本研究探討隨機運輸營收管理問題，此隨機問題為在最大化收益的目標下，如何將有限的產能分配於服從非同質性卜瓦松過程的需求(non-homogeneous Poisson process)，進而提出一個動態決策方法來決定是否接受訂單。此方法適用於多航段、多重座位等級以及多重票價等級的運輸營運管理問題。當有顧客預定時，決策者必須立刻決定是否要接受該顧客的預訂需求。此外，已接受顧客可能再出發時間前取消預約，或是在出發的時候未出現，因此在本研究中，可能會發生超額預定的情況。
由Lai (2010)提出的模擬期望價差(simulated expected revenue gap, SERG)，與Ni(2013) 提出的模擬期望收益法(simulated expected revenue approach, SERA)的概念，本研究整合出抽樣最佳營收方法(sampling optimal revenue approach ,SORA)，並藉由相同的概念，提出一個隨機規劃模型(stochastic programming model)來解決動態決策問題。此隨機規劃模型以加入一個二元變數來表示訂單的接受與否，並以抽樣可能的情境來近似隨機決策問題。因此當求出隨機規劃模型的最佳解時，同時也知道是否要接受訂單。由於此隨機規劃模型的係數矩陣符合完全單模矩陣(totally unimodular matrix)，因此藉由線性規劃的寬放就可得到整數的最佳解。所以雖然此隨機規劃模型是整數規劃，但其解題的效率與線性規劃相同。最後，根據本研究模擬的實驗結果，隨機規劃模型所得到的收益大於其他的測試方法。

This study considers the stochastic transportation industry revenue management problem of allocating finite capacity to booking requests of non-homogeneous Poisson processes, and investigates the dynamic acceptance-or-rejection decision method with the objective of maximizing the revenue. The investigated decision method is for a transportation company that consists of multiple leg service routes, multiple fare classes, and multiple seat classes. In addition, an accepted booking request may be cancelled, or does not show up at departure time. Hence, the practice of overbooking is allowed in this problem. When a reservation request arrives, the decision maker must make a prompt decision on the acceptance-or-rejection of the requests.
The concept of sampling optimal revenue approach (SORA) proposed by Lai (2010) and Ni (2013) can be used to solve the problem. Based on similar concept, this study proposes a stochastic programming model (SPM) to make such a dynamic stochastic decision problem. In SPM, a binary variable is modeled to represent the acceptance-or-rejection decision and samples a number of scenarios to approximate the stochastic natural of the dynamic decision problem. Thus, the decision on the acceptance-or-rejection can be obtained by the optimal solution of SPM. Since the coefficient matrix of SPM satisfies total unimodular property, the linear programming relaxation of SPM provides an integral optimal solution. Hence, even though the SPM is an integer programming, it can be solved as efficiently as a linear programming. According to the simulation experiments, SPM provides the highest revenue among all the tested methods.

摘要 i
Abstract ii
TABLE OF CONTENTS iii
LIST OF FIGURES v
LIST OF TABLES vi
1. Introduction 1
1.1. The characteristics of revenue management 1
1.2. The characteristics of transportation industry 2
1.3. The Problem Description 5
2. Literature Review 8
3. Decision Models 11
3.1. Notations 11
3.2. Sampling optimal revenue approach 13
3.2.1. Sampling scenarios 13
3.2.2. MIP Formulation for optimizing a scenario under either accepting or rejecting the current booking request 19
3.2.3. Average revenue and marginal profit in SORA 21
3.3. Stochastic programming model 22
3.3.1. Stochastic programming formulation 23
3.3.2. SPM and SORA make identical decision 25
3.3.3. The unimodularity of SPM 29
3.4. Three applications of SORA decision procedure 31
3.4.1. Application 1: real-time SORA method 31
3.4.2. Application 2: marginal profit matrix method 32
3.4.3. Application 3: reservation limit method 34
3.5. First-come-first-served 38
3.6. Certainty equivalent control 39
4. Experiment Design and Result Analysis 40
4.1. Experiment design 40
4.2. Procedure of problem generation 44
4.3. Compared approaches and performance measure 45
4.4. Experiment Setting and Result Analysis 45
4.4.1. Experiment 1 46
4.4.2. Experiment 2 49
4.4.3. Experiment 3 52
5. Conclusion and Future Research 56
Reference 58

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