OR/MS Today - February 1997 - Military Analysis

February 1997 € Volume 24 € Number 1

Mission (Not) Impossible

Changing technologies, capabilities and perceived threats in the post-Cold War era have complicated the role of the armed forces, reinforcing the need to teach graduate-level operation research to today's military analysts.

By Lt. Col. Jack M. Kloeber Jr., USA

Does the military analyst need graduate study in operations research? Consider the following scenario, just one of a multitude of issues modern military analysts face every day as they deal with constantly changing technology, weapon systems, perceived threats and missions.

Our nation's ability to quickly react to military situations around the world depends significantly upon our airlift capability. Our cargo planes, including C-130, C-141 and the C-5, were designed both for cargo transportation and for airmobile and airborne operations. In airmobile operations, aircraft land and rapidly deplane soldiers and offload equipment. In airborne operations, soldiers and equipment are dropped into the combat zone. These aircraft produce trailing wing-tip vortices. Because large unit airborne operations always involve trailing aircraft in a formation, parachutist-vortex encounters need to be modeled to enable design of formations that maximize parachutist safety. Tactical constraints are also extremely important. If there is too much distance (and thus time) between aircraft, the opposing forces will discover the air-drop and react accordingly, drastically decreasing the jumpers' chances of survival.

The Air Force Institute of Technology, located at Wright-Patterson Air Force Base in Ohio, has assembled a five-person team to examine the parachutist-vortex issue. The objective of the study is to discover:

What is the probability of parachutist-vortex encounters?
Is this probability sensitive to a few varied parameters (distance between aircraft, speed, vertical distance, etc.)?
What is the best (x,y,z) position for the trailing aircraft, with respect to the lead aircraft, given the tactical constraints?

A study of this type calls for a multidisciplinary approach. Team members have education in statistics, design of experiments, ANOVA, differential equations for modeling the movement of the generated vortices, aerodynamics and simulation modeling, as well as an intimate knowledge of airborne operations and tactical/operational experience.

The five-person team constructed by AFIT includes two Air Force officers who are currently master's-degree students (one of them an experienced C-141 pilot), a civilian Ph.D. who is an expert in differential equation modeling of vortices, a Ph.D. analyst Army officer with experience in combat arms operations and object-oriented simulation, and a Ph.D. Air Force simulation expert who is also an experienced C-5 pilot. The C-5 pilot serves as the team leader. Pulling together such an appropriate pool of experts may seem difficult, but it is commonplace at the AFIT where every member of the team described above is either a student or an instructor. (Fifty percent of the AFIT instructors are active duty military officers).

From use of video tapes, past documentation and a well-designed experiment with dummy jumpers, the team discovered that parachutist-vortex interactions can and do occur for all aircraft during a large, brigade-level airborne operation. Here, the size of the operation matters since the number of vortices increases as the number of aircraft increases. Given an interaction, the effects can range from a minor change in direction of the parachutist to a rapid and sudden translation.

With the effects documented, the challenge was to model the physical events and then to tweak the important parameters to find the optimal positioning of aircraft given the tactical and physical constraints. Because the movement of the vortices as well as the actual timing and location of the jumpers are probabilistic, a simulation was selected as the analysis tool of choice. Object-oriented simulation fits the situation because of the requirements for reusability, portability, and a mixing of continuous time and discrete event modeling. The master's degree students had just finished a course in object-oriented simulation theory, using the MODSIM II language, and had already successfully navigated the optimization and statistics courses. They built the model using validated vortex propagation equations from the Air Force, and verified and validated parachute jumper position equations from the Army.

The students have designed the object-oriented simulation study, have successfully modeled the paths of the vortices and the jumpers, and are now collecting encounter data for the different scenarios. A response surface from this data will be invaluable to mission planners for evaluating the risk of using alternative aircraft formations. Optimization on this response surface may be used to create a new, tactically sound and safer formation.

The above study is an indication of how invaluable the graduate-level analysts are who have military experience and are deeply interested in the defense-related problems being attacked. It is well known that operations research owes its name to mathematical models and solution techniques developed for military operations during World War II when top analysts (e.g., George Dantzig) worked on tough air, ground and sea operational problems for the Allies. Famous military problems such as underwater search techniques, cargo aircraft scheduling and the timing of the insertion of reinforcements were interesting, difficult and important issues -- a perfect combination for a mix of mathematicians, statisticians and physicists.

Since the 1940s, new techniques have been developed to solve the military's problems. As the mission, capability, size, and perceived threat of the military services have changed, the use of operations research has also changed. The military operations research community again finds itself in the midst of sweeping changes as the nation and the military become accustomed to analysis after the Cold War. Today's critical problems:

Sufficient forces (number of fleets, aircraft wings, divisions).
Proper high level force structure (types of fleets, types of aircraft wings, types of divisions).
Proper internal force structure given the mission and other constraints such as weight, fuel usage, compatibility, cost, and manpower requirements.
Information warfare -- What is it? How do we measure it? How do we model it? What are the specific problems with incorporating it with more classical warfare?
Doctrine -- How should it be changed, how should it be measured, how dependent upon technology is it?
How far do we take Joint Operations and Doctrine?

Combat Modeling
There is an ongoing mission of modeling (for describing and predicting) the results of combat. High level combat (i.e., theater-level) is often modeled using Lanchester Equations -- systems of ordinary differential equations, each of which describes the continuous loss of weapon systems as a function of other friendly and enemy forces. Methods used in thermodynamics and predator-prey models can be applied here with either simple homogeneous equations or quite complicated heterogeneous equations with many different weapons systems affecting the loss rate of each type of weapon system. Some models allow reinforcements and withdrawals to be accomplished automatically. Numerical and/or analytical solutions have been compared to empirical battle results with surprisingly close correlation [9, 8 and 5].

Downsizing
With a decrease in numbers in all services, a large base realignment and closure commission (BRAC) used a variety of OR tools to develop an acceptable plan which met all of the constraints of the downsizing of the military [2]. Facility location techniques were used which included the economic effects of closing or downsizing any of the bases, posts and forts around the world. These effects involved not only Army, Navy and Air Force budgets and operational capability, but the effects upon the local, regional and state communities.

The acquisition environment has changed from determining whether or not a weapon system is needed by doing a complete cost and operational effectiveness analysis (COEA) to doing an analysis of the trade-offs between competing alternative weapons systems. Alternative analysis recognizes the severe resource constraints that exist and places the difficult trade-offs that have to be made into the forefront of the analysis. Multiattribute decision-making and decision analysis now are key OR methodologies in this arena.

Logistics Modeling
Getting equipment to the battle area, referred to as a theater, is a complex mission that needs continuous improvement. The area of logistics modeling and subsequent optimization keeps many analysts busy DoD-wide. A single major regional conflict (MRC) requires coordination of all modes of transportation, supply and materiel handling. Networks of ports of embarkation and debarkation are often used which consider sea, air, rail and highway transportation. Levels of flows limited by port capacities (air, sea, railheads), arc capacities (highways, railroads) and supply capacities (factories and redistribution of combat resources) all need to be modeled and subsequently analyzed. Uncertainty arises from :

Unknown enemy location -- Which country we will be fighting?
Unknown enemy capability -- e.g. size of navy, air superiority.
Unknown size of conflict -- e.g. company to division to corps to army.
Unknown number of conflicts -- We are tied to the bottom-up review which assumes two nearly simultaneous major regional conflicts.

Such uncertainty suggests more stochastic approaches to modeling and analysis. Analysts are forced to give advice to commanders and decision-makers based upon large sensitivity analyses (usually one-way) of deterministic models or to work with more mathematically intractable stochastic models that attempt to include some of the uncertainties. Stochastic optimization is seen as a key tool for future logistics analysts. Peacetime operations which include humanitarian support (hurricane relief in Florida in 1994 and the refugees in Zaire), and operations other than war (both the Haiti and Bosnian efforts are good examples), all need modeling to assist decision-makers in planning support requirements and for gaming responses to possible but unexpected situations. Game theory, simulation and decision analysis all help the analyst provide some kind of quantitative decision support.

A class of costs that was uniformly underestimated was that of environmental cleanup of the closed bases before they could be declared "green" and given back to the community. Environmental restoration of not only the closed bases but also of the known sites at operating bases has become a new area of research and analysis. Responsible bases are receiving help from uniformed analysts in selecting remediation techniques, testing and evaluation of those tests to decide if remediation is necessary at all, and finally, scheduling and project management for the actual restoration. Two such analysis agencies which require uniformed analysts with appropriate graduate degrees are the AF Center for Environmental Excellence, Brooks Air Force Base, Texas, and the Army Center for Environmental Studies, Fort Leonard Wood, Mo.

The military analyst faces the same problems as the civilian analyst with respect to "selling" the analysis to the appropriate decision-maker. As more decision-makers (i.e. generals and admirals) become more familiar with the value and possibilities of good OR analysis, more analysis is being requested and, one would hope, more decisions are being made using this analysis. Analysts are also being challenged to provide more understandable and user-friendly results and to work with the decision-maker throughout the analysis rather than presenting a result at the end of an analysis.

Ongoing Research
One example of an area that has increased interest and which has several large analysis or modeling efforts ongoing is combat modeling and simulation. One effort is to model combat as a stochastic process using Markov chains with discrete state spaces and continuous time. CJ Ancker, Yang and Gafarian have initiated and made great strides in this area [1 and 4]. Other efforts attempt to model information and information warfare. Models that allow perceptions, rather than ground truth, to affect decisions and actions are being investigated. Adjudication of combat in efforts such as JSTOCHWAR (Joint Stochastic Warfare) is handled using ground truth rather than perceptions.

Several very large combat modeling efforts are being pursued by the Department of Defense. These projects are JSIMS (Joint Simulation System, mainly for training), JMASS (Joint Modeling And Simulation System, expressly for high resolution acquisition ), and JWARS (Joint Warfare Simulation). JWARS is a long-range project that will enable a variable resolution plug-and-play simulation to be run in an object-oriented environment. All of these studies require analysts and modelers that are experienced in military operations (all services), knowledgeable in modeling techniques, and capable of designing a simulation study and analyzing the results. Uniformed analysts with the required educational preparation satisfy these requirements.

Clearly, not every uniformed military analyst with a graduate degree can attack all of the problems outlined in this article. Some problems are better handled by experts outside of the military who have experience in that area. Each service depends upon civilian experts, with varying education levels, for analysis, experimentation and research. Research centers such as Los Alamos National Laboratories, Armstrong Laboratories and Waterways Experimental Station are staffed predominately with civilian researchers. Other analysis agencies such as Concepts Analysis Agency (CAA), Air Force Studies and Analyses Agency (AFSAA) and the Center for Naval Analysis (CNA) have a very large contingent of military analysts.

Because over 100 officers per year achieve a master's degree in OR or a closely related major, the military has an educated "bench" upon which to call. These graduates, combined with a handful of Ph.D. graduates each year from each service, represent an important corps of militarily savvy and theoretically sound analysts. The military experience is obtained through leadership, management and tough decision-making in military units. The education is achieved through either fully funded, full-time or partially funded, part-time programs (see accompanying story).

Conclusions
As shown in the airlift example and other problems briefly discussed in this article, operations research theory and techniques are critically important to the Army, Navy, Air Force and Marines. Most, if not all, of these problems need analysts and modelers that have experience in the specific military area, a general understanding of the environment in which the solutions will be used, a good foundation in OR methodology, and the confidence to design, conduct and close an independent study. Uniformed officers have adequate experience in the problem areas but unquestionably need to combine this with educational experience at the graduate level to meet the current needs of the Department of Defense. Often teams of civilian experts and educated military analysts are the appropriate solution for solving the larger problems. Indications are that the future military world will require even more analysis, hopefully allowing us to be more efficient, more effective, and be able to make and support more complex and uncertain decisions.

Military Match-Ups Following are examples of match-ups of OR methodologies and educational areas and military problems:

Simulation -- Deciding upon the mix of weapons built into the new Joint Strike Fighter by simulating different characteristics of weapons and running the model in different scenarios and missions.
Response Surface Methodology -- Using multiple runs of a large theater-level model, Thunder, to build a response surface allowing quick analysis of effects of changes in air apportionment [3].
Linear Programming/Integer programming -- Planning capacity and scheduling of training courses throughout the individual but dependent training bases for the U.S. Army [6].
Integer Programming -- Organization, location and manning of the recruiting hierarchy including individual recruiting stations, recruiting companies, battalions and brigades.
Queueing Theory -- Establishing policies for sending in resupply aircraft to small airfields with maximum on ground (MOG) limits. For example, the airfield at Haiti had a MOG of 3 C-5s.
Decision Analysis -- A recent study was completed that looked at methods for considering the counterproliferation effects of weapons of mass destruction when evaluating new systems [7].

References

Ancker, C.J., "A Proposed Foundation for a Theory of Combat," Warfare Modeling, Military Operations Research Society, eds. Bracken, Kress, and Rosenthal, 1996.
Department of Defense, "Base Closure and Realignment Report," March 1995.
Forsythe, Steven, "Optimization of the Air Apportionment in a TAC THUNDER Scenario using Response Surface Methodology," master's thesis, Air Force Institute of Technology, WPAFB, Ohio, March, 1994.
Yang, J., and Gafarian, A., "A Fast Approximation of Homogeneous Stochastic Combat," Warfare Modeling, Military Operations Research Society, eds. Bracken, Kress, and Rosenthal, 1996.
Lanchester, F.W., "Aircraft in Warfare: The Dawn of the Fourth Arm," Engineering, Vol . 98, 1914.
McGinnis, M., Fernandez-Gaucherand, E., and Mirchandani, P., "Military Training Resource Scheduling: System Model, Optimal and Heuristic Decision Processes," Military Operations Research, Vol. 2, No. 1, 1996.
Stafira, S., Parnell, G., and Moore, J., "A Method for Evaluating Military Systems in a Counterproliferation Role," accepted by Management Science, TBP, August, TPP 1997.
Stuk, Stephen P., and Young, Donovan, "Generalized Lanchestrian Reproduction of Iwo Jima Battle Decisions," IEEE Transactions on Systems, Man, and Cybernetics, Vol. 8, No. 1, 1987.
Taylor, J.G., "Force on Force Attrition Modeling," Military Applications Section of ORSA, Ketron, Inc., 1979.

U.S. Army Lt. Col. Jack Kloeber Jr. is an assistant professor of operations research at the Air Force Institute of Technology. Prior to obtaining his Ph.D. from the Georgia Institute of Technology, he served as a Battery Commander, an operations officer and a mathematics instructor at West Point.

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OR, Education & the Military The three service academies -- the United States Military Academy at West Point, the Naval Academy at Annapolis and the Air Force Academy at Colorado Springs -- offer undergraduate degrees specializing in mathematics, operations research or systems engineering, all good foundation programs for further work and study in OR. Hundreds of colleges and universities also feed the personnel system with ROTC graduates in related areas including all types of engineering.

Post-bachelor degree education in OR ranges from a three-month, broad-based and intensive course in the basic concepts and techniques to fully-funded master's and doctoral programs. Some of the best OR programs in the country, including AFIT, NPS, Stanford, MIT, Arizona State, University of Texas, Virginia Tech, Georgia Tech, Colorado School of Mines, Rensselaer Polytechnical Institute, George Mason, George Washington and others, provide the Army, Navy, Air Force and Marines with highly educated military analysts. A graduate course of study in modeling and simulation, one of the key areas of interest for the joint analytical community, is offered by the University of Central Florida and is geared toward the military officer, both at the master's and doctoral levels (WEB site at: http://www.ist.ucf.edu).

Two graduate schools which have programs especially designed for the military analyst are the Naval Post-Graduate School (NPS) in Monterey, Calif., and the Air Force Institute of Technology (AFIT) in Wright-Patterson AFB, Ohio. Both schools have master's and doctoral programs in operations research geared specifically towards the military analyst.

AFIT's Operational Sciences Department produces both master's and doctoral graduates. The Operational Analysis program has an applied emphasis and is geared toward students who already have experience as either an Air Force or Army officer, often either a senior captain or major. The Operations Research program has a more theoretical emphasis and does not assume operational military experience. All students take foundation courses in operations research including optimization, stochastic processes, statistics, probability and applied mathematics. More militarily oriented courses follow including military systems simulation, life-cycle cost analysis, joint combat modeling (two courses), mobility modeling, nuclear and conventional weapons effects, communications systems, decision and risk analysis, military database structures, and a capstone course entitled "Issues in Defense Analysis." Also available to the student are more traditional courses such as nonlinear optimization, advanced simulation, multivariate data analysis, integer programming, response survey methodology, project management and scheduling theory.

These 18-month programs include a sponsored individual 12-hour master's thesis which attacks a real-world problem. Guided by an advisor from the faculty (six civilians, eight Air Force officers, and one Army officer) the students complete a nine-month effort -- typically working on a DoD modeling or analysis problem.

The NPS program is similar in that it contains all of the basic operations research offerings, many similar applications courses, and many of the same electives. The NPS students, primarily from the Navy, Marines and Army, also have a 12-credit hour thesis usually focused on issues proposed by the sponsoring service. NPS master's students have an opportunity to spend a six-week experience tour funded by the organization that benefits from the research. During this period they are immersed in the problem and have daily, face-to-face contact with the principal decision makers. The NPS master's program usually takes 24 months although some shorter programs have been developed.

The department heads for these graduate schools would be excellent sources of information about the role of graduate education for military analysts:

Dr. Edward Mykytka, Acting Department Head Department of Operational Sciences, Air Force Institute of Technology, 2950 P Street, Bldg 640, Wright-Patterson Air Force Base, Ohio 45433; phone: (937) 255-6565 x4329; e-mail: emykytka@afit.af.mil
Captain Frank C. Petho, USN, Department Head, Operations Research Department

Naval Postgraduate School, Monterey, CA 93493; phone: (408) 656-2595; e-mail: fpetho@wposmtp.nps.navy.mil

In addition, there are two organizations that deal with OR-oriented projects for all the services. The Military Operations Research Society (MORS) is a clearinghouse for such projects and a meeting ground for uniformed and civilian analysts alike. MORS also publishes the Military Operations Research Journal, a peer reviewed publication emphasizing military applications of OR theory and techniques. Of course, many other peer reviewed journals publish papers on military applications of OR and management science techniques (e.g., Operations Research, Management Science, and Naval Research Logistics).

Priscilla A. Glasgow is the president of MORS (e-mail: morsoffice@aol.com); Greg S. Parnell (e-mail: GSParnell@aol.com) is the editor of MOR Journal.

The Military Applications Society is a well-known and active society within the INFORMS organization. In addition to sponsoring a large number of sessions at every INFORMS conference, the society is also a clearinghouse for interesting and difficult projects. Stephen Balut is the president of the MAS (e-mail: sbalut@ida.org).

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