Energy cost optimisation in manufacturing systems has gained more and more attention. Although there are many papers about energy consumption optimisation in serial production lines, energy cost optimisation in serial production lines has rarely been focused. In this paper, we formulate an energy cost optimisation problem in two-machine Bernoulli serial line under time-of-use pricing. We analyse the structural characteristics of the problem and transform the problem into optimally allocating the production rate among the time periods of different electricity rates. A definition of the extreme allocation is proposed and completed, and the optimal allocation is proved to be one of the extreme allocations. Using the property, an efficient method to solve the optimal allocation is proposed. With the help of the method, the multi-electricity-rate problem is transformed into several single-electricity-rate problems, which has been solved in the literature.

制造系统中的能源成本优化越来越受到关注。虽然关于串联产线能耗优化的论文很多，但很少关注串联产线能耗成本优化。在本文中，我们制定了分时定价下两机伯努利串行线路的能源成本优化问题。我们分析了问题的结构特征，并将问题转化为在不同电费的时间段之间优化分配生产率。提出并完成了极值分配的定义，证明了最优分配是极值分配的一种。利用该性质，提出了一种求解最优分配的有效方法。在方法的帮助下，