Operations Research Applications in Audit Planning and Scheduling
This paper presents a state-of-the-art survey of the
operations research models developed for internal audit planning.
Two alternative approaches have been followed in the literature for
audit planning: (1) identifying the optimal audit frequency; and (2)
determining the optimal audit resource allocation. The first approach
identifies the elapsed time between two successive audits, which can
be presented as the optimal number of audits in a given planning
horizon, or the optimal number of transactions after which an audit
should be performed. It also includes the optimal audit schedule. The
second approach determines the optimal allocation of audit frequency
among all auditable units in the firm. In our review, we discuss both
the deterministic and probabilistic models developed for audit
planning. In addition, game theory models are reviewed to find the
optimal auditing strategy based on the interactions between the
auditors and the clients.
[1] A. Mohamed, M .Qureshi and A. Behnezhad, “Reliability Evaluation
and Design of AICS: A Survey of Models and Experiments,” Review of
Accounting and Finance, vol. 4 no.2, pp. 59-85, 2005.
[2] J. Patton , J. Evans, B. Lewis, “A Framework for Evaluating Internal
Audit Risk,” Institute of Internal Auditors, Research Report number 25,
Altamonte Springs, Fl, 1982.
[3] K. Prasad, “Continuous and Periodic Audit,” Dynamic Tutorials and
Services. www.dynamic tutorials. blogspot.com, 2014
[4] P. Bernstein, “Competition Comes to Accounting,” Fortune, pp. 88-96,
July 17, 1978.
[5] E. Blocher, “Performance Effects of Different Audit Staff Assignment
Strategies,” The Accounting Review, pp. 125 -140, January 1982.
[6] J. Boritz, “Planning for the Internal Audit Function,” Institute of Internal
Auditors Research foundation, 1983.
[7] D. Wilson, and R. Ranson “Internal Audit Scheduling – A Mathematical
Model,” The Internal Auditor, pp. 42-50, July-August 1971.
[8] J. Boritz, and D. Broca,”Scheduling Internal Audit Activities,” Auditing:
A Journal of Practice & Theory, vol. 6, no. 1, pp.1-19, 1986.
[9] R. Barefield, “The Impact of Audit Frequency on the Quality of Internal
Control,” SAR # 1Sarasota, FL: American Accounting Association),
1975.
[10] J. Barzilai, D. Cook, and M. Kress, “A Generalized Network
Formulation of the Pairwise Comparison Consensus Ranking Model,”
Management Science, pp. 1007-1014, August,1986
[11] H. David, The Method of Paired Comparisons, New York: Oxford
University Press, 1988.
[12] S. Ramamootri, A. Bailey Jr, R. Traver (1999) “Risk Assessment in
Internal Auditing: A Natural Network Approach,” International Journal
of Intelligent Systems in Accounting, vol. 8, pp. 159-180, 1999.
[13] T. Saaty, “A Scaling Method for Priorities in Hierarchical Structures,”
Journal of Mathematical Psychology, vol. 15, pp. 234-281, 1977.
[14] T. Shibano, “Assessing Audit Risk from Errors and Irregularities,”
Journal of Accounting Research, vol. 28- Supplement, pp. 110-140,
1990
[15] W. Winston, Operations Research Applications and Algorithms, 4th
edition, Duxbury/Thomson, 2004.
[16] P. Carey and R. Guest, “Determining the Optimal External Audit
Interval for Private (and Family Controlled) Companies,” Journal of
Accounting, Auditing & Finance, vo. 15, no. 4, pp. 439-458, 2000.
[17] W. Knechel and H. Benson, “An Optimization Approach for Scheduling
Internal Audits of Divisions Decision Sciences, vol. 38, no. 9, pp. 1245-
1263, 1991.
[18] C. Miller, “The Simplex Method for Local Separable Programming.
Recent Advances in Mathematical Programming, New York, McGraw
Hills, 1963.
[19] R. Morey and D. Dittman, “Optimal Timing of Account Audits in
Internal Control,” Management Science, vol. 32, no. 3, pp. 272-282,
1986.
[20] L. Johnson, R. Leitch, and J. Neter, “Characteristics of Errors in
Accounts Receivable and Inventory Audits,” The Accounting Review,
vol. 56, no. 2, pp. 270-293, 1981.
[21] J. Hughes, “Optimal Internal Audit Timing,” The Accounting Review,
vol. LII, no. 1, pp. 56-68, 1977.
[22] R. Rossi, S. Tarim, B. Hinch, S. Prestwich, and S. Karacaer,
“Scheduling Internal Audit Activities: A Stochastic Combinatorial
Optimization Problem,” Journal of Combinatorial Optimization, vol. 19,
pp.325-346, 2010.
[23] E. Tsang, “Formulation of Constraint Satisfaction,” Academic Press,
London/San Diego, 1993.
[24] P. Van Hentenryck, Constraint Satisfaction in Logic Programming, MIT
Press, Cambridge, 1989.
[25] J. Flynn, S. Garstka, “A Dynamic Inventory Model with Periodic
Auditing,” Oper. Res., vol. 38, no. 6, pp. 1089-1103, 1990
[26] T. Bosch, J. Mukuddem-Petersen, M. Petersen, and I. Schoeman,
“Optimal Auditing in the Banking Industry,” Optim. Control Appl. and
Meth. DOI: 10.1002/oca.828, 2007.
[27] K. Mizgier and J. Pasia,“Multiobjective Optimization of Credit Capital
Allocation in Financial Institutions,” Central European Journal of
Operations Research, March 2015.
[28] E. Summer, “The Audit Staff Assignment Problem: A Linear
Programming Analysis,” The Accounting Review, vol. 47, no. 3, pp. 443-
453, 1972.
[29] B. Balachandran and A. Zoltners, "An Interactive Audit-Staff
Scheduling Decision Support System. The Accounting Review, vol. 56,
no. 4, pp. 801-812, 1981.
[30] K. Chan and B. Dodin, “A Decision Support System for Audit Staff
Scheduling with Precedence Constraints and Due Dates,” The
Accounting Review, pp. 125-140, January 1986.
[31] B. Dodin, A. Elimam and E. Rolland, “Tabu Search in Audit
Scheduling,” Eur. J. Oper. Res., vol. 106, pp. 373-392, 1998.
[32] C. Chang, “A Decision Support System for Audit Staff Scheduling of
Multiple and Large-Scaled Engagements,” The Review of Business
Information Systems, vol. 6, no. 1, pp. 27-32, 2002.
[33] P. Burgher, “PERT and the Auditor,” The Accounting Review, pp. 103-
120, January 1964.
[34] A. Cirtin, “Network Analysis and Internal Auditing,” .Internal Auditor,
vl. 34, no.1, pp. 27-31, 1977.
[35] C. Rackie, J. Krogstad, G. Grudnitski and D. Bryant, “PERT and
PERT/Cost for Audit Planning and Control,” Internal Auditor, vol. 36,
no. 4, pp. 57-68, 1977.
[36] B. Dodin and A. Elimam, “Audit Scheduling with Overlapping
Activities and Sequence Dependent Setup Costs,” .Eur. J. Oper. Res.,
vol. 97, pp. 22-33, 1997.
[37] B. Dodin, A. Elimam, “Erratum: Audit Scheduling with Overlapping
Activities and Sequence Dependent Setup Costs,” .Eur. J. Oper. Res.,
vol. 104, pp.262-264, 1998.
[38] S. Elmaghraby, and J. Kamburowski, “The Analysis of Activity
Networks Under Generalized Precedence Relations (GPR),”
Management Science, vol. 38, no. 9, pp. 1245-1263, 1992.
[39] J. Moder, C. Phillips, and E. Davis, Project Management with CPM,
PERT and Precedence Diagrams, Van Nostrand Reinhold, New York,
1983.
[40] S. Elmaghraby, Activity Networks: Project Planning and Control by
Network Models. Wiley, New York, 1977.
[41] B. Dodin and H. Chan, “Application of Production Scheduling Methods
to External and Internal Audit Scheduling,” .Eur. J. Oper. Res., vol. 52,
pp. 267-279, 1991
[42] B. Dodin, “Project Management in Audit Staff Scheduling,”
.International Series in Operations Research and Management Science,
vol. 14, pp. 509-527, 1999.
[43] H. Fukukawa, T. Mock, and A. Wright, “Client Risk Factors and Audit
Resource Allocation Decisions,” ABACUS: A Journal of Accounting,
Finance and Business Studies, vol. 47, no. 1, DOI: 10.1111/j.1467-
6281.2011. 00332.x, 2011,
[44] L. Noxon, “Taking the Close Look at Your Internal Controls,” The
Internal Auditor, pp. 19-25, June 1980.
[45] H. Siers and J. Blyskal, “Risk Management of the Internal Audit
Function,” Management Accounting, vol. 29-35, February 1987.
[46] B. Green and T. Calderon, “Information Privity and Internal Auditor's
Assessment of Fraud Risk Factors,” Internal Auditing, pp. 4-15, Spring
1996.
[47] B. Lacativo, “A Risk-Based Approach to Auditing for Fraud.,” Internal
Auditing, pp. 41-44, summer 1995.
[48] P. Newman, J. Park and R. Smith, “Allocating Internal Audit Resources
to Minimize Detection Risk Due to Theft,” Auditing: A Journal of
Practice &Theory, vol. 17, no. 1, pp. 69-82, 1998
[49] W. Albrecht, G. Wernz, and T. Williams, Fraud: Bringing Light to the
Dark Side of Business, Richard D. Irwin, Inc., 1995.
[50] W. Albrecht, “Employee Fraud”, Internal Auditor, pp. 26-37, October
1996.
[51] J. Hayes, “Employee Theft is no. 1 Problem Facing Today's Busy
Retailers", Discount Store News, vol. 108, September 17, 1990.
[52] D. Miltz, G. Calomme and M. Willekens M (19991) A Risk Based
Allocation of Internal Audit Time: A Case Study. Auditing: A Journal of
Practice &Theory 10: 49-61.
[53] T. Spinelli, “The Delphi Decision Making Process. Journal of
Psychology,” pp. 73-80, January 1983. [54] K. Hackenbrack and W. Knechel, “Resource Allocation Decision in
Audit Engagements,” Contemporary Accounting Research, vol. 14, no.
3, Fall 1997
[55] D. Gotlob, J. Moore, and K. Moore, “Optimizing Internal Audit
Resources: A Linear Programming Perspective,” Internal Auditing, pp.
20-30, Fall 1997.
[56] L. Killough and T. Souders, “A Goal Programming Model for Public
Accounting Firms,” The Accounting Review, vol. XL VIII, no. 2, pp.
268-279, 1973.
[57] K. Balachandran and R. Steuer, “An Interactive Model for the CPA Firm
Audit Staff Planning Problem with Multiple Objectives,” The
Accounting Review, vol. 57, no. 1, pp. 125-140, 1982.
[58] J. Gardner, R. Huefner and V. Lotfi, “An Interactive Multi-Criteria
Model for Audit Workload Planning,” Lecture Notes in Economics and
Mathematical Systems, vol. 335, pp. 234-243, 1989.
[59] J. Gardner, R. Huefner, and V. Lotfi, “A Multi-Period Audit-Staff
Planning Model Using Multiple Objectives: Development and
Evaluation,” Decision Sciences, vol. 21, pp. 154-170, 1990.
[60] P. Korhonen and M. Syrjanen, “Resource Allocation Based on
Efficiency Analysis,” Management Science, vol. 50, no. 8, pp. 1134-
1144, 2004.
[61] R. Steuer, Multiple Criteria Optimization: Theory, Computation, and
Application, Wiley, New York, 1986.
[62] H. Krüger and J. Hattingh, “A Combined AHP-GP model to Allocate
Internal Auditing Time to Projects,” ORiON, vol. 22, no. 1, pp. 59-76,
2006.
[63] L. Fellingham, D. Newman, “Strategic Considerations in Auditing,” The
Accounting Review, vol. LX, no. 4, pp. 634 -650, 1985.
[64] U. Anderson and R. Young, “Internal Audit Planning in an Interactive
Environment,” Auditing: A Journal of Practice &Theory, vol. 8, no. 1,
pp. 23-42, 1988.
[1] A. Mohamed, M .Qureshi and A. Behnezhad, “Reliability Evaluation
and Design of AICS: A Survey of Models and Experiments,” Review of
Accounting and Finance, vol. 4 no.2, pp. 59-85, 2005.
[2] J. Patton , J. Evans, B. Lewis, “A Framework for Evaluating Internal
Audit Risk,” Institute of Internal Auditors, Research Report number 25,
Altamonte Springs, Fl, 1982.
[3] K. Prasad, “Continuous and Periodic Audit,” Dynamic Tutorials and
Services. www.dynamic tutorials. blogspot.com, 2014
[4] P. Bernstein, “Competition Comes to Accounting,” Fortune, pp. 88-96,
July 17, 1978.
[5] E. Blocher, “Performance Effects of Different Audit Staff Assignment
Strategies,” The Accounting Review, pp. 125 -140, January 1982.
[6] J. Boritz, “Planning for the Internal Audit Function,” Institute of Internal
Auditors Research foundation, 1983.
[7] D. Wilson, and R. Ranson “Internal Audit Scheduling – A Mathematical
Model,” The Internal Auditor, pp. 42-50, July-August 1971.
[8] J. Boritz, and D. Broca,”Scheduling Internal Audit Activities,” Auditing:
A Journal of Practice & Theory, vol. 6, no. 1, pp.1-19, 1986.
[9] R. Barefield, “The Impact of Audit Frequency on the Quality of Internal
Control,” SAR # 1Sarasota, FL: American Accounting Association),
1975.
[10] J. Barzilai, D. Cook, and M. Kress, “A Generalized Network
Formulation of the Pairwise Comparison Consensus Ranking Model,”
Management Science, pp. 1007-1014, August,1986
[11] H. David, The Method of Paired Comparisons, New York: Oxford
University Press, 1988.
[12] S. Ramamootri, A. Bailey Jr, R. Traver (1999) “Risk Assessment in
Internal Auditing: A Natural Network Approach,” International Journal
of Intelligent Systems in Accounting, vol. 8, pp. 159-180, 1999.
[13] T. Saaty, “A Scaling Method for Priorities in Hierarchical Structures,”
Journal of Mathematical Psychology, vol. 15, pp. 234-281, 1977.
[14] T. Shibano, “Assessing Audit Risk from Errors and Irregularities,”
Journal of Accounting Research, vol. 28- Supplement, pp. 110-140,
1990
[15] W. Winston, Operations Research Applications and Algorithms, 4th
edition, Duxbury/Thomson, 2004.
[16] P. Carey and R. Guest, “Determining the Optimal External Audit
Interval for Private (and Family Controlled) Companies,” Journal of
Accounting, Auditing & Finance, vo. 15, no. 4, pp. 439-458, 2000.
[17] W. Knechel and H. Benson, “An Optimization Approach for Scheduling
Internal Audits of Divisions Decision Sciences, vol. 38, no. 9, pp. 1245-
1263, 1991.
[18] C. Miller, “The Simplex Method for Local Separable Programming.
Recent Advances in Mathematical Programming, New York, McGraw
Hills, 1963.
[19] R. Morey and D. Dittman, “Optimal Timing of Account Audits in
Internal Control,” Management Science, vol. 32, no. 3, pp. 272-282,
1986.
[20] L. Johnson, R. Leitch, and J. Neter, “Characteristics of Errors in
Accounts Receivable and Inventory Audits,” The Accounting Review,
vol. 56, no. 2, pp. 270-293, 1981.
[21] J. Hughes, “Optimal Internal Audit Timing,” The Accounting Review,
vol. LII, no. 1, pp. 56-68, 1977.
[22] R. Rossi, S. Tarim, B. Hinch, S. Prestwich, and S. Karacaer,
“Scheduling Internal Audit Activities: A Stochastic Combinatorial
Optimization Problem,” Journal of Combinatorial Optimization, vol. 19,
pp.325-346, 2010.
[23] E. Tsang, “Formulation of Constraint Satisfaction,” Academic Press,
London/San Diego, 1993.
[24] P. Van Hentenryck, Constraint Satisfaction in Logic Programming, MIT
Press, Cambridge, 1989.
[25] J. Flynn, S. Garstka, “A Dynamic Inventory Model with Periodic
Auditing,” Oper. Res., vol. 38, no. 6, pp. 1089-1103, 1990
[26] T. Bosch, J. Mukuddem-Petersen, M. Petersen, and I. Schoeman,
“Optimal Auditing in the Banking Industry,” Optim. Control Appl. and
Meth. DOI: 10.1002/oca.828, 2007.
[27] K. Mizgier and J. Pasia,“Multiobjective Optimization of Credit Capital
Allocation in Financial Institutions,” Central European Journal of
Operations Research, March 2015.
[28] E. Summer, “The Audit Staff Assignment Problem: A Linear
Programming Analysis,” The Accounting Review, vol. 47, no. 3, pp. 443-
453, 1972.
[29] B. Balachandran and A. Zoltners, "An Interactive Audit-Staff
Scheduling Decision Support System. The Accounting Review, vol. 56,
no. 4, pp. 801-812, 1981.
[30] K. Chan and B. Dodin, “A Decision Support System for Audit Staff
Scheduling with Precedence Constraints and Due Dates,” The
Accounting Review, pp. 125-140, January 1986.
[31] B. Dodin, A. Elimam and E. Rolland, “Tabu Search in Audit
Scheduling,” Eur. J. Oper. Res., vol. 106, pp. 373-392, 1998.
[32] C. Chang, “A Decision Support System for Audit Staff Scheduling of
Multiple and Large-Scaled Engagements,” The Review of Business
Information Systems, vol. 6, no. 1, pp. 27-32, 2002.
[33] P. Burgher, “PERT and the Auditor,” The Accounting Review, pp. 103-
120, January 1964.
[34] A. Cirtin, “Network Analysis and Internal Auditing,” .Internal Auditor,
vl. 34, no.1, pp. 27-31, 1977.
[35] C. Rackie, J. Krogstad, G. Grudnitski and D. Bryant, “PERT and
PERT/Cost for Audit Planning and Control,” Internal Auditor, vol. 36,
no. 4, pp. 57-68, 1977.
[36] B. Dodin and A. Elimam, “Audit Scheduling with Overlapping
Activities and Sequence Dependent Setup Costs,” .Eur. J. Oper. Res.,
vol. 97, pp. 22-33, 1997.
[37] B. Dodin, A. Elimam, “Erratum: Audit Scheduling with Overlapping
Activities and Sequence Dependent Setup Costs,” .Eur. J. Oper. Res.,
vol. 104, pp.262-264, 1998.
[38] S. Elmaghraby, and J. Kamburowski, “The Analysis of Activity
Networks Under Generalized Precedence Relations (GPR),”
Management Science, vol. 38, no. 9, pp. 1245-1263, 1992.
[39] J. Moder, C. Phillips, and E. Davis, Project Management with CPM,
PERT and Precedence Diagrams, Van Nostrand Reinhold, New York,
1983.
[40] S. Elmaghraby, Activity Networks: Project Planning and Control by
Network Models. Wiley, New York, 1977.
[41] B. Dodin and H. Chan, “Application of Production Scheduling Methods
to External and Internal Audit Scheduling,” .Eur. J. Oper. Res., vol. 52,
pp. 267-279, 1991
[42] B. Dodin, “Project Management in Audit Staff Scheduling,”
.International Series in Operations Research and Management Science,
vol. 14, pp. 509-527, 1999.
[43] H. Fukukawa, T. Mock, and A. Wright, “Client Risk Factors and Audit
Resource Allocation Decisions,” ABACUS: A Journal of Accounting,
Finance and Business Studies, vol. 47, no. 1, DOI: 10.1111/j.1467-
6281.2011. 00332.x, 2011,
[44] L. Noxon, “Taking the Close Look at Your Internal Controls,” The
Internal Auditor, pp. 19-25, June 1980.
[45] H. Siers and J. Blyskal, “Risk Management of the Internal Audit
Function,” Management Accounting, vol. 29-35, February 1987.
[46] B. Green and T. Calderon, “Information Privity and Internal Auditor's
Assessment of Fraud Risk Factors,” Internal Auditing, pp. 4-15, Spring
1996.
[47] B. Lacativo, “A Risk-Based Approach to Auditing for Fraud.,” Internal
Auditing, pp. 41-44, summer 1995.
[48] P. Newman, J. Park and R. Smith, “Allocating Internal Audit Resources
to Minimize Detection Risk Due to Theft,” Auditing: A Journal of
Practice &Theory, vol. 17, no. 1, pp. 69-82, 1998
[49] W. Albrecht, G. Wernz, and T. Williams, Fraud: Bringing Light to the
Dark Side of Business, Richard D. Irwin, Inc., 1995.
[50] W. Albrecht, “Employee Fraud”, Internal Auditor, pp. 26-37, October
1996.
[51] J. Hayes, “Employee Theft is no. 1 Problem Facing Today's Busy
Retailers", Discount Store News, vol. 108, September 17, 1990.
[52] D. Miltz, G. Calomme and M. Willekens M (19991) A Risk Based
Allocation of Internal Audit Time: A Case Study. Auditing: A Journal of
Practice &Theory 10: 49-61.
[53] T. Spinelli, “The Delphi Decision Making Process. Journal of
Psychology,” pp. 73-80, January 1983. [54] K. Hackenbrack and W. Knechel, “Resource Allocation Decision in
Audit Engagements,” Contemporary Accounting Research, vol. 14, no.
3, Fall 1997
[55] D. Gotlob, J. Moore, and K. Moore, “Optimizing Internal Audit
Resources: A Linear Programming Perspective,” Internal Auditing, pp.
20-30, Fall 1997.
[56] L. Killough and T. Souders, “A Goal Programming Model for Public
Accounting Firms,” The Accounting Review, vol. XL VIII, no. 2, pp.
268-279, 1973.
[57] K. Balachandran and R. Steuer, “An Interactive Model for the CPA Firm
Audit Staff Planning Problem with Multiple Objectives,” The
Accounting Review, vol. 57, no. 1, pp. 125-140, 1982.
[58] J. Gardner, R. Huefner and V. Lotfi, “An Interactive Multi-Criteria
Model for Audit Workload Planning,” Lecture Notes in Economics and
Mathematical Systems, vol. 335, pp. 234-243, 1989.
[59] J. Gardner, R. Huefner, and V. Lotfi, “A Multi-Period Audit-Staff
Planning Model Using Multiple Objectives: Development and
Evaluation,” Decision Sciences, vol. 21, pp. 154-170, 1990.
[60] P. Korhonen and M. Syrjanen, “Resource Allocation Based on
Efficiency Analysis,” Management Science, vol. 50, no. 8, pp. 1134-
1144, 2004.
[61] R. Steuer, Multiple Criteria Optimization: Theory, Computation, and
Application, Wiley, New York, 1986.
[62] H. Krüger and J. Hattingh, “A Combined AHP-GP model to Allocate
Internal Auditing Time to Projects,” ORiON, vol. 22, no. 1, pp. 59-76,
2006.
[63] L. Fellingham, D. Newman, “Strategic Considerations in Auditing,” The
Accounting Review, vol. LX, no. 4, pp. 634 -650, 1985.
[64] U. Anderson and R. Young, “Internal Audit Planning in an Interactive
Environment,” Auditing: A Journal of Practice &Theory, vol. 8, no. 1,
pp. 23-42, 1988.
@article{"International Journal of Business, Human and Social Sciences:70532", author = "Abdel-Aziz M. Mohamed", title = "Operations Research Applications in Audit Planning and Scheduling", abstract = "This paper presents a state-of-the-art survey of the
operations research models developed for internal audit planning.
Two alternative approaches have been followed in the literature for
audit planning: (1) identifying the optimal audit frequency; and (2)
determining the optimal audit resource allocation. The first approach
identifies the elapsed time between two successive audits, which can
be presented as the optimal number of audits in a given planning
horizon, or the optimal number of transactions after which an audit
should be performed. It also includes the optimal audit schedule. The
second approach determines the optimal allocation of audit frequency
among all auditable units in the firm. In our review, we discuss both
the deterministic and probabilistic models developed for audit
planning. In addition, game theory models are reviewed to find the
optimal auditing strategy based on the interactions between the
auditors and the clients.", keywords = "Operations research applications, audit frequency,
audit planning, audit-staff scheduling.", volume = "9", number = "6", pages = "2056-9", }
