Designing Business Processes and Communication Structures for E-Business Using Ontology-Based Enterprise Models with Mathematical Models Henry M. Kim Schulich School of Business York University 4700 Keele St., Toronto, Ontario Canada M3J 1P3
[email protected] (416) 736-2100 x77952 | (416) 736-5687 [fax] K. Donald Tham Department of Mechanical, Aerospace and Industrial Engineering Ryerson University 350 Victoria St Toronto, Ontario M5B 2K3
[email protected] (416) 979-5000 x7209 | (416) 979-5265 [fax]
Abstract Organizations are apprehensive about developing e-business systems because the endeavor is novel. If ebusiness is considered as the conduct of business using the Internet—a network of networks—then ebusiness systems design can be represented as a network design problem. This paper outlines an approach for analysis and design of business process and communications structure networks for e-business. Network design alternatives are generated by applying best practices and design principles to business requirements, using ontology-based enterprise models. Alternatives then are modeled mathematically for analysis and comparison. Domains relevant for e-business systems design are described, formally and systematically, using this approach. These formal descriptions are general axioms, used to logically and mathematically infer prescriptions for specific design problems. These descriptions and prescriptions are sharable and re-usable. The mathematical models are developed using known algorithms, heuristics, and formulae. Therefore, fidelity of prescriptions based on these models can be objectively justified. Due to these characteristics, models developed using this technique are especially useful for developing novel ebusiness systems. An example application of this technique is presented, and research questions addressed using the approach are discussed. Keywords: Ontologies, business process, communication structures, e-business, enterprise modeling
Appeared in: Proceedings of ICEIS 2002, Ciudad Real, Spain, April 2002.(c) ICEIS
Designing Business Processes and Communication Structures for E-Business Using Ontology-Based Enterprise Models with Mathematical Models Abstract Organizations are apprehensive about developing e-business systems because the endeavor is novel. If ebusiness is considered as the conduct of business using the Internet—a network of networks—then ebusiness systems design can be represented as a network design problem. This paper outlines an approach for analysis and design of business process and communications structure networks for e-business. Network design alternatives are generated by applying best practices and design principles to business requirements, using ontology-based enterprise models. Alternatives then are modeled mathematically for analysis and comparison. Domains relevant for e-business systems design are described, formally and systematically, using this approach. These formal descriptions are general axioms, used to logically and mathematically infer prescriptions for specific design problems. These descriptions and prescriptions are sharable and re-usable. The mathematical models are developed using known algorithms, heuristics, and formulae. Therefore, fidelity of prescriptions based on these models can be objectively justified. Due to these characteristics, models developed using this technique are especially useful for developing novel ebusiness systems. An example application of this technique is presented, and research questions addressed using the approach are discussed.
1. Introduction Many organizations are apprehensive about developing e-business systems because the endeavor is novel. A useful definition of e-business is “the conduct of business on the Internet, not only buying and selling but also servicing customers and collaborating with business partners” [Whatis 99]. Organizations use physical, informational, and social networks for buying, selling, servicing, and collaborating. These networks are used to support business processes and as infrastructure for communications. If the Internet is considered a “network of networks,” then the design of e-business systems can be conceptualized and modeled in part as the design of business process and communications structure networks. This abstraction decomposes a task not well understood (designing e-business systems) to tractable sub-tasks of modeling 1) business process and communications structure networks, and 2) how the Internet and other information technologies affect characteristics of such networks. Not only are these models invaluable in designing a specific system, they can be re-used, thus making general e-business systems design a less unknown task. Business processes and communications structures are general, tangible facets of the organization, and hence can be represented using a (computational) enterprise model1, “a computational representation of the structure, activities, processes, information, resources, people, behavior, goals, and constraints of a business, government, or other enterprise” [Fox & Grüninger 98]. Though seemingly less tangible, organizational knowledge about how information technologies—especially the Internet—can be leveraged for novel business process and communications structures design can also be modeled in an enterprise model as information, goals, and constraints. Enterprise models are data models; they represent enterprise facets in a data modeling language as entities, relationships, attributes, and axioms. Mathematical models can be used to state functional relationships of enterprise facets using mathematics. Math models for analyzing networks are especially useful for modeling business processes and communications structures. Whether they are represented using a data modeling language or mathematics, or another type of language, the following are desirable properties of models of business processes and communications structures for e-business: 1. Descriptive: The models should describe business processes and communications structures. 2. Prescriptive: The models should apply knowledge about developing e-business business processes and communications structures to the descriptions to prescribe to developing good designs 3. Sharable and re-usable: Since the endeavor for which the models are developed is novel, it is important that it be sharable and capable of re-use, both within and among organizations. 4. Formal. To effectively use computers to enable prescription, and sharing and re-use, the models should be represented in a formal language with limited syntax and semantics that minimizes interpretation ambiguity. These representations then can be encoded so that computers can automatically apply prescriptions and intended meanings of the model builder when the model is shared or re-used by others.
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Henceforth, the term, enterprise model, will refer to computational enterprise models.
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2. Ontology-Based Enterprise Modeling Using ontologies, Kim [99] and Tham [94] develop enterprise models for quality management and cost management, respectively, with the four desirable properties. An ontology is a data model that “consists of a representational vocabulary with precise definitions of the meanings of the terms of this vocabulary plus a set of formal axioms that constrain interpretation and well-formed use of these terms” [Campbell & Shapiro 95]. Vocabulary, definitions, and axioms that describe the enterprise are formally represented using ontologies, and prescriptions for achieving goals are formally defined using these ontologies’ representations in models by Kim and Tham. Kim describes enterprise quality and prescribes to ISO 9000 compliance; Tham describes activity-based costing, and prescribes to strategic cost management. Parts of these models can be shared and re-used by others with minimized interpretation ambiguity because they are modeled formally. Therefore, an ontology is an explicit representation of shared understanding [Gruber 93]. An example use of ontologies for business process or communications structure design is presented by Atefi [97], who represents Hammer and Champy’s [94] business process re-engineering principles as formal axioms of an ontology. These axioms are applied to different business scenarios to offer prescriptions. Alternatively, Buzacott [96] models these principles mathematically. He models networks of business processes that are consistent with each principle, and then analyzes networks’ performance using queuing models. There are merits to both modeling approaches: Business processes can be formally and systematically described using ontologies, and since there are numerous, well-known mathematical models for network analysis, prescriptions resulting from analyzing these models can be objectively justified. Next, a discussion of the four desirable properties of business process and communications structures models for e-business rationalizes an approach combining ontology-based enterprise and mathematical modeling.
3. Ontology-Based Enterprise Models and Mathematical Models To enable ontology sharing and re-use, key assumptions, vocabulary, and business rules about enterprise facets must be stated, organized, and formally defined and constrained. Thus, ontologies should be richly descriptive; what is often implicitly held is explicitly represented. Ontologies by design are constructed from existing ontologies. For example, Kim’s [99] ontologies for quality management are developed using ontologies of activity, state, causality, time, resource, and organizational structure that describe fundamental concepts about an enterprise. These are collectively called the TOVE Core Ontologies [Grüninger & Fox 95]. However ontological engineering is still a new endeavor, and sharable libraries of ontologies are not extensively available as, say, math libraries. Unless representations from robust sharable ontologies can be used, developing richly descriptive ontologies is time consuming. It entails anticipating unintended interpretations of terms in the vocabulary or improper applications of business rules, and mitigating them. Moreover, expressiveness of descriptive ontologies bounds problem solving capabilities of prescriptive ontologies constructed from them: The more expressive the descriptive ontologies, the more likely are insights from using the prescriptive ontologies. There are numerous libraries of algorithms, heuristics and formulae, and research supporting them. So, formal mathematical models whose analyses yield prescriptive insights can be constructed from existing libraries with much less work than using ontology-based models. When evaluating a math model, only the fidelity—accuracy, appropriateness of assumptions, etc—of its development to the point at which it is expressed using libraries may need to be evaluated, not the libraries themselves. Since shared ontologies are not supported by similar volume of research, the fidelity of shared ontologies’ representations may be questioned, as well as those representations built from them. It is often possible to prove, analytically 2
or by simulation, that one mathematical model performs better than a similar one as per some concrete, quantitative criteria. However, it is difficult to categorically state that a definition of a business process represented in a given descriptive ontology is better than a similar ontology’s definition, or that Hammer and Champy’s BPR principles represented in a given prescriptive ontology is better than insights from Davenport’s [93] writings about business processes, represented in another ontology. Mathematical models are more re-usable and prescriptive than ontology-based models. Extensively available libraries can be re-used, thus shortening model development time. Fidelity of mathematical prescriptive models can be objectively justified. Often however, math models can be re-used and offer prescriptions only if there is an interpreter who understand the mathematics. As well, assumptions and analysis of the domain used to develop the models are informally documented in natural language, and hence, subject to interpretation ambiguity inherent in natural language use. Even these descriptions are sometimes sparsely documented, and much knowledge is “lost” after model construction. Therefore, mathematical models are not richly descriptive. Say that the following subtle distinction is made: - Re-use: Using parts of existing models to develop new ones, where the builder of the existing model plays some role in new development - Sharing: Using parts of existing models as intended by the builder of the model, even though the model builder does not play an active role in its use. Then because they are cryptic and not descriptive, math models are often not sharable, though re-usable. Figure 1.
Relationship between Data and Mathematical Models
use as math library Statements only expressed in data modeling language
Data Model
Data Model ≡ Math Model
Statements only expressed in math modeling language
Math Model
Statements equivalently expressed in data and math languages
use as data dictionary Often data models are useful simply as descriptive abstractions of entities, relationships, and attributes. Formal models further commit to supporting automatic inference of implicit descriptions. Mathematical models formally represent functional relationships that govern behavior of systems. Formal data models can be used to infer implicit relationships between entities and their attributes, and when they access mathematical expressions, they can be used to further infer functional relationships. Used this way, mathematical models serve as libraries for a formal data model. When mathematical models access formal data model expressions, assumptions and principles of math model use, which may otherwise be implicit or informally stated, are explicitly stated using a data model, thus providing meanings of terms used in the math model and constraints on their proper use for clarification and validity testing. Formal data models serve as data dictionaries for a mathematical model. There are some expressions in either language types that are logically equivalent, namely first-order mathematical expressions —i.e. those of the form f(x), not 3
f(g(x))—can be equivalently expressed in First-Order Logic. These expressions are important because they are used to translate between ontology-based and mathematical models. Next, a formal modeling approach that combines the descriptiveness and sharability of ontology-based models with the prescriptive capability and re-usability of math models is detailed.
4. Combined Ontology-Based Modeling Approach
Enterprise
and
Mathematical
Below, different models developed using, and used for, this approach are presented. Figure 2.
Using Enterprise Models of E-Business Best Practices and Evaluation Metrics
SH
AR
AB
LE
FORMAL Mathematical Model
Data Model Industry-Specific Company-Specific
L E D O M TIY GENERAL
Prescriptive
E-Business Best Practices
E-Business Performance Models
Descriptive
E-Business Ontologies
E-Business Evaluation Metrics
Building Block
Core Ontologies
Statistical, Algebraic Models
Populated Enterprise Models
Business Performance Data
Business Requirements
There are two types of formal models, data and mathematical. These models can be characterized by the degree to which they can be shared and re-used: General, industry-specific, or company-specific. Models can also be characterized by their purpose, which also defines their generality using this approach: Prescriptive models are developed using descriptive ones, which in turn are developed using building block models. Business facts and requirements are represented as data instances of a populated (instantiated) enterprise model or raw numbers comprising business performance data. Building block models provide general form with which business facts and requirements are represented. For example, activity(A) is a Core Ontology term. The fact, lathing using equipment #1 is an activity, can be represented as an instance activity(lathing1)—i.e. the variable A is bound to the constant lathing1—in the populated enterprise model. Say that the average duration of the activity is 5 minutes. This can be represented as an instantiation of the term activity_duration(A,Tp) as activity_duration(lathing1,5). The arrows in the diagram denote that one model uses translated representations from the other. The mathematical model of business performance data translates activity_duration(lathing1,5), and represents it as s lathe1=5. Next, example uses of such representations in the modeling approach is presented.
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Relationship between Data and Mathematical Models at the Building Block Core Ontologies Figure 3.
activity(A) resource(R) has_ collection(R,Rt) sum(Qt,{Qti},N) = collection(Rt)
+ √x
Σi=1,NQti
A B B is defined in terms of A
µ, σ2
merge_ trace (A,{Rti},Rt)
Statistical, Algebraic Models Level A building block math model comprises elementary terms like Σ , which is used as a math library term in defining the ontology term sum(Qt,{Qti},N) . This term is used in turn to define merge_trace(A,{Rti},Rt) in First-Order Logic [Kim 99]: Term-1.
Qt= = Σ i=1,N Qti
sum({Qti},N,Qt) ∀N∀Qt { ∀i Qt=Σ i=1,N Qti ≡ ∀(Qt1,Qt2,,Qt N) sum({Qt 1,Qt2,,QtN},N,Qt)}. Defn-1.
A merge trace relationship exists between one merged collection (e.g. batch or lot) and the collections from which it is comprised, if there is an activity which produces one collection of quantity Qup, which is the sum of the quantities Quc1,Quc 2,,QucN of the collections that are consumed for the activity, and all the produced and consumed collections are all of the same resource type 2: Defn-2.
merge_trace(A,{Rti},Rt) ∀A∀s∀Rt∃(Rt1,,,Rt n)∃R∃St∃Quc∃so [holds(merge_trace(A,{Rt1,Rt2,,,Rt n},Rt),s) ≡ holds(primitive_activity(A),s) ∧ holds(produce(St,A),s) ∧ holds(produces(St,Rt),s) ∧ holds(has_collection(R,Rt),s) ∧ holds(amount_produced(Rt,Qup),s) ∧ ¬∃ Sto¬∃ Rto { holds(produces(Sto,Rto),so) ⊃ Rt≠Rto } ∧ ∃(St1,,,St n)∃(Quc1,,,Qucn) { ( ∩i=1,,n ( holds(consume(St i,A),s o) ∧ holds(consumes(St i,Rt i),so) ∧ holds(has_collection(R,Rti),so) ∧ holds(amount_committed(St i,Rti,Quci),so) ) ∧ so
