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研究生： 馬綱廷
Ma, Kang Ting
論文名稱： 運輸問題之進階敏感度分析
Advanced Sensitivity Analysis of the Transportation Problem
指導教授： 溫于平
Wen, Ue Pyng
林吉仁
Lin, Chi Jen
口試委員: 王小璠
Wang, Hsiao Fan
黎漢林
Li, Han Lin
時序時
Shih, Hsu Shih
張炳騰
Chang Ping Teng
學位類別： 博士
Doctor
系所名稱： 工學院 - 工業工程與工程管理學系
Department of Industrial Engineering and Engineering Management
論文出版年： 2016
畢業學年度： 104
語文別： 英文
論文頁數： 97
中文關鍵詞： 運輸問題 、敏感度分析 、退化解 、標記演算法 、供應鏈管理
外文關鍵詞： Transportation problem, Sensitivity analysis, Degenerate optimal solution, Labeling algorithm, Supply chain management
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    • 本論文考慮一個設置運輸部門的批發公司，該公司擁有倉庫以及零售店，藉由求解運輸問題能夠制定運輸部門長期的運輸計劃(供需平衡)。由於運輸問題的參數通常只是估計值，因此，為了瞭解成本、供給量與需求量的變化對運輸計畫造成的影響，運輸部門的決策者通常會進行敏感度分析。此外，若決策者有一筆經費可以用來改善運輸效率，敏感度分析可以提供決策者在不改變其短期策略下，須增加/減少那些倉庫的供給量或是零售店的需求量。許多文獻已經提出進階敏感度分析以解決主問題退化或是對偶問題退化對傳統敏感度分析所造成的影響。然而，文獻中大多是探討線性規劃問題，很少有討論運輸問題之進階敏感度分析，此外，文獻中採用輔助縮減問題來求得參數的敏感度分析範圍，因此當倉庫及零售店的數目很多時，求得所有參數的進階敏感度分析範圍必須消耗大量時間。故本研究針對以下三個議題推導出輔助縮減問題，分別是：(1)退化運輸問題成本係數之型二敏感度分析；(2)保持最佳路徑下運輸問題右手邊係數敏感度分析；以及(3)對偶問題退化運輸問題之右手邊係數型三敏感度分析。並藉由輔助縮減問題推出運輸問題敏感度分析的性質，據以發展標記演算法，使得在演算步驟中加入觀察到運輸問題敏感度分析的性質來提升演算的速度。研究結果顯示，針對這三個議題，標記演算法在求解的效果上，比傳統型一敏感度分析的範圍來的大。而在求解的速度上，標記演算法求解速度也比輔助縮減問題還快，因此不論是從管理意涵與求解速度來看，進階敏感度分析較傳統敏感度分析更適用於解決實務問題。

    A wholesale company with warehouses and retail stores has its own transportation department, which is considered in this dissertation. A long-term shipping plan from warehouses to retail stores can be obtained by the transportation problem. Since the parameters of the transportation usually are estimators, a sensitivity analysis is usually adopted to realize the perturbations of parameters to the shipping plan. In addition, if decision maker has a budget to improve the shipping plan in short-term, sensitivity analysis can address the problem that how to reallocate the resources. Many papers in the literatures point out the influences of degenerate optimal solutions to the traditional sensitivity analysis, then propose advanced sensitivity analysis. However, most papers mention about advanced sensitivity analysis of a linear programming problem, but a few papers mention about advanced sensitivity analysis of the transportation problem. In addition, papers in the literature propose the auxiliary reduced model to obtain the perturbation ranges of advanced sensitivity analysis. Once the number of warehouses and retail stores increase, the computational time would increase dramatically. In this dissertation, three major issues are addressed: (1) Type II sensitivity analysis of cost coefficients of the degenerate transportation problem; (2) Optimal-routes invariant sensitivity analysis for supplies and demands when dual optimal solutions are degenerate; (3) Type III sensitivity analysis for right-hand-side parameters in the transportation problem with dual degenerate optimal solutions. We propose the auxiliary reduced models and observe some properties of each auxiliary reduced model, then develop the algorithms with labeling procedure to address the above issues, and consider the observed properties in the procedures of the algorithms. The computational results show that the proposed algorithms can provide more complete perturbation ranges to decision makers. The computational time of the algorithms with labeling procedure are more efficient than the computational time of auxiliary reduce models.

    摘要 I Abstract II 致謝 IV Contents VI Lists of Tables IX List of Figures XI Chapter 1 Introduction 1 1.1 Background 1 1.2 Motivation and Objectives 7 1.3 Framework of the Dissertation 8 Chapter 2 Literature Review 10 2.1 Advanced Sensitivity Analysis of Linear Programming Problems 10 2.2 Sensitivity Analysis of Assignment Problems and TPs for OFCs 11 2.3 Sensitivity Analysis of the TPs for RHS Parameters 13 2.4 Labeling Algorithms 14 2.5 Summary 15 Chapter 3 Optimal-Routes Invariant Sensitivity Analysis for RHS Parameters of the TP 17 3.1 Models of Optimal-Routes Invariant Sensitivity Analysis for RHS Parameters of the TP 17 3.2 Algorithms for Optimal-Routes Invariant Sensitivity Analysis for RHS Parameters of the TP 23 3.3 Numerical Examples 29 3.3.1 Determining the Perturbation Range for s1 30 3.3.2 Determining the Perturbation Range for d2 34 3.3.3 Discussion 35 3.4 Sensitivity Analysis of Job Assignment Problem in a Parallel Machine Environment 37 3.5 Summary 39 Chapter 4 Type II Sensitivity Analysis for OFCs of the Degenerate TP 41 4.1 Models for OFCs’ Sensitivity Analysis of the DTP 41 4.2 Algorithms for OFCs’ Sensitivity Analysis of the DTP 46 4.3 Numerical Examples 51 4.3.1 Type II Range of Δ21 51 4.3.2 Type II Range of Δ24 54 4.3.3 Computational Results 56 4.3.4 Discussion 57 4.4 Extend the Proposition of Lemma 4.1 in a Fuzzy Three Dimensional Axial Assignment Problem 59 4.5 Summary 63 Chapter 5 Type III Sensitivity Analysis for Setting of Supplies and Demands 65 5.1 Models of Type III Sensitivity Analysis for Setting of Supplies and Demands 66 5.2 Algorithms for Type III Sensitivity Analysis of RHS Parameters of the TP 70 5.3 Numerical Examples 77 5.3.1 Algorithm 5.1 for the Upper Bound of Perturbation Range of s1 and the Lower Bound of Perturbation Range of d1 78 5.3.2 Algorithm 5.2 for the Upper Bound of Perturbation Range of d3 and the Lower Bound of Perturbation Range of s1 81 5.3.3 Discussion 84 5.4 Extend the Proposition of Lemma 5.1 to Fuzzy Three Dimensional Axial Assignment Problem 87 5.5 Summary 88 Chapter 6 Conclusions and Future Research 90 References 92 Appendix A 96

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