考虑加班因素的订单接受问题优化模型与算法

加班是制造商在面对客户需求增多时经常会采取的一种临时扩大产能的方法。本文将加班因素引入订单接受问题，考虑到加班容易导致生产线的工位间同时存在产能不足与产能过剩的情况，建立了以总利润最大化和生产线产能均衡为优化目标的数学模型。根据模型特征，本文采用两种分布式估计算法，即基于节点矩阵抽样算法和基于节点的偶合算法来实现问题求解。实验结果表明，基于节点的偶合算法具有良好的求解效果，并且产能均衡这一优化目标的设定可以在保证生产线产能平衡的同时有效地提高产品利润。

An Optimization Model and Algorithms for Order Acceptance Problem with Overtime Strategy

The manufacturer management often adopts the strategy of overtime for the increasing demands. Overtime factor is added into the order acceptance problem, and overall balancing between over and under capacity utilization in different production line are considered as well. An optimization model is presented to maximize total profit and balance production capacity. Based on the characteristics of the model, two of estimation of distribution algorithms (EDAs), histogram-based sampling algorithm and node-based coincidence algorithm, are proposed. The results show that node-based coincidence algorithm is a potential algorithm for solving the problem. Moreover, the capacity balancing objective can effectively balance the capacity of production line and increase the total profit at the same time.