Estimating manufacturing electricity costs by simulating dependence between production parameters

The electricity costs associated with manufacturing generally consist of an energy charge and a demand charge, which are calculated by total kWh ×  $/kWh and peak kW  ×  $/kW, respectively. While these two charges have been extensively studied with production scheduling, dependence between production parameters has not been thoroughly investigated for production energy costs when the production parameters are assumed to be independent. Such dependence, however, can significantly affect the peak kW and resulting energy costs. Therefore, industrial practitioners need a tool to simulate the production power demand and cost to evaluate energy costs for each production plan and for any dependence in the parameters. In this paper, we propose a method for simulating the power demand at the machine and facility levels, focusing on the dependence in milling machine parameters. Using probabilistic techniques with copulas, we quantify the degree of dependence between two milling parameters (processing times and processing amounts) and build a power demand simulator combining discrete event simulation and numerical simulation models. From 35 illustrative examples, we show that a production strategy to adjust dependence can reduce the peak kW and energy costs by more than 15% and 4%, respectively. In addition to dependence, less variability in processing times results in less peak kW and energy costs. Other factors such as a marginal probability distribution and copula types having the same degree of variability have been found to have limited effects on reducing energy costs.