Problem Solving and Decision Making

    What is problem solving? Initially this question may seem so broad as to defy explanation. Isn't problem solving something we all do, all the time. Numerous books and journal articles (see bibliography on Problem Solving) attest to the efforts to define, clarify and suggest methods for PS. How do these authors attempt to define it? As you may expect through a wide range of approaches from anecdotal to mathematical. For example, Newell and Simon[PS5] take a largely information processing system (IPS) approach, utilizing cognitive factors to support their hypotheses. Andriole[PS2] takes a practical approach, utilizing a task, organization, and method structure for defining a system. Twiss[PS12] presents a largely behavioral viewpoint and associated techniques, and Winston[PS13] utilizes 2 paradigms popular in artificial intelligence rule based systems, and generate & test.

    While all these definitions/approaches have merit, the viewpoint(s) of Smith[PS10] stand out as clear, succient, and simple. He defines a problem as "a gap." To expound upon his definition, think of yourself in the midst of a mountain range, standing atop a small peak. Your goal is to reach a tall mountain you see far in the distance. Your "problem" then is the traversal of the many intermediate valleys, gorges, peaks, rivers and unknown perils between here and your goal. How do we accomplish this? This traversal is problem solving. Problem solving is frequently used in a broader sense to denote an entire process which may contain some or all of the following stages:

Figure 2.1 Different Stages of Problem Recognition and Attack

Recognition	awareness that a gap exists
Identification	narrowing the scope of the available intelligence
Definition	determining the relevant problem components
Structure/Design	placing the defined components into a form for analysis
Matching	aligning the structured problem with techniques for mediating it
Choice	invoking the chosen technique/method

    These "stages" are represented in some form or another in the major problem solving/ decision making paradigms. For example: Simon[DM6] proffers the process; 1) Intelligence, 2) Design, and 3) Choice. Einhorn & Hogarth[DM1] suggest; 1) Information Acquisition, 2) Evaluation, 3) Action, and 4) Learning. Kepner & Tregoe[DM5] propose; 1) Determine objectives for evaluating alteratives, 2) Classify objectives according to importance, 3) Evaluate alternatives against objectives, 4) Choose the best alternative as a tentative decision, and, 5) Assess the adverse consequences of the tentative decision.

    Virtually every textbook on management and/or decision making lists one of these methods or some takeoff of them. In addition to processes, many authors have also sliced problems through taxonomies. The following table sets forth categories for problem types. It is interesting that the categories set forth tend to be cross disciplinary. This would seem to logically follow if one were addressing PS generically, but several of these authors are addressing problems addressed by specific techniques in DA and others techniques in AI (from the subset of expert systems (ES)).

Figure 2.2. Problem & Decision Types

	AND	G&W	SMI	HR	HR
Allocate x ³³	x
Binary DM x x ³³	x	x
Create x ³³	x
Describe x x ³³	x	x
Diagnose x x x ³³	x	x	x
Evaluation x x ³³
Explain/Interpret x x ³³
Monitor x ³³
Persuade x ³³
Predict x x x x ³³
Prescribe/Debug x x ³³
Research x ³³
Score x ³³
Strategize/Plan x x x ³³ ³³ ³³

Key:  AND Andriole[PS2]  G&W Golden & Wasil[DS2]  SMI Smith[PS10]  WEI Weick[DM8]  HR HayesRoth[ES3]

    After examining the above processes and problem "types" it should be no surprise that the term "problem solving" is frequently used interchangably with "decision making". And thus the stages of problem solving are frequently intermixed with purported stages in decision making. Some clarification as to differences is in order. Toward this end, Smith [10] also does an effective job of differentiating between "problems" and "decisions". Ideas by Holtzmann[PS3] add flavor to Smiths definition. Between the two we find that decisions are those places and times in the problem solving process when we obligate ouselves to a specific path. It follows that "decision making" is the process of selecting a path.

Decision Making

    A more detailed look at decision making is warranted. Etzioni [DM2] contrasted two broad categories rational and adaptive. Rational DM has a long history (see Reese[PS8]) right from the early philosophers Descartes and Spinoza up to a more recent "defense" by Popper[PS7]. To cover all that theory would take considerable effort, so let's establish a shortened definition, the merits of which shall remain axiomatic. Rational DM will be defined as a fully structured, analytical, verifiable approach to DM. Adaptive DM is a more "human" approach involving taking one or more of the the five following approaches; focused trial & error, tentativeness, procrastination, hedging, and reversible.Etzioni's adaptive decision making takes rational decision making to issue. He states, "... the rationalist model, which requires full scanning of all relevant data and choices, is often impossible to heed. It requires the collection of enormous quantities of facts, the use of analytical capabilities we do not command, and a knowledge of consequences that are far away in time." His adaptive model may be viewed as a more practical way to frame decision making.

    In contrast to adaptive decision making, rational DM has as one of its primary purposes the use of methods to help overcome the shortcomings of our "human" weaknesses. What does this mean? It simply means that humans are not always perfect decision makers. To demonstrate both our frailities and our strengths in decision making, we will later examine the "human" elements in DM. This will be accomplished by examining; 1) cognitive limitations & biases, and 2) values & judgements.A look at these areas is with an eye toward aiding our decision making capabilities via technology. Before we venture into them however, we need to address another "common" area in AI and DS, the model, now an integral part of DM.

Modeling

    Somewhere in time man determined that the task of closing the gap would be helped considerably by creating a model, or a representation of the "real" problem environment. Modeling is a task common to both decision science and artificial intelligence researchers. In both cases scientists are concerned with choosing the best representation. They ponder over the uncertainty of the situation, variables to be used, relationships to be established, and techniques to apply. They create static & dynamic models, play games or run simulations. And then add validity and reliability measures to their models. A forecaster might use mean absolute deviation, a statistician confidence levels, and a neural networker training tolerance and bandwidth. How then do we know if our model is accurate, complete, valid, reliable? Ultimately the proper design of models is itself a discipline and there is really no such thing as the "right" model [M3]. Yet many problems remain with creation of models. These include tractability, preference, and computability. With an eye toward understanding how far our models can go toward attacking "problem solving", Holtzmann has proposed a seven level "Taxonomy of Ignorance." This taxonomy is shown below.

Figure 2.3. Taxonomies of Problem Ignorance

Type Characteristics Example(s)  Fundamental - unaware of problem Life  Dark - aware but no model is  available to follow  Magical - model avail but contains  unexplained elements  AlkaSeltzer  Ptolemaic - model is incomplete Ptolemy v. Copernicus Gordian - model complete but awkward Gordian Knot  Columbus Egg  Watsonian - model complete, but solution method is incomplete Sherlock Holmes & Dr. Watson  Combinatorial model & solution method Very Large  complete but cannot  compute answer LP Problem

 
    We see from his taxonomy that no matter what the size or complexity of the model we build, there always remains a remnant of ignorance. Despite our best efforts our models frequently fall short of even "good enough." And beyond this choosing a problem representation is in itself a problem. Decision Scientists and Artificial Intelligence researchers have created techniques so complex and awesome that becoming an expert in just one can be a lifetime devotion. Yet the depth and breadth of technique development grows at an astounding pace. Genetic Algorithms, Chaos Theory, Catastrophe Theory, Memory Based Reasoning, and Neural Networks are all approaches meant to attack problem solving on an essentially universal basis. Yet how many management scientists have even heard of these disciplines, much less are conversant in them. So much evidence points to the need for better modeling and explanation environments to gain some control over this exapnding mass.

    In this fashion modeling itself has become a germane research topic. And in a circuitous fashion techniques borrowed from DS and AI have now found their way into model creation and maintenance. In the AI domain researchers have suggested applying analogical reasoning[M6], machine learning [M7], frames [M1] and formal logic [M5] to modeling. And Fordyce et al [GN4] have also suggested the application of AI influences to MCDM. As we will witness later, many of these suggestions have already been implemented. Finally, in the DS domain, a large focus of the decision support systems subfield is model creation, with different approaches offered by Sprague[DS4], Andriole[DS1], and Geoffrion[M4]. Now that we have established a groundwork in "state of the art" problem solving, decision making, and modeling, we can begin to delve into an area which will have significant payback if we can come to grips with it human cognitive elements.