Measuring aggregate process performance using AHP

When one undertakes a benchmarking study, it is quite typical to collect performance data on a set of business processes from a variety of organizations. While one can compare efficiency on a process-by-process level, how can one compare the overall efficiency of one organization versus another using this process-level data? This note presents a methodology that combines tournament ranking and Analytic Hierarchy Process (AHP) approaches to create a ranking scheme that deals explicitly with missing data and ties in the tournament scheme.     

A Case Study of a Non-Compensatory Approach to Ranking Transportation Projects

This paper examines the use of a concordance-type model for prioritizing transportation projects. In the particular case examined, multiple criteria are involved, and projects can be rated only on a qualitative basis. The model augments the well-known ELECTRA methodology with a tournament ranking procedure. The resulting procedure, known as SELECTRA, is presently being used to rank order over 200 investment projects within the Ontario Ministry of Transportation and Communications.     

Performance metrics in supply chain management

This survey paper starts with a critical analysis of various performance metrics for supply chain management (SCM), used by a specific manufacturing company. Then it summarizes how economic theory treats multiple performance metrics. Actually, the paper proposes to deal with multiple metrics in SCM via the balanced scorecard — which measures customers, internal processes, innovations, and finance. To forecast how the values of these metrics will change — once a supply chain is redesigned — simulation may be used. This paper distinguishes four simulation types for SCM: (i) spreadsheet simulation, (ii) system dynamics, (iii) discrete-event simulation, and (iv) business games. These simulation types may explain the bullwhip effect, predict fill rate values, and educate and train users. Validation of simulation models requires sensitivity analysis; a statistical methodology is proposed. The paper concludes with suggestions for a possible research agenda in SCM. A list with 50 references for further study is included.     

Order-based error for managing ensembles of surrogates in mesh adaptive direct search

We investigate surrogate-assisted strategies for global derivative-free optimization using the mesh adaptive direct search (MADS) blackbox optimization algorithm. In particular, we build an ensemble of surrogate models to be used within the search step of MADS to perform global exploration, and examine different methods for selecting the best model for a given problem at hand. To do so, we introduce an order-based error tailored to surrogate-based search. We report computational experiments for ten analytical benchmark problems and three engineering design applications. Results demonstrate that different metrics may result in different model choices and that the use of order-based metrics improves performance.     

A general framework on the simulation-based optimization under fixed computing budget

In many real world problems, the design space is huge and the estimation of performance measure has to rely on simulation which is time-consuming. Hence, to find the optimal design in the design space based on the simulation output is not trivial. It is important to have a computing time allocation rule to decide how much effort to spend in sampling the design space, how many designs to sample, and how long to run for each design alternative within a given computing budget. In this paper, we propose a framework for making these allocation decisions. We use the problem of assemble-to-order (ATO) systems to demonstrate how this framework can be applied. The sample average approximation (SAA) method is chosen as the sampling method used in this application example. The numerical results show that this framework provides a good basis for allocation decisions.     

Some third-order rotatable designs in three dimensions

Summary Some new third-order rotatable designs in three dimensions are derived from some of the available third-order rotatable designs in two dimensions. When these designs are used the results of the experiments performed according to the two-dimentional designs need not be discarded. Some of these designs may be performed sequentially in all three factors, starting with a one-dimensional design. Further, these third-order rotatable designs require a smaller number of points than most of the available three-dimensional third-order rotatable designs.     

Managing the order pipeline to reduce supply chain volatility

The bullwhip effect in particular, and supply chain volatility in general, has been the subject of much analytical and empirical investigation by researchers. One goal of this work has been to determine supply chain designs and policies that minimize volatility. Using a system dynamics approach, we use three distinct supply chain volatility metrics to compare the ability of two alternative pipeline inventory management policies to respond to a demand shock. The results indicate that no one policy dominates on all three metrics of supply chain volatility. A simplistic static pipeline policy minimizes the bullwhip effect and lessens the likelihood of on-hand inventory oscillations, while a more sophisticated dynamic pipeline policy may converge more rapidly to the new equilibrium. In addition, simulation results suggest that the dynamic policy provides better customer service through fewer stockouts and backorders.     

The U.S. Navy explores detailing cost reduction via Data Envelopment Analysis

In this paper we show how a variation of Data Envelopment Analysis, the Generalized Symmetric Weight Assignment Technique, is used to assign sailors to jobs for the U.S. Navy. This method differs from others as the assignment is a multi-objective problem where the importance of each objective, called a metric, is determined by the decision-maker and promoted within the assignment problem. We explore how the method performs as the importance of particular metrics increases. Finally, we show that the proposed method leads to substantial cost savings for the U.S. Navy without degrading the resulting assignments’ performance on other metrics.     

Evolution equations in Riemannian geometry

A fundamental question in Riemannian geometry is to find canonical metrics on a given smooth manifold. In the 1980s, R.S. Hamilton proposed an approach to this question based on parabolic partial differential equations. The goal is to start from a given initial metric and deform it to a canonical metric by means of an evolution equation. There are various natural evolution equations for Riemannian metrics, including the Ricci flow and the conformal Yamabe flow. In this survey, we discuss the global behavior of the solutions to these equations. In particular, we describe how these techniques can be used to prove the Differentiable Sphere Theorem.     

Examples of fuzzy metrics and applications

In this paper we present new examples of fuzzy metrics in the sense of George and Veeramani. The examples have been classified attending to their construction and most of the well-known fuzzy metrics are particular cases of those given here. In particular, novel fuzzy metrics, by means of fuzzy and classical metrics and certain special types of functions, are introduced. We also give an extension theorem for two fuzzy metrics that agree in its nonempty intersection. Finally, we give an application of this type of fuzzy metrics to color image processing. We propose a fuzzy metric that simultaneously takes into account two different distance criteria between color image pixels and we use this fuzzy metric to filter noisy images, obtaining promising results. This application is also illustrative of how fuzzy metrics can be used in other engineering problems.     

A black-box scatter search for optimization problems with integer variables

The goal of this work is the development of a black-box solver based on the scatter search methodology. In particular, we seek a solver capable of obtaining high quality outcomes to optimization problems for which solutions are represented as a vector of integer values. We refer to these problems as integer optimization problems. We assume that the decision variables are bounded and that there may be constraints that require that the black-box evaluator is called in order to know whether they are satisfied. Problems of this type are common in operational research areas of applications such as telecommunications, project management, engineering design and the like.Our experimental testing includes 171 instances within four classes of problems taken from the literature. The experiments compare the performance of the proposed method with both the best context-specific procedures designed for each class of problem as well as context-independent commercial software. The experiments show that the proposed solution method competes well against commercial software and that can be competitive with specialized procedures in some problem classes.     

Maximizing breaks and bounding solutions to the mirrored traveling tournament problem

We investigate the relation between two aspects of round robin tournament scheduling problems: breaks and distances. The distance minimization problem and the breaks maximization problem are equivalent when the distance between every pair of teams is equal to 1. We show how to construct schedules with a maximum number of breaks for some tournament types. The connection between breaks maximization and distance minimization is used to derive lower bounds to the mirrored traveling tournament problem and to prove the optimality of solutions found by a heuristic for the latter.     

Strategy selection and outcome prediction in sport using dynamic learning for stochastic processes

Stochastic processes are natural models for the progression of many individual and team sports. Such models have been applied successfully to select strategies and to predict outcomes in the context of games, tournaments and leagues. This information is useful to participants and gamblers, who often need to make decisions while the sports are in progress. In order to apply these models, much of the published research uses parameters estimated from historical data, thereby ignoring the uncertainty of the parameter values and the most relevant information that arises during competition. In this paper, we investigate candidate stochastic processes for familiar sporting applications that include cricket, football and badminton, reviewing existing models and offering some new suggestions. We then consider how to model parameter uncertainty with prior and posterior distributions, how to update these distributions dynamically during competition and how to use these results to make optimal decisions. Finally, we combine these ideas in a case study aimed at predicting the winners of next year’s University Boat Race.     

Construction of Hamilton Path Tournament Designs

A Hamilton path tournament design involving n teams and n/2 stadiums, is a round robin schedule on n − 1 days in which each team plays in each stadium at most twice, and the set of games played in each stadium induce a Hamilton path on n teams. Previously, Hamilton path tournament designs were shown to exist for all even n not divisible by 4, 6, or 10. Here, we give an inductive procedure for the construction of Hamilton path tournament designs for n = 2 ^p ≥ 8 teams.     

Orthogonal resolutions in odd balanced tournament designs

An odd balanced tournament design,OBTD(n), is ann × 2n + 1 array of pairs defined on a (2n + 1)-setV such that (1) every row of the array contains each element ofV twice, (2) every column of the array contains 2n distinct elements ofV, and (3) the pairs of the array form a (2n + 1, 2, 1)-BIBD. In this paper, we investigate the spectrum of odd balanced tournament designs with orthogonal resolutions. These designs can be used to construct doubly near resolvable (v, 3, 2)-BIBDs.     

Making efficient simulation experiments interactively with a desktop simulation package

It has been shown how a design of simulation experiments methodology can be used interactively with practical simulation models constructed in a desktop simulation package (SIMUL8). The methodology includes new ideas on how to improve the accuracy of a simulation response. It is implemented as a set of computer program modules that are not specific to a particular simulation model and provide an interface that lets the modeller construct an efficient simulation experiment with only an operational understanding of how the methodology works. The methodology and program modules are illustrated with a practical simulation model, and the results show how they can improve simulation response with negligible increase in computational effort.     

Random generation of tournaments and asymmetric graphs with given out-degrees

In this paper, we first present a polynomial algorithm which computes a random tournament with given out-degrees; any tournament having these out-degrees has a nonzero probability to be computed. Then we give a necessary and sufficient condition for a sequence of numbers to be the out-degrees (or similarly the in-degrees) of an asymmetric graph. Lastly, using the above algorithm and this characterization, we design a second polynomial algorithm to compute a random asymmetric graph with given out-degrees, and any asymmetric graph with these out-degrees has a nonzero probability to be found.     

Exponential number of quasi-symmetric SDP designs and codes meeting the Grey-Rankin bound

It is shown that quasi-symmetric designs which are derived or residual designs of nonisomorphic symmetric designs with the symmetric difference property are also nonisomorphic. Combined with a result by W. Kantor, this implies that the number of nonisomorphic quasi-symmetric designs with the symmetric difference property grows exponentially. The column spaces of the incidence matrices of these designs provide an exponential number of inequivalent codes meeting the Grey-Rankin bound. A transformation of quasi-symmetric designs by means of maximal arcs is described. In particular, a residual quasi-symmetric design with the symmetric difference property is transformed into a quasi-symmetric design with the same block graph but higher rank over GF(2).Dedicated to Professor Hanfried Lenz on the occasion of his 75th birthday.This paper was written while the author was at the University of Giessen as a Research Fellow of the Alexander von Humboldt Foundation, on leave from the University of Sofia, Bulgaria.