Naval Research Logistics Quarterly Research Articles

Testing decision-making skills in football using augmented reality

Decision-making skills are fundamental to successful performance in team sports. Current approaches to assess decision-making skills are incredibly resource intensive for both athletes and researchers. Athletes are required to travel to testing facilities and researchers invest time and effort to create representative experiments. A less resource intensive procedure is highly desired.
 In this study, the feasibility of an on-field decision-making task was assessed. The task was presented in augmented reality. The situations in the task were retrieved from open-source tracking data. Short sequences of build-up play were arranged into a testing battery based on a similarity score. For the similarity score, we harnessed the Kuhn-Munkres algorithm (Kuhn, 1955; Munkres, 1957) to select similar situations based on player positions and movement directions. The sampled situations preserve the natural variability experienced by football players in the performance environment. With the algorithmic approach, the need for selecting and creating situations manually was minimized.
 The display, which rendered the view of a regular 11v11 football situation was shown from the perspective of a midfield player. The content was displayed using a head mounted augmented reality device. The participant was free to move on a real football field onto which the other players were augmented as virtual avatars. The participant was presented with a freeze-frame of the situation and triggered the situation by moving into a visually designated area. Participants were instructed verbally to offer support to the ball-carrying team-mate. The situation ended with the participant receiving a virtual pass from the team-mate.
 Experienced football players were drawn from a pool of university students to participate in the study. During the experiment, the movement trajectory of the participant was recorded using IMU data retrieved from the head-mounted display. The movement patterns were analyzed using a timeseries-clustering approach to examine the characteristics of different movement solutions the participants deployed across the situations (Chow et al., 2008). Deviations from the original trajectories (i.e., the open-source data) were measured to gaze at the natural variability that occurs in build-up situations in football.
 In conclusion, the feasibility study attempted to facilitate the assessment of decision-making skills in team-sports. Two promising means were introduced: (1) The selection of the situations was automated to reduce efforts needed by the researcher. (2) The use of an augmented-reality device enabled testing directly on the field. The decision-making skills were assessed through the observed movement patterns which provided new insights on how players move when making decisions.
 References
 Chow, J. Y., Davids, K., Button, C., & Rein, R. (2008). Dynamics of movement patterning in learning a discrete multiarticular action. Motor Control, 12(3), 219-240. https://doi.org/10.1123/mcj.12.3.219
 Kuhn, H. W. (1955). The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2(1‐2), 83-97. https://doi.org/10.1002/nav.3800020109
 Munkres, J. (1957). Algorithms for the assignment and transportation problems. Journal of the Society for Industrial and Applied Mathematics, 5(1), 32-38.

Scheduling research and the first decade of NRLQ: A historical perspective

AbstractIt is generally recognized that the first model involving job scheduling was presented by Selmer Johnson and published in the inaugural issue of Naval Research Logistics Quarterly (NRLQ) in 1954. NRLQ also published another seminal scheduling paper by Wayne E. Smith a short time later. In the present paper, we discuss the contribution of NRLQ and the role of the Office of Naval Research in the development of the scheduling literature during the first decade (1954–1963). We also provide a critical analysis of the papers by Johnson and Smith. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 335–344, 2015

A Note on the Core of TU-cooperative Games with Multiple Membership Externalities

A generalization of transferable utility cooperative games from the functional forms introduced by von Neumann and Morgenstern (1944, Theory of Games and Economic Behavior) and Lucas and Thrall (1963, Naval Research Logistics Quarterly, 10, 281–298) is proposed to allow for multiple membership. The definition of the core is adapted analogously and the possibilities for the cross-cutting of contractual arrangements are illustrated and discussed.

Contributors

Contributors

Characterization of distributions through failure rate and mean residual life functions

Abstract Makino [Makino, T., 1984. Mean hazard rate and its applications to the normal approximation of the Weibull distribution. Naval Research Logistics Quarterly 31, 1–8] proves that, for any random variable X with finite mean μ , E ( 1 / r ( X ) ] ⩾ 1 / μ , where r ( ⋅ ) is the failure rate function of X , with equality if and only if X is exponentially distributed. Here we characterize exponential distribution and Rayleigh distribution through the expected values of r ( X ) and e ( X ) , where e ( ⋅ ) is the mean residual life function of X .

A generalization of sensitivity of the inventory model with partial backorders

Abstract In this paper, we use the elementary techniques of differential calculus to investigate the sensitivity analysis of Montgomery et al.’s [Montgomery, D.C., Bazaraa, M.S., Keswani, A.K., 1973. Inventory models with a mixture of backorders and lost sales. Naval Research Logistics Quarterly 20, 225–263] inventory model with a mixture of backorders and lost sales and generalize Chu and Chung’s [Chu, P., Chung, K.J., 2004. The sensitivity of the inventory model with partial backorders. European Journal of Operational Research 152, 289–295] sensitivity analysis. We provide three numerical examples to demonstrate our findings, and remark the interpretation of the global minimum of the average annual cost at which the complete backordering occurs.

Who has the power in the EU?

The European countries are in the process of reforming the EU’s institutions. If ratified, the Lisbon Treaty will have strong implications for the balance of power among member states. Building on the work of Shapley [Shapley, L.S., 1977, A Comparison of Power Indices and a Nonsymmetric Generalization. Paper P-5872. The Rand Corporation, Santa Monica] and Owen [Owen, G., 1972, Political games. Naval Research Logistics Quarterly, 18, 345–354], we present a measure of power that is based on players’ preferences and number of votes. We apply this measure to the Council of Ministers to see who wields power now and who is likely to wield power with the future voting scheme. Further, we show how a country’s power can change, based on the preferences of the agenda setter which, in this case, is the European Commission.

Technical note: A use of the complete squares method to solve and analyze a quadratic objective function with two decision variables exemplified via a deterministic inventory model with a mixture of backorders and lost sales

Several researchers have recently derived formulae for economic-order quantities (EOQs) with some variants without reference to the use of derivatives, neither for first-order necessary conditions nor for second-order sufficient conditions. In addition, this algebraic derivation immediately produces an individual formula for evaluating the minimum average annual cost. The purpose of this paper is twofold. Exemplifying a use of the complete squares method through solving and analyzing Montgomery et al.'s [Montgomery, D.C., Bazaraa, M.S., Keswani, A.C., 1973. Inventory models with a mixture of backorders and lost sales. Naval Research Logistics Quarterly 20, 255–263] model, i.e. the EOQ model taking into account the case of partial backordering first we can readily derive global optimal expressions from a non-convex quadratic cost function with two decision variables in an algebraic manner, second we can straightforwardly identify some analytic cases in a way that is not as easy to do this using calculus. A numerical example has been solved to illustrate the solution procedure. Finally, some special cases can be deduced from the EOQ model under study, and concluding remarks are drawn.

A route-based solution algorithm for dynamic user equilibrium assignments

The aim of this study is to establish a method to calculate good quality user equilibrium assignments under time varying conditions. For this purpose, it introduces a dynamic network loading method that can maintain correct flow propagation as well as flow conservation, and it shows a novel route-based solution algorithm. This novel algorithm turns out to be convenient and logically plausible compared to the conventional [Frank, M., Wolfe, P., 1956. An algorithm for quadratic programming. Naval Research Logistics Quarterly 3, 95–110] algorithm, because the former does not require evaluation of an objective function and it finds solutions maintaining correct flow propagation in the time-varying network conditions. The application of novel dynamic network loading method and solution algorithm to test networks shows that we can find high quality dynamic user equilibrium assignment. This is illustrated in an example network using the deterministic queuing model for a link performance function and associating costs and flows in a predictive way in discrete time.

NP-hardness of the single-variable-resource scheduling problem to minimize the total weighted completion time

Baker and Nuttle [K.R. Baker, H.L.W. Nuttle, Sequencing independent jobs with a single resource, Naval Research Logistics Quarterly 27 (1980) 499–510] studied the following single-variable-resource scheduling problem: sequencing n jobs for processing by a single resource to minimize a function of job completion times, when the availability of the resource varies over time. When the objective function to be minimized is the total weighted completion time, Baker and Nuttle conjectured that the problem is NP-hard. We show in this note that the conjecture is true.

Problem F2∥ Cmax with forbidden jobs in the first or last position is easy

Saadani et al. [N.E.H. Saadani, P. Baptiste, M. Moalla, The simple F2∥ C max with forbidden tasks in first or last position: A problem more complex that it seems, European Journal of Operational Research 161 (2005) 21–31] studied the classical n-job flow shop scheduling problem F2∥ C max with an additional constraint that some jobs cannot be placed in the first or last position. There exists an optimal job sequence for this problem, in which at most one job in the first or last position is deferred from its position in Johnson’s [S.M. Johnson, Optimal two- and three-stage production schedules with setup times included, Naval Research Logistics Quarterly 1 (1954) 61–68] permutation. The problem was solved in O( n 2) time by enumerating all candidate job sequences. We suggest a simple O( n) algorithm for this problem provided that Johnson’s permutation is given. Since Johnson’s permutation can be obtained in O( n log n) time, the problem in Saadani et al. (2005) can be solved in O( n log n) time as well.

IFORS' Operational Research Hall of Fame

International Transactions in Operational ResearchVolume 13, Issue 2 p. 169-174 Free Access IFORS' Operational Research Hall of Fame Egon Balas, Egon BalasSearch for more papers by this author Egon Balas, Egon BalasSearch for more papers by this author First published: 09 March 2006 https://doi.org/10.1111/j.1475-3995.2006.00541.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Selected Original Works Balas, E., 1965. An additive algorithm for solving linear programs with zero–one variables. Operations Research 13, 517– 546. Balas, E., 1969. Machine sequencing via disjunctive graphs: an implicit enumeration algorithm. Operations Research 17, 941– 957. Balas, E., 1970. Machine sequencing: disjunctive graphs and degree-constrained subgraphs. Naval Research Logistics Quarterly 17, 1– 9. Balas, E., 1974. Disjunctive programming: properties of the convex hull of feasible points. MSRR No. 348, Carnegie Mellon University, July. Also 1998. Discrete Applied Mathematics 89, 1– 44. Balas, E., 1989. The prize collecting traveling salesman problem. Networks 19, 621– 636. Balas, E., 1995. The prize collecting traveling salesman problem: II. Networks 25, 199– 216. Balas, E., Adams, J., Zawack, D., 1988. The shifting bottleneck procedure for job shop scheduling. Management Science 34, 391– 401. Balas, E., Ceria, S., Cornuéjols, G., 1993. A lift-and-project cutting plane algorithm for mixed 0–1 programs. Mathematical Programming 58, 295– 324. Balas, E., Fischetti, M., 1993. A lifting procedure for the asymmetric traveling salesman polytope and a large new class of facets. Mathematical Programming 58, 325– 352. Balas, E., Fischetti, M., 1999. Lifted cycle inequalities for the asymmetric traveling salesman problem. Mathematics of Operations Research 24, 273– 292. Balas, E., Fischetti, M., Pulleyblank, W.R., 1995. The precedence-constrained asymmetric traveling salesman polytope. Mathematical Programming 68, 241– 265. Balas, E., Pulleyblank, W.R., 1983. The perfectly matchable subgraph polytope of a bipartite graph. Networks 13, 495– 516. Balas, E., Vazacopoulos, A., 1998. Guided local search with shifting bottleneck for job shop scheduling. Management Science 44, 262– 275. Biographical Works Balas, E., 2000. Will to Freedom: A Perilous Journey through Fascism and Communism. Syracuse University Press, Syracuse, NY. Balas, E., 2002. Some thoughts on the development of integer programming during my research career. Lecture delivered upon receiving the EURO Gold Medal, July 9, 2001, Rotterdam. European Journal of Operational Research 141, 1– 7. Volume13, Issue2March 2006Pages 169-174 ReferencesRelatedInformation

A Conversation with Shelemyahu Zacks

Shelley Zacks was born in Tel Aviv on October 15, 1932. He earned his B.A. degree in statistics, mathematics and sociology from Hebrew University in 1955, an M.Sc. degree in operations research and statistics from the Technion in 1960, and a Ph.D. degree in operations research from Columbia University in 1962. He is perhaps best known for his groundbreaking articles on change-point problems, common mean problems, Bayes sequential strategies and reliability analysis. His lifelong enthusiasm in handling difficult problems arising in science and engineering has been a primary inspiration behind his most important theoretical publications. His studies on survival probabilities in crossing mine fields as well as his contributions in stochastic visibility in random fields are regarded as fundamental work in naval research and other defense related areas. Professor Zacks’ authoritative book, The Theory of Statistical Inference (1971), and its 1975 Russian translation have served graduate programs and researchers all over the globe very well for over 30 years. He has written other books and monographs, including Parametric Statistical Inference: Basic Theory and Modern Approaches (1981b), Introduction to Reliability Analysis: Probability Models and Statistical Methods (1992), Prediction Theory for Finite Populations (1992), co-authored with H. Bolfarine, Stochastic Visibility in Random Fields (1994b) and Modern Industrial Statistics: Design and Control of Quality and Reliability (1998), co-authored with R. Kenet. He is the author or co-author of more than 150 research publications. During the period 1957 through 1980, his career path took him to the Technion (Israel Institute of Technology), New York University, Stanford University, Kansas State University, University of New Mexico, Tel Aviv University, Case Western Reserve University (CWRU) and Virginia Polytechnic Institute and State University (VPI). During 1974–1979, he was a Professor and Chairman of the Department of Mathematics and Statistics at CWRU. In 1979–1980, he spent a year in the Department of Statistics at VPI. In 1980 he moved to State University of New York–Binghamton (now called Binghamton University) as Professor and Chairman of the Department of Mathematical Sciences, and he has continued in the department as Professor and Director of the Center for Statistics, Quality Control and Design. For nearly 20 years, Professor Zacks worked as a consultant for the Program in Logistics at George Washington University. Professor Zacks has held a steady stream of editorial positions for such journals as Journal of the American Statistical Association, The Annals of Statistics, Journal of Statistical Planning and Inference, Naval Research Logistics Quarterly, Communications in Statistics and Sequential Analysis. He served as the Executive Editor for Journal of Statistical Planning and Inference during 1998–2000. He has earned many honors and awards, including Fellow of the Institute of Mathematical Statistics (1974), Fellow of the American Statistical Association (1974), Fellow of the American Association for the Advancement of Science (1982) and elected membership in the International Statistical Institute (1975). He regularly travels to scientific conferences as an invited participant, works harder than many half his age, and continues to inspire through his writings and uniquely affectionate presence.

A comparison of different solution approaches to the vehicle scheduling problem in a practical case

The Vehicle Scheduling Problem (VSP) consists in assigning a set of scheduled trips to a set of vehicles, satisfying a set of constraints and optimizing an objective function. A wide literature exists for the VSP, but usually not all the practical requirements of the real cases are taken into account. In the present paper a practical case is studied, and for it a traditional method is tailored and two innovative heuristics are developed. As the problem presents a multicriteria nature, each of the three algorithms adopts a different approach to multicriteria optimization. Scalarization of the different criteria is performed by the traditional algorithm. A lexicographic approach is followed by an algorithm based on logic programming. Finally, a Pareto optimization approach is implemented by a modified genetic algorithm. All the algorithms are tested on the real problem, and two of them produce interesting practical results. Scope and purpose This paper presents the practical experience with a real case of Vehicle Scheduling Problem (VSP). The VSP is a classical optimization problem which is faced in the operational planning of public transportation systems (see for instance Dantzig and Fulkerson. Naval Research Logistics Quarterly 1954;1:217–222). It consists in assigning a set of scheduled trips to a set of available vehicles, in such a way that each trip is associated to one vehicle and a cost function is minimized. For some versions of it, such as when all vehicles are equal and share the same depot, efficient algorithms exist (see for instance Bodin et al. Computers & Operations Research 1983;10:63–212, Carraresi and Gallo. European Journal of Operational Research 1984;16:139–151); nevertheless, real-life applications often turn out to be complex, due to the particular requirements which are present in practical situations, but are hard to be modeled. Practical requirements for this problem, usually not considered in the literature, include considering several criteria, producing different alternative solutions, and getting hints on how data could be modified to improve the effectiveness of the solutions. The paper analyzes the features of the real problem and discusses different algorithmic approaches for it. It has basically two purposes. The first is to analyze, formalize and comply with the experienced requirements of the practical problem. The second consists in assessing the applicability and performance of non-conventional heuristics and of a traditional exact method.

The egalitarian solution for convex games: some characterizations

The egalitarian solution for TU-games as introduced by Dutta and Ray [Dutta, B., Ray, D., 1989. A concept of egalitarianism under participation constraints, Econometrica 57, 615–635] is studied. Five characterizations of the restriction of this solution to the class of convex games are given. They all involve a stability property due to the concept of the equal division core from Selten [Selten, R., 1972. Equal share analysis of characteristic function experiments. In: Sauermann, H. (Ed.), Beiträge zur experimentellen Wirtschaftsforschung, Vol. 3, J.C.B. Mohr, Tübingen, pp. 130–165] and all but the third characterization involve a property restricting maximum payoffs. The first two characterizations use in addition efficiency and the reduced game properties of Hart and Mas-Colell [Hart, S., Mas-Colell, A., 1989. Potential, value and consistency. Econometrica 57, 589–614] and Davis and Maschler [Davis, M., Maschler, M., 1965. The kernel of a cooperative game. Naval Research Logistics Quarterly 12, 223–259], respectively. The fourth and fifth characterization only need in addition weak variants of the reduced game properties mentioned above. The third characterization involves besides the stability condition, efficiency and a new consistency property.

Parametric linear programming and cluster analysis

In the cluster analysis problem one seeks to partition a finite set of objects into disjoint groups (or clusters) such that each group contains relatively similar objects and, relatively dissimilar objects are placed in different groups. For certain classes of the problem or, under certain assumptions, the partitioning exercise can be formulated as a sequence of linear programs (LPs), each with a parametric objective function. Such LPs can be solved using the parametric linear programming procedure developed by Gass and Saaty [(Gass, S., Saaty, T. (1955), Naval Research Logistics Quarterly 2, 39–45)]. In this paper, a parametric linear programming model for solving cluster analysis problems is presented. We show how this model can be used to find optimal solutions for certain variations of the clustering problem or, in other cases, for an approximation of the general clustering problem.

Bayesian inference for partially accelerated life tests using Gibbs sampling

We consider a life testing situation in which several groups of items are put, at different instances, on the partially accelerated life test proposed by DeGroot and Goel [ Naval Research Logistics Quarterly, 1979. 26, 223–235]. The combined failure time data are then used to derive empirical Bayes estimators for the failure of the exponential life length under normal conditions. The estimation which is implemented using the Gibbs sampler Monte-Carlo-based approach, illustrates once again the ease with which these new types of estimation problems often requiring sophisticated numerical or analytical expertise, can be handled using the sampling based approach.

Bayesian analysis of reliability and hazard rate function of a mixture model

The present article deals with the Bayesian analysis for a modified (general) Mukherji-Islam model [A finite range distribution of failure times, Naval Research Logistics Quarterly, 1983, 30, 487–491] on the basis of failure time data x 1, x 2, …, x r for a prefixed number of failures. Under the use of different prior densities for the parameter and the squared error loss function (SELF), the Bayesian estimates of hazard rate and the reliability functions are obtained, considering uniform, Gamma and inverted gamma densities as prior failure densities.

Constructing the set of efficient objective values in linear multiple objective transportation problems

Abstract A forward dynamic programming approach is utilized to find an algebraic representation for a polyhedron in objective space associated with a multiple objective transportation problem having k linear objectives. This polyhedron has the same efficient structure as the set of all feasible objective values, and moreover all of its vertices are efficient. The algebraic representation of this polyhedron is of the form {y ϵ R k : Hy ≧ Ua + Vd} , where the matrices H, U and V are independent of the vector a of availabilities and vector d of demands. The procedure is illustrated by the numerical example of Isermann [H. Isermann, “The enumeration of all efficient solutions for a linear multiple-objective transportation problem”, Naval Research Logistics Quarterly 26 (1979) 123–139].

Special Issue: Decision Support and Knowledge-Based Systems

Robert W. Blanning is Professor of Management Information Systems at the Owen Graduate School of Management at Vanderbilt University. He holds a B.S. in Physics from the Pennsylvania State University, an M.S. in Operations Research from the Case Institute of Technology, and a Ph.D. from the University of Pennsylvania, specializing in operations research and management information systems. He has been a member of the faculties of the School of Business at New York University and the Wharton School at the University of Pennsylvania. His teaching and research interests are in model management systems, information economics, and the management applications of artificial intelligence. He has published in Management Science, Decision Sciences, Communications of the ACM, Naval Research Logistics Quarterly, Decision Support Systems, Information and Management, Omega, Policy Analysis and Information Systems, International Journal of Policy and Information, Human Systems Management, Journal of Information Science, Long Range Planning, and Technological Forecasting and Social Change. He has presented papers at the National Computer Conference, the International Conference on Decision Support Systems, the Hawaii International Conference on Systems Sciences, the International Workshop on Expert Database Systems , and the International Workshop on Artificial Intelligence in Economics and Management. He is a member of the Board of Editors of JMIS, a member of the Editorial Boards of Decision Support Systems and Information Systems Research, and Associate Editor of Information and Decision Technologies and in the Decision Support Systems Department of Management Science.