johnnie b. linn iii , division of business, concord university

A VALUE-ADDED SYSTEM FOR EVALUATING CURRICULA OR COURSES OF STUDY AGAINST

ACCREDITATION CRITERIA—A PETRI-NET APPROACH

Johnnie B. Linn III, Division of Business, Concord UniversityPO Box 1000, Campus Box 56, Athens, WV 24712

Value Added

Value Added

Petri Nets and Their Firings

Petri Nets and Their Firings

Petri Nets and Their Firings

Petri Nets and Their Firings

Principles of Accounting

Cost Management

Intermediate Accounting I

Advanced Accounting

Intermediate Accounting II

Auditing I

Principles of Accounting

Cost Management

Intermediate Accounting I

Advanced Accounting

Intermediate Accounting II

Auditing I

Principles of Accounting

Cost Management

Intermediate Accounting I

Advanced Accounting

Intermediate Accounting II

Auditing I

Principles of Accounting

Cost Management

Intermediate Accounting I

Advanced Accounting

Intermediate Accounting II

Auditing I

Principles of Accounting

Cost Management

Intermediate Accounting I

Advanced Accounting

Intermediate Accounting II

Auditing I

Principles of Accounting

Cost Management

Intermediate Accounting I

Advanced Accounting

Intermediate Accounting II

Auditing I

Matrix Representation for A Set of Firings

Mt = Mo + A’Σ Ui

(1)

An Adjacency Matrix

PRIN ACCT -1 1 1 0 0 0 0 0 0 0 INT ACCT I 0 -1 0 1 0 0 0 1 0 0 COST MGT 0 0 -1 0 1 0 0 0 0 0 INT ACCT II 0 0 0 -1 0 1 1 0 0 0 ADV ACCT 0 0 0 0 0 -1 0 0 1 0 AUDITING I 0 0 0 0 0 0 -1 -1 0 1

The Process

• An initial marking for the system is specified. • For each performance objective, a value is

assigned to each blank place node in the system. The values added form a vector V of rank p.

• The set of firings is specified.• The sum of values of the blank place nodes

involved in the firings is the contribution that the firings make to the performance objective.

Principles of Accounting

Cost Management

Intermediate Accounting I

Advanced Accounting

Intermediate Accounting II

Auditing I

00

1 1

1 0

1

1

3

Matrix Analysis

A = N + O (2)

Substituting into (1) we have

Mt = Mo + N’ΣUi + O’ΣUi (3)

Value Added

V.A. = V’O’ΣUi (4)

subject to

Mt = Mo + A’Σ Ui

Values on Transition Nodes: An Option

• When values are on place nodes, they are counted even if subsequent courses are not taken.

• Values can be placed on transition nodes.• Only one value per transition node. The values added

form a vector W of rank t.

Principles of Accounting

Cost Management

Intermediate Accounting I

Advanced Accounting

Intermediate Accounting II

Auditing I

00

1 1

1 0

1

1

3

Principles of Accounting

Cost Management

Intermediate Accounting I

Advanced Accounting

Intermediate Accounting II

Auditing I

0

1 1

1

13

Value Added, Values on Transitions

V.A. = W’ΣUi (4’)

subject to

Mt = Mo + A’Σ Ui

PETRI LIVES!