以限制規劃構建運動排程模式-以中華職棒大聯盟賽程表排程為例

Abstract

運動賽程的安排對於各種運動的賽程規劃者而言，是件費時且費力的工作。排程人員必須將有限的對戰組合做有效的安排以滿足每天的對戰需求，並考慮符合聯盟及球團相關規定。臺灣職棒運動是近幾年相當受歡迎的運動項目，至今已正式邁入第十六年，職棒賽程表排程問題屬於組合最佳化問題，還需考量實務上中華職棒大聯盟賽程規章之相關規定為其限制條件，在模式規劃及求解上具有其難度。

本研究將賽程表排程列式為限制滿足問題求解（CSP），應用限制規劃（CP）方法，經由問題變數、對戰組合與比賽日時段之設計，將本研究中所考量各項限制模式化求解，當球隊數改變時也有探討。同時為提升求解效率，本研究以三階段指派求解，於產生每週對戰組合、時段表後，再依球隊主場票房需求及聯盟政策來指派球場。

本研究以中華職棒大聯盟2005年賽程表作為比較實例，包含6個球隊一年共300場賽事的安排。測試環境為Windows XP作業系統、2.8G Hz中央處理器速度，以OPL Studio 3.0執行求解，三個階段總求解時間約為30分鐘。與2005年賽程表及做過此類問題的文獻相比，本研究針對職棒賽程的特性，排出符合中華職棒大聯盟規定、各球團均滿意且符合實際賽程、賽制的賽程表，期望以公平性、效率性且符合賽制之賽程表解決傳統人工作業費時費力之缺點，提升賽程表的彈性與機動性，有助強化中華職棒大聯盟正面形象，並幫助中華職棒大聯盟建立排賽程之決策支援系統，將來亦可提供作為各類運動排賽程人員排程決策之參考。

The arrangement of sports scheduling for each sport scheduling planner is a time consuming and strenuous work.To meet the daily team pairing needs, a schedule planner must make efficient arrangements for the constraint team pairing, and also considers how to comply with the relevant rules for the league and baseball teams. The sport of Taiwan Professional Baseball League is very popular in recent years; up today it formally marches to its 16th anniversary, and the Professional Baseball sports scheduling problem is a pairing optimization problem, in practice, the constraints are that the relevant rules for the regulations of Chinese Professional Baseball League are also need to be considered, and for this reason it is of difficulty on both the model planning and the resolution. In this research the sports scheduling is formulated as a constraint satisfaction problem (CSP), it applies the method of constraint programming (CP), by the design of problem variables、competition pairing and the time frame in the contest day to develop models for each constraint to solve the problem. In the same time, in order to promote the efficiency of solution, this research designates three phases for the solution, and after the generation of weekly competition pairing、time frame charts, the fields will be allocated according to the demand of tickets office of the main baseball field and the policy of the league. This research applies the contests scheduling of year 2005 for Chinese Professional Baseball League as a comparative case. The testing environment includes Windows XP Operation System、2.8G Hz Central Process Unit, and running the OPL Studio 3.0 for the solution; to get the solution after three phases takes 30 minutes. Comparing the contests scheduling chart of year 2005 with the literature which resolved this kind of problems, this research focuses on the features of Professional Baseball contests scheduling, arranges the contests scheduling which complies with the rules of Chinese Professional Baseball League, satisfies each baseball team and conforms to the real contests and the contest system. It helps strengthen the positive image of Chinese Professional Baseball League, and assists establishing its decision making support system for contests scheduling, it could also provide as a reference for the sports scheduling planners for various sports.