通常已建立的指數基金，經過一段時間後其追蹤指數的效能已經無法滿足初期建購時的要求，此時管理者便面臨指數基金投資組合的調整問題。本論文融合建構指數基金的方法及最小化交易成本的概念，提出一個新的混合整數線性規劃模型以調整指數基金投資組合。模型亦考慮實務中交易成本、最小交易單位及批量、固定交易費用比率、以及資產總類數等限制。因此，模型包含整數變數及二元變數，求解也較為困難許多。本論文以啟發式演算法增進求解的效率，並以台灣50指數的相關資料做為實證研究的對象。 / The efficiency of index-tracking in index fund, which has been built, has usually been incapable to meet the needs after a period of time. In this moment, the managers have to face with the problems of the adjusting for index fund portfolio. In this paper, we integrate the methods of constructing index fund and the concepts of minimum transaction cost with it, and propose a new mixed integer linear program model to adjust the index fund portfolio. Moreover, the model also considers some limitations, such as the transaction costs, minimum transaction units and lots, fixed proportional transaction rates, and cardinality constraint in practical operating. For this reason, a set of integer variables and binary variables are introduced. However, they increase the computational complexity in model solution. Due to the difficulty of the MILP problem, a heuristic algorithm has been developed for the solution. The computational results are presented by applying the model to the Taiwan 50 index.

本論文研究股票分類與否對投資組合報酬有無差別，因此以目標規畫方式提出兩個混合整數線性規劃模型建立投資組合。在考量市場風險上，兩模型的差別在於一個是單股比重的限制，另一個是類股數目的限制。兩模型中均考慮交易數量為整數與實務中的交易成本，且採用了0-1決策變數，決定股票及類股的選取與否。並以台灣股票市場作為實證研究對象，探討兩模型投資組合在市場不同走勢下的表現，同時也觀察股票分類後，探討選幾個類股數會有較佳的績效，並分析投資組合建立後多久應該進行調整。 / This thesis studies the effect of return of a portfolio while restricting the number of asset category. Two mixed-integer linear programming models are proposed by using the goal programming technique. In consideration of the risk, the difference between these two models is that one focuses on a single stock restriction, and the other is on the asset category restriction. The integer restriction and transaction cost are included in the model while using binary decision variable to indicate the selection of an asset and the selection a category. Finally, an empirical study will be presented by applying to Taiwan’s stock market. The performances of these two models are discussed. Moreover, the best number of category in the portfolio and the best timing of rebalance are also investigated.

隨著經濟的高度成長及電廠興建的日益困難，電力的需求問題是愈來愈嚴重。如何有效率地安排核能機組進行例行性的停機大修及燃料再裝填工作是重要的課題。本論文中考慮核能發電機組五年時程的大修排程問題，我們將這個大修排程問題描繪成一個大型混合型整數線性規劃模型。由於問題的龐大與複雜，此問題的最佳解難以求出。因此，我們發展數個邏輯條件式有效地縮小解集合空間；另外並發展出一個啟發性演算法，採用合併變數法將0/1決策變數合併，使原問題轉成較小的合併模型。先解合併後的合併模型，利用合併模型答案的資訊來固定原始模型的部分變數值之後，再解原始問題。幾個實例計算顯示此演算法的可行性。 / Since the growth of economics and the difficulty to build a new power plant, the supply of electric power has become very tight. It is important to ensure the efficient operation of nuclear power plants, including timely shutdown, refueling and maintenance schedule. In this thesis, we deal with the scheduling shutdown and maintenance of nuclear power plants for a five-year time period. This problem can be formulated as a large-scale mixed integer linear problem. The difficulty of solving this problem is due to the large number of binary variables. We then develop several valid logical constraints to reduce the complexity in processing using the branch and bound technique. Also, a heuristic based on the aggregation and dis-aggregation techniques has been developed to yield a good solution. Several examples are given to show the applicability of the algorithm.

本文提出一個新的混合整數線性規劃模型建立投資組合。這個模型所採用的風險函數為最大損失的絕對值，而不是一般常用的損失變異數。在給定的報酬水準下，模型尋找在觀測期間中最小的最大損失的投資組合，即為大中取小的原則。模型也同時考慮實務上常遇見之情況，如：交易成本、最小交易單位、固定交易費用比率、資產總類數等限制。因此，模型內需使用整數變數及二元變數，導致模型的計算求解過程變得比不含整數變數及二元變數的模型困難許多。我們以固定整數變數的啟發式演算法增進求解的效率，並以台灣股票市場的資料做為實證計算的對象。 / A new mixed integer linear program (MILP) for selecting portfolio based on historical return is proposed. This model uses the downside risk rather than the variance as a risk measure. The portfolio is chosen that minimizes the maximum downside risk over all past observation periods to reach a given return level. That is a mini-max principle. The model incorporates the practical characteristics such as transaction costs, minimum transaction units, fixed proportional transaction rates, and cardinality constraint. For this reason a set of integer variables and binary variables are introduced. The introduction, however, increases the computational complexity in model solution. Due to the difficulty of the MILP problem, a heuristic algorithm has been developed for the solution. The computational results are presented by applying the model to the Taiwan stock market.

投資者面對到期日相同的一序列不同履約價格的選擇權時，應如何建立最佳的組合交易策略，這個問題雖已有許多標準的交易公式可依循，但這些標準的交易策略無法全面涵蓋複雜多變的組合策略。本論文提出整數線性規劃模型用來建立選擇權的最佳交易策略。模型針對到期日相同的買權、賣權如何買賣的組合，建立最佳交易策略。若我們預期在到期日時，標的股價將會落在某一範圍內，則我們可修改原來的規劃模型配合此項預期，以尋求最佳的交易策略。最後，我們以Ericsson的選擇權為例，驗証本模型的效能。 / The problem of how to construct the optimal combination trading strategy for investors when they face a series of options of different exercise prices on the same maturity date can be solved by many standard trading rules. Yet these standard trading rules cannot completely cover the complex and highly changeable combination strategy. This thesis proposes an integer linear programming (ILP) model to construct the optimal trading strategy for option portfolio selection. This model focuses on constructing the optimal strategy for an option portfolio of call- and put-options on the same maturity date. Given the investor's belief of the stock price, we also provide an extended ILP model to include this belief. Finally, an empirical study will be presented by using the ILP model applied to the Ericsson's call and put options.

在全球化的環境下推出新產品，企業除了面臨隨著產品生命週期改變的顧客需求以及成本上的不確定因素外，同時還必須考量全球營運帶來的種種挑戰。 許多供應鏈管理數量模式相關文獻針對全球運籌、新產品供應鏈等議題多有所探討，利用數量模式的計算以反應真實世界中的種種不確定性，讓管理者在供應鏈策略規劃時有所依據，但卻少有同時探討全球運籌以及新產品供應鏈的相關文獻。學者Butler, Ammons, and Sokol認為過去新產品供應鏈模式忽略了新產品將有可能無法存活下來的情形，因此發展一套新產品供應鏈模式，使新產品供應鏈能夠順利從上市成長到成熟階段，並利用此模式決定新設施、新機器購入的時機。 本研究延伸Butler等人之新產品供應鏈模式，考量更完整之全球運籌相關議題，透過混合整數線性規劃描述新產品發展時全球運籌配置問題，並利用情境為基礎的穩健最佳化以取得低風險的供應鏈配置，此外加入可靠度的影響，以彌補供應鏈規劃與實際操作的差距，並加入缺貨之懲罰成本，最後以範例資料進行計算與分析此數量模式，經由模式計算結果發現本研究規劃之結果，相較於原Butler等人之模式有較低的缺貨的發生可能性，且所求得之配置整體可靠度皆有所提升。 本研究所提出之規劃與分析方法可提供決策者在進行新產品全球佈局規劃時，能當作其新產品運籌配置之決策參考。 / When putting out new products under the environment of globalization, enterprise not only faces the uncertain factors in the demand of the customers and the costs that change with product life cycles, but considers all sorts of challenges which come with global operation. Many researches into supply chain quantitative model that probe into global logistics and the new product supply chain employ the quantitative model to reflect all sorts of uncertainty in the real world. They provide managers with the basis for the supply chain strategy and management. But few researches discuss about the global logistics and the new product supply chain simultaneously. Bulter, Ammons, and Sokol argue that the model of new product supply chain of the past neglects the condition which new products may not survive. Thus they developed a new product supply chain model to enable new products to launch the market and grow to maturity as well as decide when to purchase new supply chain facilities and equipments. This research which extends the new product supply chain model of Bulter et al. considers issues on global logistics from a more integrated view. First of all, it solves the global logistic settings problem in new product development by means of mixed-integer linear programming. Secondly, it uses the scenario-based robust optimization to lower the risk in the supply chain design. Then it adds the reliability calculation to make up for the gap between the plan and the real operation. At last it calculates and analyzes the quantitative model on the basis of the case data. This research establishes a methodology for decision makers to apply to plan and analyzing their new product supply chain when they make the global arrangement of new products.

投資者面對到期日相同的ㄧ序列不同履約價格的選擇權，已有許多文獻提出如何建立選擇權最佳投資組合，但模型中均未考慮交易成本。選擇權在實際市場的交易過程中，投資者所支付的手續費與賦稅即為選擇權的交易成本。本論文針對買賣到期日相同但不同履約價格的買權與賣權如何組合，提出考慮交易成本的整數線性規劃模型，建立選擇權最佳交易策略。我們不考慮股價變動的機率分配型態，延伸楊靜宜 (2004)所建立之整數線性規劃模型和Liu與Liu (2006)的大中取小模型，建構考慮比例制、固定制與混合制交易成本之整數線性規劃模型。最後，我們以台指選擇權(TXO)為例，驗證模型的效能。 關鍵字：交易成本，選擇權交易策略，整數線性規劃，選擇權套利機會。 / There are many researchers focus on constructing the optimal strategies and propose integer linear programming (ILP) for a series of options which are on the same maturity date with different strike price, but they neglect transaction costs in their models. The transaction costs of options are the handling charge and taxes which investors should pay for trading in the market. The thesis proposes an ILP with transaction costs to construct the optimal strategy for an option portfolio of call- and put- options on the same maturity date with different strike price. We leave the distribution of the variety of stock price out of consideration and extend Yang’s (2004) model and Liu & Liu’s (2006) min-max regret model to construct ILP with proportional, fixed, and mixed transaction costs. Finally, we take the trading data of TXO as an empirical study to test and verify the efficiency of our models. Key words: transaction costs, option trading strategies, integer linear programming, option arbitrage opportunities.