本論文所探討之內容為半指派問題參數分析。在一般實務問題中，人力配置往往因為工作內容與工作需要而出現分組、分群作業的情形，因此，傳統的一對一指派問題便不適用在這一類型的問題上。相對的，半指派問題可有效地將人力針對工作內容進行分組，所建立出的模型能夠更加貼近實務狀況。然而，由於半指派問題具有高度的退化情形，在進行參數分析時，若以傳統分析手法操作，則會因為考量最佳解基底不變的條件，造成得出的擾動範圍與實際情況較不吻合，對於決策者的參考價值也不高。
在本研究中，我們提出一演算法去解決退化所產生的問題，相較於傳統參數分析方法，於新演算法中只需專注於維持原問題的正基底不變，退化解是可以自由改變的，如此一來，便可以得到相較於傳統擾動範圍更為寬敞的結果，也為決策者提供更為彈性且正確的決策空間。
本論文中，我們利用此一演算法來求得在成本係數沿特定方向變動時，其參數分析之擾動範圍，同時也以數值例的方式來呈現此演算法的運作流程。在文末，亦提供了數據分析結果以顯示此演算法的效率，並與傳統分析手法所得之結果進行比較。

This thesis concentrates on parametric analysis of the semi-assignment problem (semi-AP). Since there are identical tasks or works to be assigned in a company in real world, the semi-AP can be more practical as a planning tool than classic assignment problem. Due to the high degeneracy of the semi-AP, traditional parametric analysis, which decides the perturbed ranges where the current optimal basis remains optimal, is not suitable. The decision maker may not make the right decision by using informations.
In this study, we proposed an advanced parametric analysis algorithm of the semi-AP which determines the range without changing the current positive variable set, but allowing the change of the degenerate basic variables. Concerning high degeneracy of the semi-AP, we can broaden the perturbed ranges and provide more flexible informations for the decision maker in making decisions.
In this thesis we propose an algorithm for determining the perturbed ranges of cost coefficient which is perturbed in a specific direction. An illustrative example is presented to demonstrate the procedure of our proposed algorithm. In the end, we show the computational results to demonstrate the efficiency of the proposed algorithm and to compare the final result with traditional parametric analysis’s.

Pentico, D.W., “Assignment problems: a golden anniversary survey”, European Journal of Operational Research, 176, 774–793, (2007).
Barr, R., F. Glover and D. Klingman, “A new alternating basis algorithm for semi-assignment networks”, Computers and Mathematical Programming, Gaithersburg, 223-232, (1976) .
Duffuaa, S. O. and M. S. Ghassab, “A successive shortest path algorithm for the semi-assignment problem”, Technical Report.(1994).
Bazaraa, M.S., J.J. Jarvis and H.O. Sherali, “ Linear programming and network flowers”, 4th edition, Wiley-Interscience, New York, (2010).
Hadigheh, A.G and T. Terlaky, “Sensitivity analysis in linear optimization: invariant support set intervals”, European Journal of Operational Research, 169, 1158–1175, (2006).
Ma, Kang-Ting, Chi-Jen Lin and Ue-Pyng Wen, “Type II sensitivity analysis of cost coefficients in the degenerate transportation problem”, European Journal of Operational Research, (2013).
Toth, P and D.Vigo, “The vehicle routing problem”, Society Industrial and Applied Mathematics, Philadelphia, (2002).
Marshall L. Fisher, Kurt O. Jornsten and Oli B. G. Madsen, “Vehicle routing with time windows: two optimization algorithms”, Operations Research, Vol. 45, No. 3, 488-492, (1997).
Mason, S. J. and E. A. Pohl, “Network design analysis for special needs student services”, MBTC DOT 3019 Final Report, (2010).
Votaw, D.F. and A. Orden, “The personnel assignment problem”, Symposium on Linear Inequalities and Programming, US Air Force, 10, 155–163, (1952).
Kuhn, H.W., “The hungarian method for the assignment problem”, Naval Research Logistics Quarterly, 2, 83–97, (1955).
Volgenant, A., “Linear and semi-assignment problems: A Core Oriented Approach”, Computers & Operations Research, 23, 917-932, (1996).
Lin, Chi-Jen and Ue-Pyng Wen, “Sensitivity analysis of the optimal assignment”, European Journal of Operational Research, 149, 35–46, (2003).
Yan, S., “Approximating reduced costs under degeneracy in a network problem with side constraints”, Networks, 27, 267–278, (1996).
Balinski, M. L. and R. E. Gomory, “A primal method for the assignment and transportation problems”, Management Science, 10, 578-593, (1964).
Namkoong, S., J.-H. Rho and J.-U. Choi, “Development of the tree-based link labeling algorithm for optimal path-finding in urban transportation networks”, Mathematical and Computational Modeling, 27, 51-65, (1998).
Euge ́nia, C. M., J. Clìmaco, J. Figueira, E. Martins and J. L. Santos , “Solving bicriteria 0–1 knapsack problems using a labeling algorithm”, Computers and Operations Research, 30, 1865–1886, (2003).
Zeng, Shih-Ting, “Advanced Sensitivity Analysis of the Semi-Assignment Problem”, master thesis, National Tsing Hua University, Department of IEEM (2012).