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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.

Energy cost optimisation in two-machine Bernoulli serial lines under time-of-use pricing