Jeffrey B Goldberg

Interests

Research

- Models to evaluate the best placement of emergency services, such as fire stations.- Models for approximating performance of spatial queueing systems, such as those in automated factories and service systems.- Mathematical programming models of products and processes to improve production systems design and operation. - Mathematical models used to make decisions in games of chance.- Design of standard modules for manufacturing.- Design of products for manufacturability; i.e. economical and efficient manufacture.

Teaching

- Design of educational systems that are effective for students, instructors, and society.- Active learning and inverted classroom strategies- Using web-based content alone and in conjunction with live classroom teaching

Courses

Scholarly Contributions

Journals/Publications

• Goldberg, J., Raub, R. M., & Goldberg, J. B. (2012). Assessment of metformin as an additional treatment to therapeutic lifestyle changes in pediatric patients with metabolic syndrome. Cholesterol, 2012.
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  Objective. To assess the effectiveness of metformin and therapeutic lifestyle changes (TLCs) in a clinical setting, compared to TLC alone in adolescents with metabolic syndrome (MS). Methodology. This study was a retrospective trial consisting of 60 patients, aged 8-18 years, who were treated for MS at an outpatient clinic. Two groups were formed: the metformin group (M group) and the control group (C group). The M group had been given metformin along with TLC, and the C group had been given TLC alone. Several outcome measures were obtained; the main outcome measure was measuring the change in percentile and z-score of weight and BMI. Results. There were no significant differences between the two groups at the conclusion of the study, except for height percentile (P = 0.02) and z-score (P = 0.03). Both groups showed promising significant intragroup decreases in weight z-score but BMI percentile and z-score were only significantly decreased in the M group. Conclusion. Metformin at an average dose of 1033 mg, when added to TLC, did not show any clinically important efficacy compared to TLC alone in a pediatric population with MS. However, both groups made significant changes in a positive direction, which may be solely due to TLC.
• Baygents, J. C., Goldberg, J. B., & Hunter, J. (2011). Development of the supply chain-an ap engineering experience for high school students at the state level. ASEE Annual Conference and Exposition, Conference Proceedings.
• Goldberg, J., Smalley, C. M., & Goldberg, J. B. (2008). A pilot study in the efficacy and safety of gemfibrozil in a pediatric population. Journal of clinical lipidology, 2(2).
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  Gemfibrozil reduces plasma triglycerides and raises high-density lipoprotein cholesterol (HDL-C) in adults and also reduces the incidence of cardiovascular endpoints in adults. Its efficacy in improving lipid abnormalities has not been evaluated in children.
• Shayevich, A., Goldberg, J., & Edson, J. (2008). Performance and retention of transfer engineering students. ASEE Annual Conference and Exposition, Conference Proceedings.
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  Abstract: The College of Engineering at the University of Arizona (UA) and The Engineering Program at Pima Community College (PCC) have a long history of partnership. In a typical year, nearly 100 engineering students formally transfer from PCC to UA. These students have at least 24 transfer credits. Also, UA students take single classes at PCC as the schedule may be more flexible, class sizes are smaller, and instructors have a reputation for effective instruction. In a given academic year, students who originally transferred from PCC can account for 15% of the UA engineering graduate BS degrees. This paper makes two contributions. First we describe survey results that compare key differences in PCC and UA students. Differences in age, hours working and classroom experience are clear. Also, the survey suggests key reasons why students select PCC over the UA when they actually have a choice. The second contribution is an analysis of PCC student success after transferring to the UA. We consider both graduation rates and grades in follow-on classes. This analysis is interesting since there is a UA faculty perception that students from PCC are weaker and less prepared than UA lower division students. Specifically we examine the graduation rates of the fall 1999 and fall 2000 transfer cohorts and the grades in some key junior level classes in civil and electrical engineering.
• Belshe, T., Goodhuc, J., Yeh, J., Lindberg, D., & Goldberg, J. (2007). Emergency medical services vehicle redeployment recommendation based on complete system state analysis (EMS redeploy). Proceedings of the 2006 IEEE Systems and Information Engineering Design Symposium, SIEDS'06, 298-303.
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  Abstract: Emergency Medical Services (EMS) dispatchers are given the stressful task to redeploy EMS vehicles to maintain adequate coverage of a city. Most city dispatchers perform this task by looking at a physical or computer map and forming a decision based on their experience and intuition. This can result in inefficient redeployment of vehicles costing the city wasted resources (e.g. gas. vehicle maintenance) and manpower. The purpose of this research project is to create a tool to assist dispatchers in redeploying vehicles in a quick and efficient manner through algorithm analysis of total system state. An integrated software application was created to quickly provide the dispatcher with a recommendation, and in conjunction with their experience, a final redeployment decision would be made. © 2006 IEEE.
• Domm, M., Engel, A., Pierre-Louis, P., & Goldberg, J. (2005). An integer support vector machine. Proceedings - Sixth Int. Conf. on Softw. Eng., Artificial Intelligence, Netw. and Parallel/Distributed Computing and First ACIS Int. Workshop on Self-Assembling Wireless Netw., SNPD/SAWN 2005, 2005, 144-149.
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  Abstract: Data mining is a technique to discover patterns and trends in data and can be used to create a model to predict those patterns and trends. This is particularly useful for data sets that are not amenable to traditional statistical analysis. One particular data mining task is classification, predicting a quantity that can only take on a finite number of values. An important class of binary classifiers are Support Vector Machines (SVMs). Traditional SVMs use constrained optimization to find a separating hyperplane. A new data point is classified based on which side of the separating hyperplane it happens to fall on. All SVMs try to minimize the number of potential errors the classifier will make by minimizing a sum of distances from the hyperplane. However, the actual task of classification does not place any importance on a distance. In order to model this more closely, we propose the Integer Support Vector Machine Classifier (ISVM). ISVM uses binary indicator error variables to directly minimize the number of potential errors the classifier can make. © 2005 IEEE.
• Lunday, B. J., Smith, J. C., & Goldberg, J. B. (2005). Algorithms for solving the conditional covering problem on paths. Naval Research Logistics, 52(4), 293-301.
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  Abstract: Consider the conditional covering problem on an undirected graph, where each node represents a site that must be covered by a facility, and facilities may only be established at these nodes. Each facility can cover all sites that lie within some common covering radius, except the site at which it is located. Although this problem is difficult to solve on general graphs, there exist special structures on which the problem is easily solvable. In this paper, we consider the special case in which the graph is a simple path. For the case in which facility location costs do not vary based on the site, we derive characteristics of the problem that lead to a linear-time shortest path algorithm for solving the problem. When the facility location costs vary according to the site, we provide a more complex, but still polynomial-time, dynamic programming algorithm to find the optimal solution. © 2005 Wiley Periodicals, Inc.
• Williams, B., Blowers, P., & Goldberg, J. (2004). Integrating information literacy skills into engineering courses to produce lifelong learners. ASEE Annual Conference Proceedings, 7719-7729.
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  Abstract: One criterion of the Accreditation Board for Engineering and Technology (ABET) is that engineering students must develop lifelong learning skills in order for a program to be accredited. We argue that developing information literacy skills will allow students to exert more control over their own learning within and beyond the classroom so they will develop these skills. We have developed several methods of injecting information literacy skills seamlessly into engineering courses so students will see the value of being able to find information on their own. These activities incorporate discussions on peer reviewed materials, the appropriateness of using the Web for gathering information, and databases common to a core discipline. Pre- and post-implementation evaluations by sophomore, junior, and senior engineering students from two different engineering disciplines show that the incorporation of information literacy skills strengthens students' understanding of how to find and use information in engineering contexts. Future work would investigate whether students are indeed becoming lifelong learners by surveying their use of library information tools after they graduate.
• Aronson, M., Reyes, M., & Goldberg, J. (2003). Giving back: Engaging young women Engineers in community-based design. ASEE Annual Conference Proceedings, 5277-5286.
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  Abstract: Starting in 2001, the Virtual Development Center (VDC) at the University of Arizona committed itself to increasing retention of women students through improving the quality of educational experiences. Our approach was to develop programming and coursework for cohorts of women engineering undergraduates. We focus on opportunities both within and outside the curriculum spanning the 4 undergraduate years: in building community during the freshman year, and in building commitment to engineering by focusing on community projects during the sophomore, junior, and senior years. At this point, we have implemented our junior and senior programs. The basic process starts with a 1-day "innovation workshop" led by facilitators from the Institute for Women and Technology. Next we have a 1-semester class organized around getting to know the client and developing a needs statement and a requirements document. We finish with a 1-year class where a team designs and builds a system or device to meet all requirements. Our first VDC team had six women students and engaged in developing an information system for a "Promotora" group in Nogales Arizona (providers of lay health care and health information). The team completed development of a requirements document in May 2002 and this has since been passed to a mixed-gender design team (led by women from our team). The project will be completed in May 2003. We ramped up the requirements-design cycle with fifteen new students and three new clients in November 2002. This paper outlines the rationale for this work, describes the specific approaches, goals, and outcomes of our early program activities, and reports on our early evaluation efforts.
• Goldberg, J. (2003). Bachelor of arts in engineering program at the university of Arizona. ASEE Annual Conference Proceedings, 5541-5556.
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  Abstract: In this paper, we report the progress of the Bachelor of Arts in Engineering (BAE) Program (formerly named the ELITE program - Engineering with Liberal and Technical Education). The program is novel in that it leads to a BA in Engineering degree at the University of Arizona, a large land-grant institution. We have 25 students and we are becoming more established on campus with each additional semester. We have had 24 graduates with placement in both industry and graduate school. Each year approximately 60 students hear our informational presentations and seek information about the program. The program allows students exceptional flexibility in designing a degree program to meet their needs. Requirements ensure that-the students cover areas within engineering and outside of engineering and we focus on the application of technology. Our requirements are designed to be agile in that students can quickly piece together degree programs in "hot" areas. We have formulated research questions based on the needs of our key stakeholders. In this report, we present initial findings on three of the questions. Our results suggest that we are achieving our mission of keeping high quality students in engineering related fields and we have succeeded at developing and operating a program that allows students an opportunity to tailor an educational experience to their direct needs. We also have areas where we could improve, and suggestions and strategies are included.
• Wang, F., Lai, G., Frank, W. u., Goldberg, J., Bahill, A. T., & Gao, H. (2003). Distance learning of engineering courses with web-based real experimental experience. ASEE Annual Conference Proceedings, 8063-8073.
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  Abstract: Distance learning has been greatly enhanced through the use of the Internet. In Arizona, a joint effort has been made by the three state universities to offer a Master of Engineering Degree primarily through Internet and video distance learning. However, engineering courses often use hands-on laboratory projects with actual physical systems as an integral part of the curriculum and learning process. It is difficult to include these labs in web-based instruction unless one uses simulations or virtual experiments. This paper presents the development of web-based lab projects with actual hardware for courses in linear systems and systems control. Students download control programs to the equipment. Sensor data and a streaming video of the ongoing equipment are transmitted back to the student. The approach allows a higher utilization of lab equipment, saves student travel time, and provides an effective tool for learning as students can debug programs based on visual and sensor information. This development has been jointly conducted in the University of Arizona's Web-based Audio Video Educational Systems (WAVES) Laboratory and the Chinese Academy of Sciences' Complex Systems and Intelligence Science Laboratory. The web site for the materials is: http://pallas.sie. arizona.edu/newwaves/ and the work has been supported by an NSF CRCD grant and an Outstanding Scientist Program grant from the State Planning and Development Commission of China. We focus on system architecture, programming environment, user interface, application and experience in course instruction.
• Goldberg, J., Jolma, C. D., Samson, R. A., Klewer, S. E., Donnerstein, R. L., & Goldberg, J. B. (2002). Acute cardiac effects of nicotine in healthy young adults. Echocardiography (Mount Kisco, N.Y.), 19(6).
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  Nicotine is known to have many physiologic effects. The influence of nicotine delivered in chewing gum upon cardiac hemodynamics and conduction has not been well-characterized.
• Goldberg, J., Klewer, S. E., Samson, R. A., Donnerstein, R. L., Lax, D., Zamora, R., & Goldberg, J. B. (2002). Comparison of accuracy of diagnosis of congenital heart disease by history and physical examination versus echocardiography. The American journal of cardiology, 89(11).
• Fitzpatrick, E., Askin, R., & Goldberg, J. (2001). Using student conative behaviors and technical skills to form effective project teams. Proceedings - Frontiers in Education Conference, 3, S2G/8-S2G/13.
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  Abstract: Throughout much of the past century, manufacturing efficiencies were gained by constructing systems from independently designed and optimized tasks. Recent theories and practice have extolled the virtues of team-based practices that rely on human flexibility and empowerment to improve system performance. The formation of teams requires the consideration of innate tendencies and interpersonal skills as well as technical skills. In this paper, we discuss an experiment that was run for developing effective student teams. We used the Kolbe Index to help ensure that student conative tendencies are considered along with technical skills. We then developed and solved mathematical programming models to form effective teams. The method can easily moved to an industrial setting.
• Goldberg, J. (1999). Engineering economics on the web. ASEE Annual Conference Proceedings, 2111-2117.
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  Abstract: In Fall 1996, an NSF workshop on Engineering Economics and Design 1 was presented in conjunction with the Salt Lake City FIE Meeting. At that workshop, multimedia instructional material was used and given to the participants. In this paper, we present an outgrowth of that multimedia material - the development of a web site for engineering economics. The site is located at www.sie.arizona.edu/sie265. The site was first designed to supplement a one semester (45 hour) course and was then expanded to enable use as a stand-alone course. Materials included in the site include a set of lecture notes and alternate explanations, homework assignments and solutions, example exams and solutions, class organization, spreadsheet downloads for experimentation, learning tools for special topics, and links to sites with engineering economics data and topics. During the first semester of use with an accompanying lecture, students extensively evaluated the site and textual materials and the navigation interface were changed to be more effective. The site was used as a stand alone course during the summer 1998 term (5 weeks) and results on student outcomes from a final exam given to three student groups - no web usage, lecture-web usage, and web only usage is included. Usage statistics for various portions of the site from both groups and estimates of time on the system are also included.
• Goldberg, J. (1998). Engineering economics on the web - progress report. Proceedings - Frontiers in Education Conference, 1, 198-.
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  Abstract: A Web site for the course SIE 265 Engineering Economic Analysis is developed. The site is acts as a stand-alone learning tool for students to use to learn the course material. The design and evaluation of site for progress report are discussed.
• Sen, S., Goldberg, J., Higle, J., & Ferrell, R. (1998). Progress with B.A. in Engineering (ELITE) at the University of Arizona. Proceedings - Frontiers in Education Conference, 2, 953-.
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  Abstract: The University of Arizona is offering a new program that allows students to combine engineering as well as liberal arts, leading to a Bachelor of Arts in Engineering (ELITE). Due to the difficulty of the students to form cohorts, they are required to participate in innovative seminar series in which various non-traditional applications of engineering are discussed. The seminars not only provide the student a broad exposure to the applications of engineering, but also help create a sense of attachment with the program. The design and delivery of these seminars are presented.
• Ghamasaee, R., & Goldberg, J. B. (1997). Convergence of the synaptic weights for the elastic net method, and its application. Proceedings of SPIE - The International Society for Optical Engineering, 3069, 145-153.
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  Abstract: Solution procedures for the traveling salesman problem (TSP), i.e. the problem of finding the minimum Hamiltonian circuit in a network of cities, can be divided into two categories: exact methods and approximate (or heuristic) methods. Since TSP is an NP hard problem, good heuristic approaches are of interest. The neural networks heuristic solutions of TSP was initiated by Hopfield and Tank. One such heuristic called the elastic net method is illustrated by the following, an imaginary rubber band is placed at the centroid of the distribution of n cities. Then some finite number (m greater than n) of points (nodes) on this rubber band changes their positions according to the dynamics of the method. Eventually they describe a tour around the cities. We express the dynamics and stability of the elastic net algorithm. We show that if a unique node is converging to a city, then the synaptic strength between them approaches one. Then we generalize to the case where more than one node converges to a city. Furthermore, a typical application that could make use of the elastic net method (e.g. multi-target tracking) will be pointed out for later studies. In order to verify the proof of the concept and the associated theorems, computer simulations were conducted for a reasonable number of cities. ©2004 Copyright SPIE - The International Society for Optical Engineering.
• Jaeger, M., & Goldberg, J. (1997). Polynomial algorithms for center location on spheres. Naval Research Logistics, 44(4), 341-352.
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  Abstract: When locating facilities over the earth or in space, a planar location model is no longer valid and we must use a spherical surface. In this article, we consider the oneand two-center problems on a sphere that contains n demand points. The problem is to locate facilities to minimize the maximum distance from any demand point to the closest facility. We present an O(n) algorithm for the one-center problem when a hemisphere contains all demand points and also give an O(n) algorithm for determining whether or not the hemisphere property holds. We present an O(n3 log n) algorithm for the two-center problem for arbitrarily located demand points. Finally, we show that for general p, the p center on a sphere problem is NP-hard. © 1997 John Wiley & Sons, Inc.
• Sen, S., Higle, J. L., Goldberg, J. B., & Ferrell, W. (1996). Engineering with liberal and technical education (ELITE). Proceedings - Frontiers in Education Conference, 2, 545-548.
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  Abstract: We discuss a new project that will enable students at the University of Arizona to plan a course of study that reflects their interests in the arts, humanities, business or social sciences, and applications of engineering methods to these disciplines. By providing a well rounded education that combines the quantitative analytical approach of engineering with the societal and cultural dimensions of the traditional liberal arts, the ELITE program will prepare graduates who have the breadth of vision to lead this nation into the twenty-first century. The project will include an innovative seminar series that provides an in-depth examination of the social context within which engineering is carried out. The new program will lead to a Bachelor of Arts in Engineering. Graduates of this program are expected to be involved in the service sector, with applications in banking, entertainment, finance, health care, public policy and many more. On an experimental level, we will attempt to demonstrate that it is possible to increase student demand for engineering, recruit and retain a greater percentage of women and minorities, and attain a higher graduation rate by increasing the degree of flexibility in engineering education.
• Askin, R. G., Mitwasi, G., & Goldberg, J. B. (1993). Determining the number of kanbans in multi-item just-in-time systems. IIE Transactions (Institute of Industrial Engineers), 25(1), 89-98.
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  Abstract: Kanbans (cards) are one means of controlling Just-in-time production systems. The kanbans serve as production authorization orders and essentially become the information system. The presence of a production ordering kanban for a specific part type constitutes an instruction to the workcenter to produce a 'container' of that part. In this paper are assume workcenters produce multiple part types and address the issue o f the number of kanbans needed for each part type. Our objective is to minimize the sum of inventory holding and backorder cost. A stochastic model is formulated. Steady-state results are derived for the cases of a few and many part types. Modifications for the case of expediting of backorders are also provided. Simulation results demonstrate the accuracy of the model for a large number of kanbans, but an investigation of a finite population queueing model for small numbers of kanbans is suggested as a worthwhile extension.
• Askin, R. G., Cresswell, S. H., Goldberg, J. B., & Vakharia, A. J. (1991). Hamiltonian path approach to reordering the part-machine matrix for cellular manufacturing. International Journal of Production Research, 29(6), 1081-1100.
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  Abstract: The formation of machine and part groups is a central issue in the design of cellular manufacturing systems. The part-machine incidence matrix has formed the basis of several techniques for cell formation. In this paper, we propose formulating machine and part ordering as a Hamiltonian Path Problem. Similarity coefficients are used to form a distance measure for machines and parts. The resulting solutions are shown to be better than those obtained from binary clustering on a set of test problems.
• Cheh, K. M., Goldberg, J. B., & Askin, R. G. (1991). A note on the effect of neighborhood structure in simulated annealing. Computers and Operations Research, 18(6), 537-547.
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  Abstract: The simulated annealing method is a neighborhood search algorithm that can be used as a heuristic for many combinatorial problems. Recent research has concentrated on the viability of the approach and the appropriate algorithm parameter settings to use in implementation. In this note we consider a problem specific parameter; the neighborhood structure. We motivate the importance of considering the neighborhood by appealing to results on the convergence rate of simulated annealing and previous empirical results. We test several neighborhood structures on four different problems: the traveling salesman problem, the quadratic assignment problem, the quadratic selection problem and the stochastic quadratic selection problem. Our results suggest that for these problem classes and the particular annealing schedule used, small neighborhoods are better. © 1991.
• Goldberg, J. (1991). The continuous modular design problem with linear separable side constraints. European Journal of Operational Research, 54(2), 210-226.
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  Abstract: This paper describes a heuristic for designing a single module in the presence of linear side constraints and nonlinear requirements constraints. The objective is to minimize the total parts cost to satisfy demand for a set of end products. We model the problem as a nonconvex programming problem and show that the problem can be transformed into an equivalent convex problem. Due to the size of the potential applications we develop a heuristic procedure that is an extension of the Shaftel and Thompson algorithm. Closed form expressions are derived for determining feasible movement directions and step lengths. Computational results are promising since the CPU time required to run the heuristic is small and the solutions compared favorably with solutions generated by standard nonlinear programming software. © 1991.
• Goldberg, J., & Paz, L. (1991). Locating emergency vehicle bases when service time depends on call location. Transportation Science, 25(4), 264-280.
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  Abstract: This paper deals with the problem of locating emergency vehicles in an urban area. We formulate an optimization model that extends previous work by allowing stochastic travel times, unequal vehicle utilizations, various call types, and service times that depend on call location. The basis of the model is a procedure for approximating the performance of spatially distributed queueing systems. In previous work the model has been validated using data from the Tucson Emergency Medical Services (EMS). We test the computational effectiveness of pairwise interchange heuristics on 192 test problems. Demand and service time components of the test data are generated using characteristics of the Tucson data set. For these test problems, simple pairwise interchange techniques yield reasonable solutions with little computational effort. Also solutions obtained from the model differ from those generated using methods previously presented in the literature.
• Goldberg, J., & Szidarovszky, F. (1991). Methods for solving nonlinear equations used in evaluating emergency vehicle busy probabilities. Operations Research, 39(6), 903-916.
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  PMID: 10116044;Abstract: In this paper we present two iterative methods for solving a model to evaluate busy probabilities for Emergency Medical Service (EMS) vehicles. The model considers location dependent service times and is an alternative to the mean service calibration method; a procedure, used with the Hypercube Model, to accommodate travel times and location-dependent service times. We use monotonicity arguments to prove that one iterative method always converges to a solution. A large computational experiment suggests that both methods work satisfactorily in EMS systems with low ambulance busy probabilities and the method that always converges to a solution performs significantly better in EMS systems with high busy probabilities.
• Goldberg, J., Dietrich, R., Chen, J. M., Mitwasi, M., Valenzuela, T., & Criss, E. (1990). A simulation model for evaluating a set of emergency vehicle base locations: Development, validation, and usage. Socio-Economic Planning Sciences, 24(2), 125-141.
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  PMID: 10108911;Abstract: This paper describes our experiences in developing a simulation model for evaluating a set of emergency response vehicle base locations. The project was undertaken jointly by the University of Arizona and the Tucson Fire Department. The issues of model development, data collection, model validation, and experimentation are discussed. The critical nature of the problem and the clients' lack of experience with mathematical models, made model validation (he major step in gaining user acceptance. We show that looking solely at standard performance statistics such as the calls successfully serviced, may lead to the acceptance of an invalid model. We also show that the high level of detail used in many simulation models for evaluating bu.se locations is unnecessary in the current case. An analysis evaluating two alternative sets of locations for the Tucson system is discussed. © 1990.
• Goldberg, J., Dietrich, R., Chen, J. M., Mitwasi, M., Valenzuela, T., & Criss, E. (1990). Validating and applying a model for locating emergency medical vehicles in Tuczon, AZ. European Journal of Operational Research, 49(3), 308-324.
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  Abstract: This paper deals with the problem of locating emergency medical vehicles in Tuczon, AZ. The model is based on a general service time approximation model for spatially distributed queueing systems. Provisions for unequal vehicle utilizations, stochastic travel times, and multiple call classes are included. The model is tailored for emergency medical systems that experience low vehicle utilizations. Validation of the model using the Tucson system is discussed in detail. The predictive ability of the model is demonstrated by comparing model output with actual system data. The model has been used to evaluate potential changes in the paramedic services provided by the Tucson Emergency Medical System and two cases are discussed. © 1990.
• Valenzuela, T. D., Goldberg, J., Keeley, K. T., & Criss, E. A. (1990). Computer modeling of emergency medical system performance. Annals of Emergency Medicine, 19(8), 898-901.
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  PMID: 2372172;Abstract: Emergency medical services (EMS) system managers face difficult problems when determining the need for system expansion and unit deployment. Information relevant to the decision is often limited and frequently not in a usable format. This lack of usable information often results in decisions that create less-than-optimal EMS systems. A constant search for greater efficiency prompted the development of a computer simulation model to analyze the current EMS system operated by the Tucson Fire Department and to provide statistical information on the effects of potential vehicle base locations on system performance. The simulation model generates data that reflect a variety of parameters necessary in base location analysis. Included in the performance statistics for each unit and for the entire system are indicators of unit use rates, minimum and maximum response times, and proportion of calls reached within the critical response time of eight minutes or less. The model has been carefully validated and used in unit redeployment and unit activation in Tucson, Arizona. © 1990 American College of Emergency Physicians.
• Goldberg, J., & Zhu, J. (1989). Module design with substitute parts and multiple vendors. European Journal of Operational Research, 41(3), 335-346.
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  Abstract: In this paper, we present a model to design a single standard module when many parts can satisfy a particular technical requirement and parts may be purchased from a variety of vendors. The model attempts to minimize the total fixed costs for using vendors and parts, and the total variable costs for parts. Technical requirements for the set of products are modeled by requiring a miniml number of parts from each substitution group in each product. Also, life cycle demand must be met. We present an algorithm and a heuristic to solve the model. We include initial computational results that demonstrate that the heuristic performs well on the problems tested. © 1989.
• Goldberg, J., & Zhu, J. (1987). DECISION SUPPORT MODEL FOR DESIGNING MODULES WHEN SUBSTITUTED PARTS AND MULTIPLE VENDORS ARE PRESENT.. Array, 486-491.
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  Abstract: The design of standard integrated-circuit modules for an entire product line is examined as an alternative to individual product design. A model is presented for designing a single standard module when many parts can satisfy a particular technical requirement and parts may be purchased from a variety of vendors. This is important in defense-related industries, where there is a high fixed charge when the designer uses a part from an unapproved vendor list. The model attempts to minimize the total fixed costs for using vendors and parts as well as the total variable costs for parts. Technical requirements for the set of end items are modeled by requiring that each end item be designed with a minimal number of parts from each substitution group. Life cycle demand must also be met. A solution heuristic that decomposes the problem into a set-covering problem and a simpler modular design problem is presented. Some initial computational results that are encouraging are included.
• Taqqu, M. S., & Goldberg, J. B. (1982). Regular multigraphs and their application to the Monte Carlo evaluation of moments of non-linear functions of Gaussian random variables. Stochastic Processes and their Applications, 13(2), 121-138.
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  Abstract: This paper expands on the multigraph method for expressing moments of non-linear functions of Gaussian random variables. In particular, it includes a list of regular multigraphs that is needed for the computation of some of these moments. The multigraph method is then used to evaluate numerically the moments of non-Gaussian self-similar processes. These self-similar processes are of interest in various applications and the numerical value of their marginal moments yield qualitative information about the behavior of the probability tails of their marginal distributions. © 1982.