OMEGa4 Int. J. of Mgmt Sci.. Vol. 16. No. 5. pp. 421-428, 1988 0305-0483/88 53.00 + 0.00 Printed in Great Britain Pergamon Press plc

A Conceptual Scheme of Knowledge Systems for MS/OR

A B R A H A M M E H R E Z

Ben Gurion University, Beer Sheva, Israel and Kent State University, Ohio, USA

G A D R A B I N O W I T Z

A R N O L D R E I S M A N

Case Western Reserve University, Ohio, USA

(Received November 1987; in revised form March 1988)

This lmlmr ~ • ¢onoelt~tmd scheme to repreml rite knowledge base of Mmmgement S¢iem:elO~rtttem ~ (MS/OR). S t ~ • ~ could be utilized wlthln the framework of a Decbioa Support System (DSS). Its purpoee is to facilitate exptmiou of knowledge. An Illustrative example JJ provided to i~lJcate the potential_of • DSS with the scheme suuested. Finally, some of the beues of development and implem~tatiog_ of the suggested DSS are discussed.

INTRODUCTION

LITERATURE in the management sciences has experienced an explosive growth during the last two or three decades. Journals are proliferating. The means of storage and especially the retrieval of information from this vast literature leave much to be desired in spite of key word filing and electronic indexing. The student, the re- searcher and the practitioner often end up spending much time reading papers which turn out to be irrelevant to their task while ignoring the more relevant literature. This observation motivated the work which follows.

Recently Reisman [21, 22] emphasized the importance of developing taxonomies for (MS/OR) knowledge so as to expand its uni- verse and facilitate its usage by researchers and practitioners. Acar, Ackoff and Churchman [1, 3, 8] as well as others have, over time, also discussed these and related issues. This paper suggests a general conceptual framework for knowledge systems. We believe that the "knoweldge-production process', in MS/OR

421

could be supported by developing such a system and embedding it in a Decision Support System (DSS). The MS/OR community can be per- ceived as an'inquiring system (IS) or part of a world wide IS consisting of all researchers and their research facilities. Churchman [8] discusses different philosophical views for the design of such a man-machine system. From a practical point of view, the differences between those views stem from different answers to the follow- ing question: What is the optimal way of presenting knowledge to a decision maker in an IS3 The answer might be a net of true, false and irrelevant facts as in the Liebnizian IS, an expert approved net of facts as in the Lockean IS, various modes of representation as suggested in the Kantian IS, or by displaying two alternative explanations: thesis and antithesis for a given data set, as in the Hegelian IS [8]. Our under- standing is that a practical IS will probably use all of the above ideas, as well as others. Though we do not restrict our discussion to any specific IS. A DSS, which can be defined as the machine part in a man-machine IS, consisting of three

422 Mehre: et al.--A Conceptual Scheme of Knowledge Systems for MS~OR

components [6,7,9] LS (Language System), PPS (Problem Processing System), and a KS (Knowledge System). Here only the latter is discussed. More specifically the purpose of this paper is threefold: (I) to identify a conceptual scheme for such a KS, (2) to raise its potential advantages, and (3) to discuss a few strategies for the development of the system in recognition of the inherent complexities of the undertaking. Clearly the identification of the conceptual scheme is a non-unique process. The focus of the scheme we suggest is primarily research oriented.

From our point of view, a KS should be based on a set of elementary knowledge units (EKU's) and a dictionary of Concepts. The EKU might be different than the traditional article or any other currently used physical manuscript on one hand, but it need not neces- sarily satisfy the properties required for being organized and processed as a 'facts-net' in a Liebnizian IS on the other hand.

The essential condition for a bit of knowledge to be called an EKU is that it must have, at the time of codification some added value to MS/OR knowledge. The EKU includes refer- ences, implicit and explicit relationships to other EKU's or to other entities in the environment of the KS.

KS in general and for OR/MS in particular can be evaluated via three basic features. Here we differentiate between what we call basic features vs performance measurements. Whether the evaluation process is established by a community of guarantors (or experts) as dis- cussed in [8], or is a part of economic process, is important for the implementation of the DSS, but not for the design of the EKU's conceptual scheme. The basic features of a KS are the following: the conceptual structure, the physical structure and the content of the system.

The Logical Structure of the KS is essentially based on the logical structure of the EKU's, and type of relations between them. The logical structure of the EKU's, refers to the typical processes of knowledge expansion handled while generating the EKU. Reisman [23] defines six types of knowledge expansion strategies.

This paper will set down what is believed to be a unified conceptual schema for a KS robust enough to encompass various areas of research and practice. The detailed logic for the

KS will be discussed in future papers on the subject.

The physical structure refers to the detailed scheme of the KS in a given implementation. The content of the system refers to the knowledge itself.

The performance of a DSS (e.g. respons- iveness) is determined by the system's configuration and use, both of which are im- plied by its objectives and constraints. Typical measurements of performance for information systems are mentioned in the MIS literature [301.

The domains of the EKU's logical structure, as well as its data of these values must be defined by the general dictionary. One of the difficulties in constructing the dictionary stems from the interdisciplinary nature of MS/OR. The re- lationships between MS/OR and other scientific fields must be considered [5, 8, 31]. Many au- thors have suggested taxonomies for specific subareas of MS/OR, Reisman [23] suggests a taxonomy of taxonomies, a general method which could be used as a guide for the devel- opment of the dictionary. Clearly the dictionary should be flexible to changes under appropriate regulations, e.g. by the theory sector, suggested in [8, p. 137] for a Kantian IS.

The selection of a new DSS should be evaluated on the system's measurements of performance, based on cost and benefit consid- erations. This type of project selection problem typically falls into the category of unstructured problems. See [1, 8] for a discussion of how to deal with such problems. We will not attempt to pursue such analysis in this paper inasmuch as the paper is limited to addressing only one basic feature of the system, namely its conceptual schema. To the best of our knowledge, such a scheme was not previously suggested in the MS/OR literature. Development of a DSS for MS/OR may well catalyze the discussions re- garding the definition, boundaries, main objec- tives, and future development trends of the MS/OR field, as well as its potential added value to society. The physical structure of the cur- rently used MS/OR KS is very similar to those of other scientific and science based fields. How- ever, the development and the implementation of a new DSS should take into consideration the peculiarities of MS/OR, may or may not fit other scientific fields (especially in some branches of social or natural science where

Omega, Vol. 16, No. 5 423

Lever 5

Lever 4

Lever 3

Lever 2

Lever t

Statements framework ]

t Modet to statement J

l

transformation framework I t

Model framework ]

t ReaLity to reader I

l

transformation framework I t

I Reotity ,,am.ark I

Fig. I. General conceptual structure of an EKU.

the emphasis may be on descriptive notions rather than prescriptive ones). However, some of the ideas might fit disciplines which provide the basis and the principles of MS/OR, e.g. Mathematics, Economics, Engineering, etc.

Since we deal with only one of the three components of a DSS (namely the KS), issues such as data manipulations, content reliability or user views are not considered from our perspective [6, 7].

The next section defines and describes the conceptual scheme. Then, an example of two related EKU's is presented. A qualitative ana- lysis which compares the existing KS with the suggested one is provided in section three. Finally, some strategies for development of the KS are discussed.

CONCEPTUAL SCHEME

The EKU is defined by five levels of knowl- edge classifications, (Fig. 1) which refer to the basic entities of concern to MS/OR.

The approach of viewing the MS/OR as a problem formulating and solving discipline [2, 4, 17, 25] is the basis for the identification of the EKU levels. This approach defines the pro- cess required to formulate an MS/OR model as a sequential procedure. Here we use this idea, for the purpose of presenting valuable state- ments both on abstract and real world levels. In addition the suggested structure is sufficiently general to express knowledge of all the various methodological subfields of MS/OR (e.g. math- ematical programming, stochastic processes and decision theory, or areas of applications) within the boundaries of the same framework.

In general, the identification of EKU might correspond to a subset of Levels: For example Levels 1-3, or Levels 3-5.

Some clarifying remarks regarding each of the EKU levels follow:

Level 1. At Level 1 the KS cannot encompass the reality but only a subjective perception. Clearly, the presentation of reality is not a simple task. It is agreed [1,2, 8] that there is a lack of methodologies for Levels 1 and 2. We believe that the development of a KS will re- quire new research directions to identify the components of Levels l and 2. The modeling methods suggested by Geoffrion [1 l/ are im- portant advance in this lane. The illustrative example which we present here derives Level's 1 components from an MS/OR perspective. These components identify the problem's features from the point of view of the reality as perceived by the decisionmaker.

Level 2. Level 2 is concerned with for exam- ple, the relaxations, approximations, and as- sumptions which are required to transform Level 1 into Level 3. Recently [16] suggested a conceptual scheme for planning and control models that can be used to present both Level 1 and Level 3 situations. The underlying as- sumption of their approach is that both levels should be related to the same subset of concepts. These authors perceive the reality and the mod- els by their features as related for example to the types of uncertainties, dependencies and other characteristics of the problem. The view of Mehrez and Enrick is less technically oriented than the one used in the illustrative example of this paper. We are aware of the bias and re- strictions related to any specific mode of repre- sentation, which as mentioned before, might be partially solved as in the Kantian or Hegelian IS's [8]. The technical approach is probably more appropriate for research and for teaching activities, whereas the Mehrez and Enrick approach may be employed for practical applications.

Level 3. The literature has recorded different definitions of the concept "model". Here we define a model as any subset of qualitative and quantitative concepts that are required to iden- tify the abstraction of reality [10, 15]. On the aggregated level the set of MS/OR models must be classified into mutually exclusive subsets which might include, for example, prescriptive

424 Mehre'. et a l . - -A Conceptual Scheme of Knowledge Systems for MS~OR

vs descriptive models [22]. The features of a model can be presented by a hierarchical struc- ture using the idea of Keeney and Raifa [14] for the primary and secondary attributes and the hierarchical database approach. A possible way of presenting knowledge of Level 3 is illustrated by the example provided below. As will be shown, the identification of the model's frame- work in the second EKU examined (a sensitivity analysis problem) is identical to the first EKU including its statement framework.

Level 4. The Transformation of Knowledge from the model framework to the statements framework is basically a reasoning process which should be based on statements of other EKU's. This process should result in a different type of knowledge organized and saved (preserved) separately. Examples of possible classifications at this level include algorithms, proof techniques, determined causality, proba- bilistic causality, and others. Various tax- onomies of these methods are suggested by different authors in the MS/OR literature. Fur- ther research must be conducted in order to achieve a consistent and sufficiently detailed classification that can furnish the dictionary.

Level 5. The debate on what is MS/OR may stem from the identification of the detailed logical structures allowed by the statements framework. In the very broad sense it may include different structures for theorem (mathe- matical, logical, etc.), conjecture, statistical in- ference, policy, a counter example, an illustra- tive example or other concepts. We do not intend to provide here a specific definition for each structure. It should be noted that the classification of statement structures is a matter of a subjective judgement. For example, in mathematics, conjecture or policy are not al- lowed as conceptual structures, but could be argued in MS/OR depending on the nature of the subfield, editorial policy or views. Finally, we note that we allow in general for a set of statements corresponding to a given EKU. These statements may be based on knowledge of other EKU's.

EXAMPLE

The example we present here is based on the work o f Rabinowitz et al. [20]. Two EKUs were identified with respect to this work. To simplify the knowledge presentation we describe.the KS

as if it includes only these EKU's. For the convenience of the reader we first quote the abstract and the background of this work.

An optimal decision and control model was developed and used for dual purpose allocation of water from a reservoir. The model was constructed for the Hazbani-Dan System in the Upper Galilee (Israel). In this system about half of the Dan River water enters and is stored in a reservoir and is then released via a 70" pipe either to a hydroelectric power station or to agricultural fields for irrigation. The electricity generated is sold to the national electricity utility according to a three-tiered pricing sys- tem which is a function of the time of day and the season.

The decision and control model maximizes the expected return on energy production sub- ject to storage capacity and flow limitations. According to the policy of the system manage- ment, water demand for irrigation has to be satisfied and so it is taken as a constraint in the model.

The following paper develops the model and explores the feasibility conditions of the model and the uniqueness of the solution. An example containing a sensitivity analysis is given.

BACKGROUND

The following work deals with a control problem of the Hazbani-Dan System (HDS). The system is operated as a commercial enter- prise, under a number of managerial con- straints. The decision and control mission was defined as a two-stage, deterministic, opti- mization problem with a finite planning hori- zon. The long term model (LTM), and the short term model (STM).

This paper deals only with definition and exploration of the LTM. The LTM is analyzed including: solution feasibility, proof of the solution's uniqueness and determination of the Kuhn-Tucker (K-T) conditions of the solution. The proof is based on the concavity of the objective function subject to a convex set of constraints. Results of the LTM for a typical summer week, including sensitivity analysis for the storage capacity and for the length of the planning horizon are presented.

The knowledge in this paper can be organized into two EKUs. The first one consists of the initial process of that research which deals with the problem definition (Level 1), formulation of the LTM (Levels 2 and 3), and the model exploration which produces statements regard- ing its properties (Levels 4 and 5).

The second EK U relates to a different part of this research and reported in the same paper.

Omega, Vol. 16, No. 5 425

This part deals with sensitivity analysis on oper- i.3.2.2 ational parameters in the same water system. In this EKU we perceive the model framework as 1.3.2.3. derived in the first EKU (same Level). The properties of the model, e.g. feasibility condi- 2. tions, concavity and uniqueness are derived from the statements of the first EKU. A simu- lation study (Level 4) produces the sensitivity analysis (Level 5). Hence, the second EKU 2.1 involves Levels 4 and 5.

For simplicity, both of the EKU's are only roughly outlined. The reader can recognize the conceptual scheme (5 Levels), the logical struc- ture (hierarchical formulation with the EKU's and the hybrid interconnecting relations), the physical structure (specific attribute structure) and the content (the specific concepts, attributes 2.2 and their values). The reader can get the feeling of the EKU idea without the need of studying the referenced paper. Clearly a deeper in- vestigation might require reading this paper. The EKUs are presented following the five level structure. 3.

3.1. First EKU

1. Level I Reality Framework - 3.2 Reality structures: system, policy, prob- lem. 3.3

1.1 System 3.3.1 1.1.1 System type: water resource 1.1.2 System input: single resource: water 3.3.2 1.1.3 System output:

1.1.3.1 Consumption for irrigation by 3.4 a set of consumers

1.1.3.2 Release for hydroelectric en- ergy production

1.1.4 System's components 4. 1.1.4.1 Single reservoir 1.1.4.2 Pipe networks 4.1 1.1.4.3 Hydroelectric plant 4.2 1.1.4.4 Control system

1.2 Policy 4.2.1 1.2.1 Policy type: managerial priorities, oper-

ational constraints (could be further decomposed).

1.3. Problem 1.3.1 Problem type: Infinite horizon, real

time, discrete sequential decision and 5. control of production problem with 5.1 uncertain inputs and outputs.

1.3.2 Problem parts 5.2 1.3.2.1 Objectives: maximize expected annual

revenue

Decision variable: energy production plan Constraints: operational limits, sys- tem's structure Level 2 Reality to Model Trans- formation Framework Transformation structure: assump- tions, approximations Assumptions 2.1.1 Predictable, deterministic in-

puts and outputs 2.1.2 Discrete time inflow, decision

and control 2.1.3 Immediate and accurate reac-

tion to control 2.1.4 Pure mass balance Approximations 2.2.1 Finite planning horizon 2.2.2 Bounded state planning hori-

zon 2.2.3 Quadratic hydroelectric effici-

ency functions Level 3 Model Framework Model structure: properties, parts, scale dimensions. Properties: finite horizon, bounded state, nonlinear, deterministic Parts Objective function: A nonlinear piece- wise separable 5 degree polynomial Constraints: Mass balance, linear bounds Scale dimensions: 3.3.4.1 2n-I variables 3.3.4.2 n-I constraints 3.3.4.3 2n-I bounds Level 4 Model to Statement Trans- formation Framework Transformation Structure: Reasoning Reasoning methods: Mathematical Proof Proof Steps: 4.2.1.1 Implicit function theorem for

linear constraints 4.2.1.2 Negative definite Hessian ma-

trix 4.2.1.3 Convex feasible set Level 5 Statement Framework Statement structure: Mathematical Theorems Theorems List 5.2.1 Feasibility Conditions 5.2.2 Uniqueness

426 Mehre: et al.--A Conceptual Scheme of Knowledge Systems for MS~OR

Second EKU

References: Level 3 and Level 5 of the first EKU

4. Level 4 Model to Statement Trans- formation Framework

4.1 Transformation Structure: Reasoning 4.2 Reasoning Methods: Simulation and

statistical inference 5. Level 5 Statement Framework 5.1 Statement structure: Numerical Results 5.2 Numerical Results

5.2.1 Convergence to planning hori- zon

5.2.2 Sensitivity of net return to storage capacity

DISCUSSION

The central issue that must be addressed is concerned with the benefits of developing and implementing a DSS for MS/OR knowledge. While the scope of the analysis based on a single paper is limited it appears that the knowledge system proposed could support further research and education activities. The example used in- voked general approaches and methods, includ- ing simulation, database management, teal time systems, optimization, statistical analysis and computational experience. Experience with that study indicated that existing MS/OR literature (knowledge base) including books, abstracts, journals indices, information systems, etc., was limited in the sense that its use was highly time consuming and inefficient in solving the main theoretical and applied research problems. Hence, the researchers compromised between spending much time reading possibly irrelevant papers and ignoring probably relevant ones. The poor standardization of concepts, definitions and report structures also caused less efficient searches. For example (as non-experts in the field of Mathematical Programming) they spend a few months looking for a reference for a proof of globality. With the suggested KS, on the other hand, one could cross all the existing knowledge searching for concepts similar to those of the problem at hand.

In particular, very important issues could be studied along the research project's life time. For example:

(1) What assumptions were made for the set of similar systems? (relations between Lev- els 1 and 2)

(2) What relations exist between assumptions and statements regarding the model's properties for similar models 9 . (relations between Levels 2 and 5).

(3) What relations exist between models (or even assumptions) and algorithms (or packages) used for solving the models? (relations between Levels 2 or 3 and 5)

(4) Comparing statistical inferences of similar systems. (relations between Levels 4 and 5)

(5) Comparing models of similar systems. (relations between Levels 1 and 3)

Clearly, queries relating the model's concepts to the MS/OR paradigm should not be re- stricted to systems or models with similar reality (e.g. water resource systems).

As user interface, the same semantics could be used both for queries regarding existing knowl- edge and definitions of new knowledge. A more enhanced DSS can react as an expert. Via an interactive process the system can use MS/OR expert's rules and reasoning capabilities to raise relevant questions or evaluate different options, see Churchman [8, pp. 25-28] for Spinoza's taxonomy of IS's.

ASSESSMENT

In principle, a DSS for scientific use is a public good, the development of which will probably require governmental intervention. Technological and marketing uncertainties are inherent in any R&D project [19], especially in developing a DSS based on the suggested con- ceptual structures for a field such as MS/OR, which is characterized by huge varieties of meth- ods and by fuzzy boundaries.

Clearly it will be difficult to evaluate the system's performance in advance. However, many advantages may result from the use of such a system. Let us mention some of them using a bottom-up ordering:

System's capabilities

(1) more consistency in the definition of Concepts,

(2) better connections between pieces of knowledge (better defined relations and

Omega, VoL 16, No. 5 427

(3)

ease of searching and improving such relations),

reduced direct time required for the search of existing knowledge.

(1) To build the system starting with the latest knowledge and going backward into his- tory (i.e. a LIFO policy). This may be easier to implement and its more likely to be used.

(4) better differentiation between relevant and irrelevant matter,

(5) reduced storage volume required for pre- serving a bit of knowledge.

User performance

(6) more effective learning (as part of the professional education as well as part of any academic research),

(7) reduce attention to irrelevant matter (one of the very problematic and time con- suming disadvantages of current practice),

(8) provide a better interaction within the MS/OR field and between MS/OR and other disciplines,

(9) reduce duplication of work,

(10) support the research process by efficient construction and search methods.

Goals contributions

(11) increase the volume and the quality of research output,

(12) improve the identification of new direc- tions in the field,

(2) To concentrate on only one (or few) specific subfields at a time (e.g. queueing theory, water resources systems, etc).

(3) To extend the system's developers and users via membership in the utility or other incentives.

(4) To establish an efficient development environment including decision making processes and control procedures, see for example [18, 26, 27, 28, 29].

(5) To encourage and direct research and teaching efforts for the needs of the systems construction (e.g. taxonomy, Knolwedge consolidation, etc.).

Following are criteria for evaluating the alternative strategies:

(1) The usefulness of the system, for what it covers, at each point in time during the development process.

(2) The potential quality and efficiency of the developers learning process.

(3) The expected development 'leverage' to be achieved, in terms of researcher's cooperation and financial resources.

03) improve the volume, quality, variety of cases of practical implementation of MS/OR.

DEVELOPMENT STRATEGIES

In principle, there are two basic alternatives for development strategies for the suggested MS/OR--DSS, a one shot strategy vs a se- quential one. Each has its own advantages and disadvantages. It seems that in the presence of high risks and costs, a sequential development process is preferred. There are a variety of R&D strategies in the literature [12, 13]. A few of them were chosen as reasonable for the systems development policy:

(4) The various performance evaluations expected from the system.

Beyond the above suggested strategies a very deep conceptual understanding is required for the implementation of a highly structured KS. This is true for any area, but especially so for an interdisciplinary field such as MS/OR.

Clearly, there is a tight relationship between the structure in which the knowledge is main- tained and the potential expansion rate of the knowledge as well as the added value of such expansion.

Various journals already require different reg- ulations for maintaining the knowledge. Com- puters & OR for example, requires scope, other

428 Mehre: et al.--A Conceptual Scheme of Knowledge Systems for MS~OR

journals require key words. There are impor tan t steps in knowledge organization, but relevant knowledge might be lost if the product ion pro- cess o f the knowledge is not considered.

Clearly, various managerial methods includ- ing database management and Artificial Intel- ligence (AI) [30] might be useful in searching for the structure o f a KS. The system must be flexible to changes, without damaging content. Rout ine changes are required if a new E K U is added.

These changes may or may not affect the dictionary. Non-rout ine changes refer to any changes which require modification in the con- ceptual structure. These changes are due for example to new methodologies or subfields which cannot fit the existing structures.

We agree with those who believe that creativity cannot be designed [8], but as an inquiring task, it's capability is very much de- pendent on availability, structure accuracy and relevancy o f the knowledge that is accessible.

The suggested KS probably seems like science fiction but those o f us who deal with M S / O R problems believe that difficulties related to knowledge ambiguity in this field, justify greater efforts for knowledge maintenance.

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ADDRESS FOR CORRESPONDENC~ G. Rabinowitz, Department o fOR, Weatherhead School of Management. Case West- ern Reserve University, Cleveland, OH 44106, USA.