Flow Shop Scheduling for Energy Efficient Manufacturing

Hao Zhang, Purdue University


A large number of new peaking power plants with their associated auxiliary equipment are installed to meet the growing peak demand every year. However, 10% utility capacity is used for only 1%~2% of the hours in a year. Thus, to meet the demand and supply balance through increasing the infrastructure investments only on the supply side is not economical. Alternatively, demand-side management might cut the cost of maintaining this balance via offering consumers incentives to manage their consumption in response to the price signals. Time-varying electricity rate is a demand-side management scheme. Under the time-varying electricity rate, the electricity price is high during the peak demand periods, while it is low during the off-peak times. Thus, consumers might get the cost benefits through shifting power usages from the high price periods to the low price periods, which leading to reduce the peak power of the grid. The current research works on the price-based demand-side management are primarily focusing on residential and commercial users through optimizing the “shiftable” appliance schedules. A few research works have been done focusing manufacturing facilities. However, residential, commercial and industrial sectors each occupies about one-third of the total electricity consumption. Thus, this thesis investigates the flow shop scheduling problems that reduce electricity costs under time-varying electricity rate. A time-indexed integer programming is proposed to identify the manufacturing schedules that minimize the electricity cost for a single factory with flow shops under time-of-use (TOU) rate. The result shows that a 6.9% of electricity cost reduction can be reached by shifting power usage from on-peak period to other periods. However, in the case when a group of factories served by one utility, each factory shifting power usage from on-peak period to off-peak hours independently, which might change the time of peak demand periods. Thus, a TOU pricing combined with inclining block rate (IBR) is proposed to avoid this issue. Two optimization problems are studied to demonstrate this approach. Each factory optimizes manufacturing schedule to minimize its electricity cost: (1) under TOU pricing, and (2) under TOU-IBR pricing. The results show that the electricity cost of each factory is minimized, but the total electricity cost at the 2nd hour is 6.25% beyond the threshold under TOU pricing. It also shows that factories collaborate with each other to minimize the electricity cost, and meanwhile, the power demand at each hour is not larger than the thresholds under TOU-IBR pricing. In contrast to TOU rate, the electricity price cannot be determined in ahead under real-time price (RTP), since it is dependent on the total energy consumption of the grid. Thus, the interactions between electricity market and the manufacturing schedules bring additional challenges. To address this issue, the time-indexed integer programming is developed to identify the manufacturing schedule that has the minimal electricity cost of a factory under the RTP. This approach is demonstrated using a manufacturing facility with flow shops operating during different time periods in a microgrid which also served residential and commercial buildings. The results show that electricity cost reduction can be achieved by 6.3%, 10.8%, and 24.8% for these three time periods, respectively. The total cost saving of manufacturing facility is 15.1% over this 24-hour period. The results also show that although residential and commercial users are under “business-as-usual” situation, their electricity costs can also be changed due to the power demand changing in the manufacturing facilities. Furthermore, multi-manufacturing factories served by one utility are investigated. The manufacturing schedules of a group of manufacturing facilities with flow shops subject to the RTP are optimized to minimize their electricity cost. This problem can be formulated as a centralized optimization problem. Alternatively, this optimization problem can be decomposed into several pieces. A heuristic approach is proposed to optimize the sub-optimization problems in parallel. The result shows that both the individual and total electricity cost of factories are minimized and meanwhile the computation time is reduced compared with the centralized algorithm.




Zhao, Purdue University.

Subject Area

Mechanical engineering

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