根據台灣關稅總局的統計資料庫顯示，台灣蝴蝶蘭一直在台灣花卉市場佔有極大的出口價值，且每年的出口總值一直不斷地攀升。而為了降低生產成本，蝴蝶蘭業者目前大多採用接單生產的模式，但是蝴蝶蘭的存活率式隨機不確定的，業者若只以經驗法則來決定投入生產量，容易造成生產過剩或是缺貨的情形。
為了能達到供給與需求吻合的最佳情境，本研究利用管理科學的方法考量蝴蝶蘭的單期存活率不具機率分配，以「報童問題」模式單位合約售價、生產成本、缺貨損失及過剩殘值等參數，建立期望利潤最大化為目標，推導出最佳期初投產量的封閉解。
最後探討若蝴蝶蘭的存活率分別呈現均勻、右三角及貝它三種分配下，利用數值範例及對各參數進行敏感度分析。結果發現：最佳期初投產量與利用機率分配直覺期望值有顯著差距；另外，最佳期初投產量以反方向地受單位生產成本與存活率的變化影響，但是與單位售價、單位殘餘價值、單位缺貨損失與接單需求量共四個參數分別有相同的改變方向。在三種特殊分配中，當蝴蝶蘭存活率呈現均勻分配時，參數改變時對最佳期望利潤的邊際影響最大。

According to the statistical database of the Taiwan Directorate General of Customs, Taiwan has a large phalaenopsis export market that grows continuously every year. Many phalaenopsis contractors use the make-to-order production mode and, based on their experience to determine the initial production quantity, but this approach is imprecise.
Since the phalaenopsis survival rate is stochastic, this thesis models the decision of the initial production quantity to the make-to-order production mode as a “single-period newsboy problem”. Parameters in the proposed model include unit selling price, production costs, the loss of stockout, and the salvage of overproducing. First, for the distribution free survival rate, we derive the closed-form for the initial production quantity to achieve the maximum expected profit. Then, there special distributions for the survival rate are examined and sensitivity analysis is implemented.
We make some conclusions. First, large gaps exist between the optimal initial production quantity and the phalaenopsis contractor’s intuitive one. Second, the initial production quantity is an increasing function of the unit selling price, the salvage value, the stockout loss, and the make-to-order demand, respectively; but, is decreasing with the respect to the unit production cost. Third, when the survival rate is uniformly distributed, all parameters in sensitivity analysis have larger marginal impact on the expected profit than right triangular and Beta distribution cases.

Content

指導教授推薦書
口試委員會審定書
長庚大學博碩士論文著作授權書摘要 iii
摘要 iv
Abstract v
Content vi
List of Figures viii
List of Tables ix
Chapter 1. Introduction - 1 -
1.1 Background and motivation - 1 -
1.2 Research objective - 4 -
1.3 Thesis framework - 4 -
Chapter 2. Literature Review - 6 -
2.1 Newsboy problem with random yield - 6 -
2.2 Make-to-order production policy - 9 -
2.3 Taiwan’s phalaenopsis industry - 11 -
Chapter 3. The Model - 13 -
3.1 Notations - 13 -
3.2 Assumptions - 13 -
3.3 Distribution free survival rates - 14 -
Chapter 4. Survival Rates with Special Distributions - 20 -
4.1 Uniform distribution - 20 -
4.2 Right triangular distribution - 23 -
4.3 Beta distribution - 28 -
Chapter 5. Numerical Examples - 31 -
5.1 The optimal solutions - 31 -
5.2 Sensitivity analysis - 33 -
Chapter 6. Conclusion - 36 -
References - 38 -
Websites - 42 -

List of Figures

Figure 1: The year export value of Taiwan phalaenopsis - 2 -
Figure 2: Research framework of this thesis - 5 -
Figure 3: Product positioning strategy - 10 -
Figure 4: Uniform distribution’s probability density
function - 21 -
Figure 5: Right triangular distribution’s probability
density function - 24 -
Figure 6: Beta distribution’s probability density function - 29 -
Figure 7: The relationship between expected profit and
initial production quantities - 32 -

List of Tables

Table 1: The life cycle of phalaenopsis - 2 -
Table 2: The difference between intuitive and seience method - 33 -
Table 3: The parameters stand for sensitivity analysis
- 34 -
Table 4: The numerical analysis result in uniform
distribution - 34 -
Table 5: The numerical analysis result in right triangular
distribution - 34 -
Table 6: The numerical analysis result in Beta distribution - 34 -

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Websites

Taiwan Directorate General of Customs Statistic Database. Taiwan Annual Export Value. Retrieved June 4, 2009, http://web.customs.gov.tw/statistic/statistic/statisticlist.asp. (In Chinese)
Taiwan International Orchid Show. Taiwan’s Orchid Industry, Retrieved June 4, 2009, http://www.tios.com.tw/5_2taiwan.php. (In Chinese)
The Executive Yuan, Council of Agriculture. The Promoting of Agriculture Technology. Retrieved June 4, 2009, http://www.coa.gov.tw/view.php?catid=7692. (In Chinese)
The Executive Yuan, Council of Agriculture. Yearly Report of Taiwan’s Agriculture. Retrieved June 4, 2009, http://www.coa.gov.tw/view.php?catid=11173. (In Chinese)