## Abstract

This study presents a novel model for assignment of internal auditors to branches of businesses. Previous studies have concerned with minimizing the cost but in this model, aim is maximizing auditor’s utility. For this purpose an integer programming model introduced. The objective is maximizing the auditors’ total utility. Each branch has different impact values for auditors, which indicate auditors’ utility level in terms of location, size and type of branches. Also to keep the balance of auditor’s working days and total gained impact values particular constraints are defined for the integer programming model. This implementation has 3 particular steps; first is quantification of the branches’ effects on the auditors. AHP method is used to define branches’ impact values. The second is simulating the durations of auditing process. To minimize the effect of abnormal situations, durations are simulated. Last step is to reach the rotation of auditors, total working days and the total utility of the auditor; the integer programming model is solved by Python-Gurobi Optimizer.

### Downloads

## References

- Abdioğlu, H. (2008). Bölgesel Kalkınma Ajansları: Muhasebe İşlemleri ve Denetimi. I. Güney Marmara Bölgesel Gelişme Sorunları Sempozyumu, Bandırma-Balıkesir.
- Bailey, A. D., Boe, W. J., & Schnack, T., 1974. The audit staff assignment problem: a comment. Accounting Review, pp. 572-574.
- Balachandran, K. R., & Steuer, R. E. , 1982. An interactive model for the CPA firm audit staff planning problem with multiple objectives. Accounting Review, pp: 125-140.
- Balachandran, B. V., & Zoltners, A. A., 1981. An interactive audit-staff scheduling decision support system. Accounting Review, pp: 801-812.
- Blocher, E., 1979. Performance effects of different audit staff assignment strategies. Accounting Review, pp: 563-573.
- Brody, R. G., & Lowe, D. J., 2000.The new role of the internal auditor: implications for internal auditor objectivity. International Journal of Auditing,4(2), pp: 169-176.
- Burkard, R. E. 2002. Selected topics on assignment problems. Discrete Applied Mathematics, 123(1),pp: 257-302.
- Chan, K. H., & Dodin, B., 1986. A decision support system for audit-staff scheduling with precedence constraints and due dates. Accounting Review, pp: 726-734.
- Chang, C. J. (2002). A decision support system for audit staff scheduling of multiple and large-scaled engagements. Review of Business Information Systems (RBIS), 6(1), 27-40.
- Chen, R. C., Huang, C. C., & Suen, S. P. (2012). On the Optimization of Auditor Assignment. In Information and Business Intelligence (pp. 617-622). Springer Berlin Heidelberg.
- Dantzig, G. B., 1954. Letter to the Editor—A Comment on Edie's “Traffic Delays at Toll Booths”. Operations Research, 2, pp: 339-341.
- Dodin, B., & Huang Chan, K., 1991. Application of production scheduling methods to external and internal audit scheduling. European Journal of Operational Research, 52(3),pp:267-279.
- Dodin, B. (1999). Project Management in Audit Staff Scheduling. In Project Scheduling (pp. 509-527). Springer US.
- Edie, L. C., 1954.Traffic Delays at Toll Booths. Operations Research, 2,pp:107-138
- Ernst, A. T., Jiang, H., Krishnamoorthy, M., & Sier, D., 2004. Staff scheduling and rostering: A review of applications, methods and models. European journal of operational research, 153(1),pp:3-27.
- Ford Jr, L. R., & Fulkerson, D. R., 1956.Solving the transportation problem.Management Science, 3(1),pp: 24-32.
- Fowler, J. W., Wirojanagud, P., & Gel, E. S., 2008. Heuristics for workforce planning with worker differences. European Journal of Operational Research,190(3),pp: 724-740.
- Kir, H. (2010). Stratejik Denetim ve Denetimde Risk Odaklılık. Denetişim Dergisi, 4, 47-62.
- Kuhn, H. W., 1955. The Hungarian method for the assignment problem. Naval research logistics quarterly, 2(1‐2),pp: 83-97.
- Munkres, J., 1957. Algorithms for the assignment and transportation problems.Journal of the Society for Industrial & Applied Mathematics, 5(1), pp:32-38.
- Motzkin, T. S., 1956. The Assignment Problem1. Numerical analysis, (6), pp: 109.
- Van den Bergh, J., Beliën, J., De Bruecker, P., Demeulemeester, E., & De Boeck, L., 2013. Personnel scheduling: A literature review. European Journal of Operational Research, 226(3), pp: 367-385.
- Saaty, T. L., 1977. A scaling method for priorities in hierarchical structures.Journal of mathematical psychology, 15(3),: 234-281.
- Summers, E. L., 1972. The audit staff assignment problem: a linear programming analysis. Accounting Review, pp: 443-453.
- Von Neumann, J., 1953. A certain zero-sum two-person game equivalent to the optimal assignment problem. Contributions to the Theory of Games, 2, pp: 5-12.
- Winston, W. L., & Goldberg, J. B., 1994.Operations research: applications and algorithms.