expert systems: past, present, and future

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Expert Systems: Past, Present, and FutureHugh J. Watson & Robert I. MannPublished online: 13 Jul 2010.

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Expert Systems: Past, Present, and Future Hugh J . Watson and Robert I. Mann

Expert systems recently have become the object of much attention. Many IS researchers, practitioners, and corporate managers are actiuely inuolued in the study and application of these systems. This article places this development in perspective, recogniz- ing that business expert systems have been in existence for more than two decades. It reuiews the history of expert systems, dis- cusses their current status, and makes pre- dictions about theirfuture. In addition, the article explores assimilation issues, con- siders hardware and software, reuiews the nature of the applications, and highlights application developers.

he information systems field has a new star-expert systems, applications that capture the expertise of hu- mans in a computer program. With such overnight sensations as MYCIN,

PROSPECTOR, and *ON, many IS professionals and managers are paying attention to this new star. Many people, however, do not realize that-expert systems have been around for some time. Will their popularity fade as quickly as it seemed to appear, or will these systems continue to prosper? The IS field is infamous for promising mroe than it delivers.

fessionals and managers must function. Recent developments provide clues about the future. Fi- nally, this article predicts what the future holds for expert systems.

A Brief History of Expert Systems

People have always been fascinated with the possibility of creating intelligent machines. Real progress in machine intelligence began with the dawn of the computer age. One of the first to address the issue of whether computers could process symbols as well as numbers (and therefore simulate human thought processes) was British scientist Alan Turing in the 1930s and 1940s. In 1950, Turing proposed what is now known as Turing's Test for artificial intelligence. The test calls for an interrogator to submit questions to both a human and a computer. If the interrogator cannot determine whether the person or the machine has provided the response, it is said that artificial intelligence (AI) has been realized.

Expert Sys tems Pioneers

It is widely recognized that A1 as a science began at the 1956 Dartmouth Summer Research Project on Artificial Intelligence.' Such luminaries as Marvin Minsky, John McCarthy, Nathaniel Rochester, Claude Shannon, and Allen Newell at- The purpose of this article is to place expert sys-

tems in perspective, h t by tracing its origins: By tended this conference. They brought together backgrounds in mathematics, logic, and psychol- examining the background, IS managers can bet-

ter understand what is happening in the field to- ogy and identified the fist goals and methodolo-

day. This section highlights the conMbutions of gies for A1 research. McCarthy popularized the term artificial intelligence at this time. In addition, business school researchers, because their efforts, the development of what many consider to be the which generally have been overlooked, set the first expert system was announced. stage for today's expert systems as well as those in

the future. Second, the article examines the cur- The program, called Logic Theorist, was cre- rent situation-the world in which current IS pro- ated by Allen Newell and Herbert Simon of the

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Carnegie Institute of Technology (now Carnegie- Mellon University) and by J.C. Shaw of Rand Corp. It was designed to solve logic and calculus problems and was used to prove theorems taken from Alfred North Whitehead and Bertrand Rus- sell's Pnncipia Mathematics.

In 1957, their research efforts switched to another program, the General Problem Solver. It had advanced capabilities for performing a broader set of tasks, including solving puzzles and high school algebra word problems and answering questions phrased in ambiguous English.

Research in Al continued throughout the 1960s and 1970s, led by the efforts of Minsky at MIT, McCarthy and Edward A. Feigenbaum at Stan- ford, and Newell and Simon at Carnegie-Mellon. Much of their efforts were directed toward learning about the nature of intelligence rather than developing commercial products. It was not until the 1980s that AI products, and often A1 researchers, came out of the laboratories and into the market- place.

Contributions of Business School Researchers

Often overlooked in discussions of expert systems are the early contributions of business school researchers. Their research during the late 1950s and early 1960s set the stage for many of the expert systems that are being developed today and will continue to be developed in the future. Al- though these early applications did not possess all of the chiracteristics often associated with expert systems today (e.g., the ability to explain their reasoning process), they did capture an expert's decision-making skills. As with most business school research, the focus was on the applicati~n of the technology rather than on its development. The research also was often conducted by various universities rather than centralized at a few.

One of the earliest expert systems was developed by Geoffrey Clarkson. His system captured the expertise of a bank trust investment officer re- sponsible for selecting portfolios of stocks for clients. Given information on the client's personal characteristics and goals, the system identified a suitable list of stocks for current investment, for-

mulated an investment policy for the client, and selected the recommended portfolio.

Another early expert system was developed by Gary Dickson. His system simulated the decisions made by a purchasing agent when selecting a vendor. Depending on the item to be purchased (e.g., paint, desks, computers), characteristics of potential vendors (e.g., product quality, guarantees, potential for adherence to promised delivery dates) were provided along with the price bid. The expert system processed this information and recommended a vendor for each item.

Usually, specific expert systems are developed In-house rather than purchased as an end product.

Another example of an expert system is the personnel selection system developed by Robert Smith and Paul Greenlaw. The system screened applicants for clerical and clerical administrative positions (e.g., billing clerk, statistical clerk, executive secretary). Input to the expert system con- sisted of employment test scores, personal information (e .g., age, previous work experience, and whether the individual is a new applicant or a current employee), and job requirements (e.g., ability to process numerical data, vocabulary and verbal fluency, accuracy, and speed). The expert system processed this data and provided a written de- scription of the applicant's skills, abilities, and per- sonality characteristics as related to the job as well as a recommendation regarding hiring (or promot- ing) the individual.

This and other expert systems developed by business school researchers in the 1960s had several factors in common. First, they were research projects and were never implemented. Like other A1 research being conducted, the projects explored possible applications of this technology. They demon&ated the potential for expert systems in various business areas. They also used general-purpose rather than special-purpose hardware and software; the significance of this is explored later in the discussion of the current status and future potential of expert systems.

As the 1970s progressed, Hugh Watson, among others, focused attention on expert sys-

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tems that actually would be used in organizations. haps their greatest contribution has been creating In various studies of overdraft processing, appli- an awareness of the potential for expert systems. cant screening, and loan processing (among other More important to the long-run business use of applications), insights were gained about the po- expert systems was the introduction of expert sys- tentiat value of when might tems hardware and sohare, Specia~-purpose be used, and conditions conducive to their suc- computers from such companies as Xerox Corp, cessful development, implementation, and use. Symbolics Inc, and LISP Machine Inc provided

The work led by Michael Parks is a notable ex- the powerful parallel processing capabilities re- ception to the statement that business school re- quired by large expert systems applications. Over searchers were more interested in the application time, the performance-to-price ratio of these ma- of expert systems than in the development of its chines has improved considerably.

He a program the Similarly to decision support systems, expert Heuristically Operative Model for Binary-Decision systems software can be perceived as existing at Replication (HOMBRE), which has several char- three levoh: specific expert systems, expert sys- acteristics that will become increasingly important tems generators (or shells, as they are more com- to expert systems software. monly called), c;ld expert systems tools. Specific

To some extent, the development of HOMBRE products are available at each level. automated the work of knowledge engineers. Given the relevant variables about the decision- making task from a protocol analysis and decision- making case data (i.e., data for the input variables and the decisions made by the expert), HOMBRE develops a model that duplicates the expert's decisions by employing a series of heuristics and statistical tests. The knowledge engineer would not have to extract the specific production rules used by the expert.

.HOMBRE also contains a learning capability. As more data becomes available, HOMBRE re- formulates an appropriate model. The program can also consider the consequences of wrong decisions. When the costs of wrong decisions are supplied, it. creates an expert system to minimize those costs rather than merely simulating the expert's decisions.

The Current Status of Expert Systems

Throughout the 1980s, much attention has been given to such expert systems as PROSPEC- TOR (developed by SRl International), ACE (developed by ATT), XCON-XSEL (developed by Digital Equipment Corp), and MYClN and DEN- DRAL (both developed by Stanford University). Many of these expert systems were developed under ideal conditions: brilliant programmers, an abundance of time, and generous funding. Per-

Special-purpose hardware and software often place expert systems

outside the mainstream IS environment, reducing their use

in organizations.

Expert systems tools are the basic building blocks for creating these systems. They include expert systems workstations and such programming languages as LISP and PROLOG. Expert systems tools are now readily availabIe at the microcomputer level.

Expert systems shells combine a set of tools to provide powerful capabilities for building and using expert systems. They have features that facilitate the building of a knowledge base of facts and rules for solving a specific problem. The inference engine provides one or more reasoning mecha- nisms for processing queries against the knowledge base. A user-friendly front end simplifies the system's use. Available expert systems generators include KEE (Knowledge Engineering Environ- ment) from IntelliCorp, M . l and S . l from Teknowledge, Personal Consultant from Texas In- struments, and the Insight 2+ development environment horn Level Five Research. A growing number of expert systems generators are now available for microcomputers.

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Specific expert systems are used to support the actual decision-making and problem-solving tasks. In most cases, specific expert systems are developed in-house rather than purchased as an end product. This is changing, however, as seen by the introduction of Plan Power, developed by Applied Expert Systems. This product helps financial plan- ners quickly develop financial plans for clients.

Special-purpose expert systems hardware and software offer many advantages. In addition to those already mentioned, they:

Facilitate expert systems maintenance-Many decision-making processes vary over time as conditions change or as more is learned about the decision-making task. It is much easier to modify an expert system when a tool, or especially a generator, is used. Automatically handle complex associations- When a procedure-oriented language is used for an expert system, all connecting logic must be specified. Much of this is handIed automatically by expert systems tools and generators. Reduce application development time-Expert systems tools and generators leverage the knowledge engineer's time, assuming, however, that the developer is familiar with the tool or generator. Expand knowledge representation capabilities -Some expert systems tools and generators support a variety of knowledge representation approaches (e.g., production rules, frames). This capability allows the most appropriate knowledge representation approach to be used for each application. Reduce reliance on IS-Because expert systems tools and generators help end users develop their own applications, reliance on IS is reduced.

Despite the advantages of special-purpose expert systems hardware and software, their use creates problems. Most notably, they often place expert systems outside the mainstream IS environment, which (as some of the early business school research on expert systems has shown) may significantly reduce their use in organizations.

Many organizations are experimenting with expert systems. It is estimated that approximately 150 of the Fortune 500 corporations collectively have spent a total of approximately $1 billion on expert

systems development .' A. D. Little Decision Re- sources predicts that spending for artificial intelligence will grow from $5 billion to $10 billion in 1990, to between $30 billion and $70 billion in 1995, and to between $50 billion and $110 billion in 2000. These expenditures will represent 2% to 4% of thecomputer industry in 1990,5% to 15% in 1995, and 10% to 20% in 2000.

The maturing of the expert systems market is seen in IBM's entry. IBM has introduced LISP/VM, VM/PROLOG, and Expert Systems Environ- ment/VM, an expert systems generator. It is widely recognized that IBM usually does not enter a market until it is well established.

Expert Systems Applications

A wide variety of expert systems have been and are being developed. Perhaps the largest number are for diagnosis and correction applications. Not only do medical applications lead in this category but so do applications for the detection, diagnosis, and correction of equipment problems. Another major category includes applications for educa- tion, training, and computer-aided instruction. An expert system can present a decision-making case, record and evaluate the student's response, provide feedback, and select the next appropriate training experience.

In addition, the military is working on a variety of expert systems applications. These applications are particularly useful for situations in which fast response time is crucial. Industrial applications are also popular. Leaders in this category are very large scale integration electronic circuit design systems in computer-aided engineering applications, whose functions are becoming so complex that human beings are finding it very difficult to per- form them. Financial applications for audit planning and financial planning are also in demand. Petroleum and mineral resources exploration, one of the earliest expert systems applications, is still important.

Assimilating Expert Systems Technology

Changes taking place in organizations can be viewed from a technology assimilation perspective. This is the evolutionary organizational pro-

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cess of learning and changing as new technology One of the groups that are developing expert is introduced. systems includes those individuals and organiza-

Cyrus Gibson and Richard Nolan first popularized this concept for information systems with their stages-of-growth hypothesisa3 Originally, they sug- gested that an organization's aggregate information systems evolve through four stages: initiation, expansion, formaliration, and maturity. In a sub- sequent article, Nolan further divided the formali- zation stage into three areas: control, integration, and data administration.'

tions that are outside the organizations using expert systems- university researchers, university research centers, consultants, consulting firms, and expert systems software vendors, all of whom developed the early expert system. They possess high levels of expertise and have access to state- of-the-art hardware and software resources. Their objectives are either to extend the understanding, knowledge, and technology of expert systems or to realize a profit from their expertise and

It is now recognized that there is a need for products. technology assimilation, whether an organization is considering a new information system (e.g., a decision support system), information systems service (e.g., an information center), or a computer product (e-g., a microcomputer). Warren McFarlan and James McKinney suggest that there are four generic phases for technology a~similation:~

Investment or project initiation-The decision to invest in an information processing technology that is new to the organization. ' Technology learning and adaptation-Learning how to adapt the technology to particular tasks beyond those identified in the initial proposal. Rationaiiation and management control-A

, change in the organization, continued evolution in the uses of technology to uses not odg- -.

nally considered, and most important, development of precise controls to guide the design and implementation of systems that use these technologies. Maturity and widespread technological transfer-Broad-based communication and implementation of the technology to other groups in theorganization.

Most organizations are in the fist stage of expert systems technology assimilation-investment or project initiation. The initial projects are viewed as research projects whose purpose is to gain experience with the technology and assess its potential for the organization. A few organizations that were initially successful with their expert systems are moving on to a broader range of applications. They are in the technology learning and adaptation phase. Few organizations have progressed to either of the last two phases, but such an evolution is certain to occur.

In some cases, organizations have designated specific, existing organizational units to lead the expert systems effort. This group might emerge from such areas as IS, operations research/ management science, manufacturing, or finance. Some organizations have created new organizational units for this purpose. A few companies, such as Boeing, have established extensive in- house training programs to create their own expert systems staff. Internal expert systems groups typically have less training and experience in expert systems and have less access to special- purpose hardware and software resources than external groups do but are more familiar with the organization and its needs, personnel, and potential appkations

End users are the final group of expert systems developers. These are the innovators who recog- nize the potential for expert systems in their own work or for their work unit. They have the least amount of training in expert systems and rely heavily on expert systems generators. Their strength Is their knowledge of the potential areas of application.

Recent Expert Systems Development

Expert systems are undergoing significant changes, which provide clues to the future for expert systems. Stated directly, vendors are trying to move their products into the IS mainstream.

For example, Symbolics introduced SNA Facil- ity Link, a hardware and software package that connects IBM mainframes to the Symbolics 3600 series of symbolic processing systems through SNA. With this product, Symbolics applications

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can access mainframe data bases directly, use the data in expert systems applications, and transmit the output from the application back to the mainframe data base. This development recognizes that the data for many expert systems applications is mainkame resident.

Teknowledge rewrote its S.l and M. l expert systems generators so that they are now written in C rather than in LISP and PROLOG. With this advancement, applications can be developed on standard hardware and therefore are more portable.

Not all firms, however, have managed the tran- sition as expert systems moved from a specialized to a mainstream IS environment. LISP Machine is in Chapter 11 bankruptcy, and Symbolics is losing money and laying off personnel. Many organizations are choosing to run LISP applications on a general-purpose workstation. This approach provides lower-cost Al systems that can be better integrated with general-purpose systems.

planning. It uses an in-house-developed expert systems shell written in Gold Hill Computers' Golden Common LISP and runs on a 640K-byte IBM PC XT or PC AT or an IBM-compatible system. The disk storage requirement for the knowledge base is less than 10M bytes. The hardware and software implementation of ExperTAX was selected with its user environment in mind-the clients' offices using on-site computers.

It is expected that expert systems will be developed on a chip embedded in equipment. Donald Waterman of Rand Corp called them intelligent systems.6 They might be used, for example, to continuously monitor and diagnose equipment operations. This expert system on a chip might receive sensor data, process the data against the knowledge base, and indicate when faults are likely to occur.

Expert systems shells currently create a friendly dialogue for the user by making it easy to commu- nicate commands to the system. In the future, however, it is expected that voice will be an addi-

Dishibution Management Systems Inc introduced tional dialogue option for both input and output. l m ~ a c t / A ~ ~ l i c a t i O n a ex- The technolqy is available today. Because expert pert systems generator. It allows COBOL applica-

systems deal with relatively narrow problems, a tions to run on an expert system created using the

large vocabulary and unconstiained I/O usually generator. This development is significant because are unnecessary, thus further simplifying commu- it recognizes that many COBOL-based transaction

nication between a user and the system. processing applications are potential expert sys- - - -

tems applications.

The Future of Expert Systems

A further integration of expert systems into the mainstream of IS operations can be expected. In- creasingly, expert systems shells will be written in conventional programming languages, and the applications will be implemented on standard computing equipment. When special-purpose hardware and software are used, they often will interface with conventional hardware and software.

Although many expert systems will be mainframe resident, the use of PCs for expert systems will grow. As PC5 become more powerful, the potential for larger, more complex applications will increase. A current example of an expert system on a PC is ExperTax, which was developed by Coopers & Lybrand to support corporate tax

Expert systems employ symbolic rather than numeric processing capabilities. Many decision- making tasks, however, are best supported by a combination of symbolic and numeric processing. For example, personal loan processing may involve symbolic processing of previous repayment history and personal references and numeric processing of the ratio of fixed-debt obligations to in- come. In the future, expert systems shells will support more numeric processing, whereas decision support system generators will provide more symbolic processing capabilities.

It is widely recognized that knowledge engineering is the bottleneck in the development of expert systems because it is imprecise and time- consuming. As Michael Parks's research showed,' however, automation of this process is feasible. Al- though the tools will be very different, there will be knowledge engineeering workbenches similar to those for systems analysts.

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~ u t u r e Assimilation into Organizations

Organizations will move beyond the early phases of expert systems assimilation into the ra- tionalization and management control phase and the maturity and widespread technological transfer phase. Although the details of how this will occur are unclear, the broad outline is emerging. As initial expert systems projects begin to contribute to the business, new projects are created. These projects are likely to include applications not originally considered and to involve other groups in the organization. One example is the experience at Digital Equipment Corp. Digital Equipment began working on XCON in the mid-1970s to support the configuration of VAX computers. After its success, XSEL was added as an interactive front end to help Digital Equipment sales representa- tives develop specifications for customers. Today, more than 8 0 expert systems are in use or under development throughout the 'organization.

In the beginning, expert systems developers were the "high priests." To some extent, they still are, but this situation is changing because more people are trained in expert systems and especially because expert systems shells place application development in the hands of end users. Al- though complex, organizationwide expert systems are likely to be created by specialists, much of the application development will shift to end users, because they often have the need, interest, resources, and talent to develop their own applications.

Ssme end users fail to understand all of the ex- citement about expert systems. They correctly claim that expert systems are not all that new and that they personally developed expert systems over the years through use of conventional hardware and software. They believe that only the ter- minology and special-purpose hardware and software are new.

Potential Applications

The most famous expert systems were created to solve complex problems, and undoubtedly expert systems of this type will continue to be developed. There are, however, many more potential applications that require competence rather than reai expertise. The banking and .insurance indus-

hies contain many appropriate examples. Many of these expert systems wilI be embedded in transaction processing applications. One example is American Express's Authorizer's Assistant. This automated credit card authorization system was developed using Inference Corp's Automated Reasoning Tool and is integrated with an IBM 3090 to handle online processing of credit card charges. Other expert systems will reside on PCs and will be used by managers and especially by professionals. The recent evolution of expert systems products by vendors supports this conten- tion.

Criteria for Successful Expert Systems Development

As organizations expand their use of expert systems, they must address the selection, development, implementation, and use considerations that were first explored by business school researchers. Their research showed that the follow- ing conditions are important to successful expert systems development:

The commitment of management and the expert. Applications with a high payoff, either because of their strategic importance or because of their consumption of organizational resources. Acceptability of applications to employers, customers, suppliers, and society-For example, mortgage Ioan decisions by an expert system might be judged unacceptable by applicants because the computer lacks human instincts and feelings. A stable knowledge base for the application or provisions for updating the expert system as needed. Provision of input data for a particular decision- making case-It may be entered by the user, drawn from an existing data base, or provided by sensing devices.

Business school research on expert systems also revealed that attention frequently evolves from how the expert currently makes decisions to how the decisions should be made. The expert system building process may be the fist time that the expert seriously examines the production rules being used. The expert often changes a rule after reflection or asks what the rule should be. In other

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words, the expert seeks to move from a descrip- vard Business Review (March-April 1979), pp 115- . .

tive to a prescriptive model. This is a natural pro- 126. 5. W. McFarlan and J . McKenney, "The Information gression that occurs with many expert systems. Archipelago-Maps and Bridges," Haruard Business Re-

view (September-October 1982), pp lb9- 119. expert systems can be for 6. 'Diagnostic Problems Suited to Expert Systems Applica- complex decision-making tasks, they currently are tions," Computerworld (January 13, 1986), p 45. a ~ ~ l i e d to fairlv well mctured decisions-at least 7. M.S. Parks, N. Siemens, and H.J. Watson, 'A General- . * - -

as far as the expert is whether for ized Model for Automating Judgmental Decisions," Man- agement Science (April 1967), p p 841 -851.

complex or well-structured decisions, all expert systems contain an algorithm and the expert must know enough about the decision so that the production rules can be conveyed and an algorithm created.

This does not mean that expert systems will not be used for less structured decisions. Today's poorly structured decisions usually are better understood over time. Perhaps more important, an expert system has the potential to guide decision making, even if the process is not sufficiently understood. For example, consider senior management's strategic planning responsibilities. Although this process is not sufficiently understood to be fully modeled by an expert system, progress is being made in guiding it by suggesting possibilities or analyzing alternatives. When expert systems begin to have a strategic impact on organizations, they will overcome the misconception of their being a new arrival and will achieve a permanent place in the structure of the organization.

Recommended Reading "AI-Based Financial System Allocates Assets Based on Goals." Computenuorld (March 17, 1986), p 6.

"A1 Pendulum Swings to Generd-Purpose Firms." Compu- terworld (April 20, 1987), p 14.

Clarkson, G.i?E. Portfolio Selection: A Simulation of Trust Investment. Englewood Cliffs NJ: Prentice-Hall, 1962.

'COBOL-Based A1 Shell Bows." Computerwarld (Septem- ber 1, 19861, pp 1, 12.

Dickson, G.W. A Generalized Model of Vendor Selection, eds C.E. Weber and G. Peters. Scranton PA: international Textbook, 1969, pp 115-136.

Ernst, G.W., and Newell, A. A Case Study in Generality and Problem Solving. New York: Academic Press, 1969.

Newell, A., and Simon, H.A. Human Problem Solving. Englewood Cliffs NJ: Prentice-Hall, 1972.

"LISP Systems Tied to SNA." Computerworld (March 10, 1986), p 13.

Newquist. H.P. 'American Eipress and Al: Don't Leave Home Without Them." A1 Expert (April: 1987), pp 63-65.

Shpilberg, D.; Graham, L.E.; and Schatz, H. 'ExperTAX: An Expert System for Corporate Tax Planning." Expert Sys- tems (July 1986), pp 136-151.

Smith, R.D.. and Greenlaw, P.S. "Simulation of a Psycho- Hugh J. Watson is the chair of business administration and director of MIS programs at the University of Georgia. His logical Decision Process in Personnel Selection." Manage- professional activities include providing and participating in ment Science 1967)3 pp 8409-8419. Executive 2000, a research program investigating how to symonds, A, J. ulntrodudion to IBM's K ~ ~ ~ ~ ~ , . J ~ ~ - s ~ ~ ~ ~ ~ provide support to senior executives. Products." IBM Systems Journal 25. no 2 (1986). pp 134- Robert I . Mann is assistant professor of MIS at Virginia Corn- monwealth University, Richmond VA, and was formerly affili- nTeknowledge Retools E~~~~~ systems for B~~~~~~ M ~ ~ - ated with the University of Georgia. He specializes in systems analysis and design and in artificial intelligence applications. ket." Computerworld (August 4, 19861, pp 76, 78.

Notes 1. J.N. Shurkin, "Expert Systems: The Practical Face of Ar-

tificial Intelligence," Technology Reuiew (November- December 1983). pp 72-78.

2. Handbook Unravels Mystery of Expert Systems Applica- tions." Computerworld (October 13, 19861, p 148.

3. C. Gibson and R. Nolan, "Managing the Four Stages of EDP Growth," Narvard Business Review (January- February 1974), pp 76-88. '

4. R. Nolan, "Managing the Crisis in Data Processing," Har-

Turing, A.M. "Can a Machine Think?" The World of Mathe- matics, ed J .R . Newman. New York: Simon &'Schuster, 1956, pp 2099-2 123.

Watson, H.J. Computer Simulation in Business, Chapter 9. New York: John Wiley & Sons, 1981.

Watson, H. J . ; Anthony, T.E; and Crowder, W.S. 'A Heuris- tic Model for Law School Admissions Screening." College and University (Spring 1973), pp 195-204.

Watson. H.J., and Vroman, H.W. 'A Heuristic Model for Processing Overdrafts." Journal o/ Bank Research (Autumn 1972), pp 186-188.

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