## 1 Introduction
### Motivating Example  
An IMM activates its function by receiving the raw material via a hopper, which is then heated by a heater barrel and subjected to rotation by a screw until the material melts. The molten plastic is then injected into the mold, where it solidifies under pressure applied by the clamping unit. Process parameters, such as barrel temperature, clamping force, and screw rotation velocity, are remotely controlled by a computerized unit. The injection molding process includes seven steps: (i) mold closing, (ii) clamping, (iii) injecting, (iv) holding, (v) plastification, (vi) cooling, and (vii) ejection. The injection, clamping, and plastification phases are the most energy-intensive stages of the injection molding cycle [19]. In this study, we focused on an industrial plastic facility that manufactures equipment for scuba diving, freediving, snorkeling, spearfishing, and swimming. The plant utilizes a variety of plastic components and products that are produced in IMMs and later employed in the assembly of the final product. The production catalog encompasses fins in 32 variants, masks in 42 variants, speargun components, regulators, and buoyancy control devices. Nine all-electric IMMs were used to produce plastic products including fins, masks, and thermoplastic components. These machines are powered solely by electricity and can be remotely controlled. Their energy consumption represented 65% of the company's total energy consumption. Figure 1 illustrates the production flow schema for fins, which employs two specific IMMs (labeled machines 1 and 2). The first IMM is designated as the base product, which is a paddle, whereas the second IMM is responsible for the colored bodies. Plastic granules are loaded into the hopper of the first IMM. Afterward, the plastic material is heated and injected into the mold cavity. The molded product and paddles are cooled using water and the duration of the cooling phase is configurable during the configuration phase. The cycle time for a single puddle is 70 s. Once the paddles are manufactured, the bootic rubber is overprinted by inserting the previously molded base parts of the fins into the molds, which are subsequently placed into the machine. The heated colored plastic is then molded to fill the mold cavities, and the cycle time per fin pair is 160 s. The fins are cooled, inspected for quality, tested, and stored before packaging and shipment. Recently, the industrial plant entered into contracts with a utility provider to supply electricity. According to the contract terms, the plant is priced for electricity at three different rates, depending on the time of day (7-19, 19-24, and 24-7). Therefore, the industry needs to develop production schedules that consider the hourly energy consumption and related costs over time. Regarding the daily energy consumption, historical data from January to December 2021 indicate that the plant had an average daily consumption of 135.5 kWh. The data from January to March 2022 show an average daily consumption of 156.5 kWh for the entire plant. The energy consumption of machines 1 and 2, which are referenced in Figure 1, was collected every hour, stored in a database, and presented in table format. Figure 2 presents a set of 30 profiles related to the hourly energy consumption in kWh for machine 1 over 24 h. The vertical axis indicates energy consumption in kWh. Energy consumption in the dataset ranged from a minimum value close to zero to a maximum value of approximately 20 kWh. The graph indicates that during the first 5 h, the energy consumption was relatively low. From hour 6, during the first working shift of the day, the energy consumption increased to a peak and remained high during the subsequent 16 h. However, it should be noted that this pattern is not invariant because the energy consumption profile may exhibit different patterns that depend mainly on the production schedule and process parameters. Figure 1: Process flow chart for fins production. The production of fins is managed through two IIMs (machine 1 and 2).