近年來人力成本不斷提升，尤其客服中心的人事成本佔了總營運成本的百分之七十，因此客服中心的人員排班問題越來越為重要。
本研究提出兩個混整數數學規劃模型求解二十四小時營運之客服中心的長期排班問題，這兩個數學規劃可以求得問題規劃期間最佳的人員班別指派，數學規劃中所考慮的法規限制比起過去以最佳化求解排班問題的研究，本研究所考慮的限制條件較完整。
過去求解人員排班問題或是客服中心之人員排班問題的文獻，所考慮的範圍大多都是在預測每個時間區段的人力需求數量以及每個班別應該安排的人數，只有少數的文獻有考慮人員的指派。過去考慮人員指派的文獻，大都是以啟發式演算法求解，非以最佳化演算法的方式處理問題。而且大部份之文獻都是分開來以兩個階段分別求解，一個求解每個班別應安排的人數，另一個將班別分配給特定的人員。分兩階段求解的缺點是可能找到的解和最佳解差距很大。為了避免分兩個階段求解，本研究用單一個數學規劃最佳化模式直接決定人員被分配的班別。
整數規劃的求解速度主要是受限於整數變數個數的影響，本研究提出一些新的數學規劃模式建制的技術，以減少整數變數的個數，並利用該建制的技術在本研究的數學模式二。期望數學模式二擁有比數學模式一更好的求解效率。
實驗驗證後，發現雖然數學模式二的整數變數個數比數學模式一少，但在固定求解時間下，數學模式一的解明顯比數學模式二好。
關鍵字：客服中心、人員排班、多技能

The personnel cost has been increasing in recent years. Especially, for a call center, the personnel cost has accounted for 70% of total operation cost. Therefore, recently, call center agent shift scheduling has become an important problem.
This study proposes two mixed integer programming formulation to solve the long-term agent shift scheduling problem for a 24-hours call center. This formulation will find the optimal agent shift schedule. We consider more thoroughly on the government regulation in our formulation than previous literatures.
Most of previous studies in this subject deal with the demand forecast and shift man power allocation problem by determining the number of people is needed for a particular shift. Only a few studies considers personnel shift schedule problem and most of them use heuristic method to solve the problem; furthermore, they use two separated steps to solve the problem. The first one is to find the man power requirement for each time period. The second one calculates the detailed shift assignment for each individual agent. The potential shortcoming of using two separated steps to solve the problem is the gap between the obtained solution and the optimal solution might be too large. The study proposes a mixed integer program formulation that can be solved in one step; thus, avoid the shortcoming of the two-step approaches.
Since the number of integer variable is the major determinant for the computation time of a mixed integer program, this study proposes a number of new modeling techniques that help reducing the number of integer variables, and use the modeling techniques in second mixed integer program in this study.
Although the number of integer variables of the second mixed integer program is less than that of first mixed integer program, the first mixed integer program has better solutions than the second mixed integer program when the solution time is fixed.

Keywords: call center, agent shift scheduling, multiple skill agent

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