應用動態區位模式於國民中學學校設施區位選擇之研究

The Applications of Dynamic Location Models to the Junior High School Facility Location Choice

10.6128/CP.31.2.113

衛萬明(Wann-Ming Wey)；林千琪(Chiem-Chi Lin)

學校區位 ； 動態設施區位 ； 漸進式P-中位數 ； School location ； Dynamic facility location ； Progressive P-median

都市與計劃

31卷2期（2004 / 07 / 01）

113 - 142

繁體中文

本文主要乃以時間(time)因素對學校設施區位選擇的影響做一探討及研究。一般在規劃學校區位時大都以P-中位數(P-media)之問題形式來做為設施區位點的取決方法，然實際情形往往並非如傳統規劃方式進行後之結果。台灣都市目前多已朝向多元化發展，部份地區學校之需求數量亦隨時間的改變而有所不同，因此傳統的固定式需求預測方式已無法解決及時性(in-time)及動態性(dynamic)的需求問題。也因此，實有必要發展出一套可依時間及需求的不斷演變及更新，而提供最新且符合所需的學校區位設置選擇之動態設施區位(dynamic facility location)的解決方法，藉以尋求並解決較理想的學校設施區位問題。本文對於學校設施區位的選擇可依各相關理論及研究步驟分別以下列四點說明之：一、探討漸進式P-中位數(progressive P-median)法及學校設施需求預測方法；二、針對需求預測模式加入時間之因素，並應用統計迴歸模式以推導出學生人口之預測數量；三、應用漸進式P-中位數法結合多元迴歸之學生人口預測模式建構學校區位選擇模式；四、利用AMPL (A Modeling Language for Mathematical Programming)數學規劃軟體作為解學校區位選擇之動態模式工具以求解最佳學校設施區位。本研究並以台中市北屯區為實證研究對象，依據各分區的學生人口預估量以進行學校設施興建之最佳區位位置選擇。

A model of dynamic school facility location choice is proposed in this thesis research. A dynamic p-median problem of school facility is considered. One important characteristic of this research is that the school students demand predicted in our model is changing over a given time horizon, i.e., the demand is time-dependent. Besides, the school facilities are built one at a time at given times. Once a new school facility is built, some of the students will use its services and some of them will patronize an existing facility. At any given time, students patronize the closest school facility under enough capacity. The problem is to find the best school facility location for the new facilities. The problem is formulated and the potential algorithm is proposed for this present time. However, a standard mathematical programming code AMPL(A Modeling Language for Mathematical Programming) is adopted here to solving our formulated problem. In this research it is assumed that new facilities are added to the area in given future points in time. The construction of schools, hospitals, public parking lots, stores, restaurants and other facilities in a growing area is typical for such applications. A real-world case study located in Pai-toun district of Taichung City in Taiwan will be proposed in this research to evaluate the performance of the research algorithm.

1. Chardaire, P.,Sutter, A.(1996).Solving the dynamic facility location problem.Networks,28,117-124.
2. Current, J.,Min, H.,Schilling, D.(1990).Multiobjective analysis of facility location decisions.European Journal of Operational Research,49,295-307.
3. Current, J.,Ratick, S.,Revelle, C.(1998).Dynamic facility location when the total number of facilities is uncertain: A decision analysis approach.European Journal of Operational Research,110(3),597-609.
4. Daskin, M. S.(1983).A maximum expected covering location model: formulation, properties and heuristic solution.Transportation Science,17(1),48-69.
5. Drezner, Zvi(1995).Dynamic facility location: the progressive P-median problem.Location Science,3(1),1-7.
6. Hakimi, S. L.(1964).Optimum locations of switching centers and the absolute centers and medians of a graph.Operations Research,12,450-459.
7. Hotelling, H.(1929).Stability in competition.Economic Journal,39,41-57.
8. Melachrinoudis, E.,Min, H.,Xing, W.(1995).A multiobjective model for the dynamic location of landfills.Location Science,3(3),143-166.
9. Min, H.,Melachrinoudis, E.(1996).Dynamic location and entry mode selection of multinational manufacturing facilities under uncertainty: A chance-constrained goal programming approach.International Transactions in Operational Research,3(1),65-76.
10. Min, H.,Melachrinoudis, E.,Xing, W.(1997).Dynamic expansion and location of an airport: a multiple objective approach.Transportation Research Part A: Policy and Practice,31(5),403-417.
11. Moon, I. D.,Chaudhry, S. S.(1984).An analysis of network location problems with distance constraints.Management Science,30(3),290-307.
12. Owen, S. H.,Daskin, M. S.(1998).Strategic facility location: A review.European Journal of Operational Research,111,423-447.
13. Revelle, C.,Swain, D.,Lieman, J. C.(1970).An analysis of private and public sector location model.Management Science,16(11),692-705.
14. Scott, A. J.(1971).Dynamic location-allocation systems: Some basic planning strategies.Environment and Planning,3,73-82.
15. Wesolowasky, G. O.(1973).Dynamic facility location.Management Science,19,1241-1247.
16. Wesolowasky, G. O.,Truscott, W. G.(1975).The multiperiod location-allocation problem with relocation of facilities.Management Science,22,57-65.
17. 任懷嗚(1995)。從人口趨勢看小班小校的規劃。教改通訊，13，31-37。
18. 林義男(1983)。台閩地區小學學生人數之預估。人口學刊，6，87-97。
19. 韋彰武(1991)。臺北，國立政治大學地政研究所。
20. 國立台中師範學院(1988)。台灣區八十至八十四學年度國小教師需求量之推估研究報告。
21. 國立台灣師範大學教育研究所(1983)。臺北，國立台灣師範大學教育研究所。
22. 張家生(1979)。臺北，國立政治大學企業管理學。
23. 張登欽(1984)。臺北，國立中興大學都市計劃研究所碩士論文。
24. 黃定國(1999)。都市計劃通盤檢規定對國民小學用地配置之課題分析。臺北科技大學學報，32，233-263。
25. 蔡輝昇(1987)。網路系統中解單一中心場站位置方法之研究。運輸計劃季刊，15(2)，117-128。
26. 蕭再安(1992)。新竹，國立交通大學交通運輸研究所。
27. 賴光真(1995)。臺北，政大教育研究所。
28. 鍾靜(1985)。臺北，淡江大學管理科學研究所。
29. 簡茂發(1992)。臺灣區八十至八十四學年度國民小學教師需求量推估研究。臺中師院學報，6，587-632。