concept of generalized optimum distance spectrum convolutional codes, which are the optimum codes for QAM-based BICM transmissions.     

Computation of the exact bit-error rate of coherent M-ary PSK with Gray code bit mapping

The problem of calculating the average bit-error probability (BEP) of coherent M-ary phase-shift keying (PSK) over a Gaussian channel has been studied previously in the literature. A solution to the problem for systems using a binary reflected Gray code (BRGC) to map bits to symbols was first presented by P.J. Lee (see ibid., vol.COM-34, p.488-91, 1986). We show that the results obtained by Lee are incorrect for M/spl ges/16. We show that the reason for this is an invalid assumption that the bit-error rate (BER) is independent of the transmitted symbols, an assumption which has also propagated to textbooks. We give a new expression for the BER of M-PSK systems using the BRGC and compare this with Lee's results.     

Exhaust Gas Catalysts for Heavy-Duty Applications: Influence of the Pd Particle Size and Particle Size Distribution on the Combustion of Natural Gas and Biogas

In this study, an experimental investigation concerning exhaust gas catalysts for heavy-duty diesel engines fuelled by natural gas or biogas is presented. Miniature monoliths, 2.5 wt% Pd/Al₂O₃, have been prepared, characterised and tested. Various methods have been used in order to obtain different palladium particle sizes, including incipient wetness and microemulsion technique. Crystallite sizes between 2 and 40 nm were obtained. We observed that the metal particle size influences the activity for methane oxidation. Moreover, the homogeneity of the active material was found to affect the reaction rate.     

Upper bounds for constant-weight codes

Let A(n,d,w) denote the maximum possible number of codewords in an (n,d,w) constant-weight binary code. We improve upon the best known upper bounds on A(n,d,w) in numerous instances for n⩽24 and d⩽12, which is the parameter range of existing tables. Most improvements occur for d=8, 10, where we reduce the upper bounds in more than half of the unresolved cases. We also extend the existing tables up to n⩽28 and d⩽14. To obtain these results, we develop new techniques and introduce new classes of codes. We derive a number of general bounds on A(n,d,w) by means of mapping constant-weight codes into Euclidean space. This approach produces, among other results, a bound on A(n,d,w) that is tighter than the Johnson bound. A similar improvement over the best known bounds for doubly-constant-weight codes, studied by Johnson and Levenshtein, is obtained in the same way. Furthermore, we introduce the concept of doubly-bounded-weight codes, which may be thought of as a generalization of the doubly-constant-weight codes. Subsequently, a class of Euclidean-space codes, called zonal codes, is introduced, and a bound on the size of such codes is established. This is used to derive bounds for doubly-bounded-weight codes, which are in turn used to derive bounds on A(n,d,w). We also develop a universal method to establish constraints that augment the Delsarte inequalities for constant-weight codes, used in the linear programming bound. In addition, we present a detailed survey of known upper bounds for constant-weight codes, and sharpen these bounds in several cases. All these bounds, along with all known dependencies among them, are then combined in a coherent framework that is amenable to analysis by computer. This improves the bounds on A(n,d,w) even further for a large number of instances of n, d, and w     

Positive and normative use of fuzzy DEA‐BCC models: A critical view on NATO enlargement

Data envelopment analysis (DEA) is a widely used mathematical programming approach for comparing the input and output of a set of comparable decision‐making units (DMUs) by evaluating their relative efficiency. The traditional DEA methods require accurate measurement of both the inputs and outputs. However, the real evaluation of the DMUs is often characterized by imprecision and uncertainty in data definitions and measurements. The development of fuzzy DEA (FDEA) with imprecise and ambiguous data has extended the scope of application for efficiency measurement. The purpose of this paper is to develop a fuzzy DEA framework with a BCC model for measuring crisp and interval efficiencies in fuzzy environments. We use an α‐level approach to convert the fuzzy Banker, Charnes, and Cooper (BCC) (variable returns to scale) model into an interval programming model. Instead of comparing the equality (or inequality) of the two intervals, we define a variable in the interval to satisfy our constraints and maximize the efficiency value. We present a numerical example to show the similarities and differences between our solution and the solutions obtained from four fuzzy DEA methods in the literature. In addition, a case study for NATO enlargement is presented to illustrate the applicability of the proposed method.     

Optimal lattices for sampling

The generalization of the sampling theorem to multidimensional signals is considered, with or without bandwidth constraints. The signal is modeled as a stationary random process and sampled on a lattice. Exact expressions for the mean-square error of the best linear interpolator are given in the frequency domain. Moreover, asymptotic expansions are derived for the average mean-square error when the sampling rate tends to zero and infinity, respectively. This makes it possible to determine the optimal lattices for sampling. In the low-rate sampling case, or equivalently for rough processes, the optimal lattice is the one which solves the packing problem, whereas in the high-rate sampling case, or equivalently for smooth processes, the optimal lattice is the one which solves the dual packing problem. In addition, the best linear interpolation is compared with ideal low-pass filtering (cardinal interpolation).     

Spatial and temporal variation of polychlorinated biphenyl (PCB) in precipitation in southern Sweden

Spatial and temporal variations in polychlorinated biphenyl (PCB) concentrations were studied in precipitation at 11 sampling-sites over a period of 1 year and compared with PCB concentrations in the air. The study was carried out in a region of southern Sweden approximately 11 000 km2 in area. The PCB concentration in precipitation ranged between 1.18 and 81.4 ng l(-1). Two of the sampling sites showed concentrations that were approximately 30 times higher than at the rest of the sites. The variation in concentration between sites may be explained by location as well as by differences in weather conditions and particle content in the air. Wind direction played an important role for PCB concentration in precipitation in coastal areas, while at the inland sites this variable seemed to have a minor influence. We found no seasonal trends in PCB concentration in precipitation or any dependence on air temperature. To examine the intensity of precipitation scavenging, the total washout ratios (Wt) were calculated. There was a large variation in Wt over time, and the highest ratios were observed at the two sites where PCB concentration in the air was high. Furthermore, high concentrations of PCB in precipitation correlated with a high-chlorinated pattern, as shown by principal component analysis. For most of the sites there was a significantly negative relationship between PCB concentration and rain volume.     

The Hadamard transform-a tool for index assignment

We show that the channel distortion for maximum-entropy encoders, due to noise on a binary-symmetric channel, is minimized if the vector quantizer can be expressed as a linear transform of a hypercube. The index assignment problem is regarded as a problem of linearizing the vector quantizer. We define classes of index assignments with related properties, within which the best index assignment is found by sorting, not searching. Two powerful algorithms for assigning indices to the codevectors of nonredundant coding systems are presented. One algorithm finds the optimal solution in terms of linearity, whereas the other finds a very good, but suboptimal, solution in a very short time