中小呼叫中心月度排班优化模型与算法

国内中小呼叫中心制定坐席人员月度排班表时，通常考虑劳动法规合同约束和体现企业自身用工管理诉求。构建坐席人员月度排班优化问题的二次整数规划模型。鉴于问题模型难解性，依据调研企业需求和模型逻辑结构分析，把问题分解成三个子问题。通过构建整数规划模型和提出启发式算法来求出子问题解，从而生成排班问题优化解。问题实例计算表明，模型算法能够有效控制人力成本和兼顾员工同班次管理目标。与周排班方法比较，该方法能够充分体现月度排班人力灵活性来实现人力优化配置。

Modeling and Algorithm for a Monthly Shift Scheduling and Rostering Problem in Small-Size Call Centers

In order to effectively manage human resources, small and medium-sized call centers in China usually work out monthly schedule schemes for agents. The problem under study is how to determine on/off duty dates of agents in the month and how to assign shifts to agents with the constraints of various enterprise employment regulations and the service level, so as to minimize the number of the on duty agents (i.e. optimize the cost of manpower), while keeping the shifts of each agent in the week as same as possible. A quadratic integer programming model of the problem is constructed. Considering the intractability of the model, the problem is decomposed into three sub-problems based on enterprise demands and logical analysis of the model structure. The subproblems are solved by either integer programming models or heuristic algorithm, to generate optimal solutions. The computational results show that the proposed models and heuristic algorithm can control manpower cost and meet the demands for same shift management effectively. Compared with existing weekly scheduling methods, this method can fully exploit the monthly manpower flexibility to achieve good effect on human resource allocation. The research scenario of this paper comes from a practical call center in China. The proposed model and algorithm can be used for inspiration to solve various scheduling problems in small and medium-sized call center enterprises.