Impact of Disturbances on the Operations

We are interested in investigating how typical disturbances affect both the economic value of the process (i.e., profitability) and the operations to be scheduled and carried out in the plant. The following scenarios are proposed to simulate the 40-days closed-loop scheduling:

• Scenario 5.1: There are no disturbances in the process.

• Scenario 5.2: Only disturbances 1 and 2 (i.e., flows), presented in sections 5.3.5.1 and 5.3.5.2, are assumed to happen. There is 50% probability that any flow incoming to or outgoing from any blender is subject to a noise, in which the respective flow is uniformly randomized to be between ± 20% of its original value.

• Scenario 5.3: Only disturbance 3 (i.e., feedstock arrival), presented in section 5.3.5.3, is assumed to happen. The feedstocks R2 and R3 are supposed to arrive at the end of Day 2 and Day 25, respectively. However, each arrival is assumed to

be delayed by three days, so that the feedstocks arrive at Day 5 and at Day 28, respectively. Moreover, the feedstock R2 not only arrives late, but also with unexpected properties (sg = 0.86 instead of sg = 0.85, and sul = 1.01 instead of sul = 1.00).

• Scenario 5.4: Only disturbance 4 (i.e., market fluctuations: amounts), presented in section 5.3.5.4, is assumed to happen. There is a probability of 5% that any of the demands (for each product at any of the ten future days) is subject to market fluctuation changes. Whenever there is a demand change, it is assumed a uniform fluctuation of ± 20% of its original value.

• Scenario 5.5: Only disturbance 4 (i.e., market fluctuations: due dates), presented in section 5.3.5.4, is assumed to happen. There is a probability of 3% that the due date of a given product changes at a given day. In that case, the respective demand is preponed or postponed by one day. The only exception is that the demand of the current day (first day of the optimized time horizon) cannot change.

• Scenario 5.6: Only disturbance 5 (i.e., blender breakdown), presented in section 5.3.5.5, is assumed to happen. There is a probability of 3% that any blender breaks down at any day.

• Scenario 5.7: There are all five disturbances simultaneously. Their respective triggering probabilities are such as in Scenarios 5.2 to 5.6.

When there are no disturbances, there is a unique closed-loop solution because there is no randomization in the algorithm. However, whenever any disturbance is assumed to happen, they are randomly simulated by the algorithm, so that multiple distinct possibilities could happen (e.g., there could be multiple demand peaks of product D1, or sequential breakdowns of a blender), depending on the sequence of random numbers generated. Thus, aiming at more robust analyses and conclusions, multiple closed-loop simulations are performed for each scenario (using distinct seeds for the randomization) to improve the reliability of our approach by providing more representative results. Figure 5.6 presents a box plot chart to illustrate how the disturbances impact the profitability of the process, in which five closed-loop schedules were simulated for each scenario (except for Scenario 5.1, as there is no randomization). The profit shown regards the entire 40-days closed-loop scheduling.

Figure 5.6: Impact of Scenarios 5.1 to 5.7 in the closed-loop scheduling profitability.

Source: Author (2021).

As expected, although disturbances may eventually lead to an increase in the profit, their impact is usually negative. Moreover, disturbances regarding demands amount and unit breakdowns typically have a worse effect in the closed-loop simulated solution. The worst scenario is when all disturbances are assumed to happen, which is indeed the most representative situation in industrial operations.

Despite the expected economic impact of noises and disturbances to the closed-loop solution, another meaningful insight regards the process operations and its respective schedule. Not accounting for changes in the process does not only limit the economic value of that process and increase the risk of infeasibilities on the model optimization, but also leads to significant differences regarding the optimal scheduling to be implemented in the real plant. Figures 5.7 to 5.9 present the trend or line plots for the flows from the F tanks to the blenders, and the inventories of F and S tanks, respectively, over the entire simulated time horizon of 40 days for one case of Scenario 5.7. The blue dashed line represents the scheduling operations when disturbances are not assumed to happen, and the red solid line when all the five types of disturbances are considered in the modeling and optimization.

Figure 5.7: Closed-loop operational schedule for flows from the F tanks to the blenders without (blue dashed line) and with (red solid line) disturbances (Scenario

5.7).

Source: Author (2021).

Figure 5.8: Closed-loop operational schedule for inventories of F tanks without (blue dashed line) and with (red solid line) disturbances (Scenario 5.7).

Source: Author (2021).

Figure 5.9: Closed-loop operational schedule for inventories of S tanks without (blue dashed line) and with (red solid line) disturbances (Scenario 5.7).

Source: Author (2021).

Figures 5.7 to 5.9 show that there is a significant difference between the two plotted cases (with and without disturbances). The direct impact for industrial operations is that not considering noises and disturbances (assuming that they happen) would lead to the implementation of a completely different schedule rather than the real optimal schedule (considering the real state of the process, which includes all the changes resulted from disturbances and unexpected events). It is also worth mentioning that even though we do not address inventory costs in the proposed example, it is clear that they might be relevant for the topic, as there is a significant difference in the inventories of tanks between the closed-loop schedules with and without disturbances, as shown in Figures 5.8 and 5.9. In summary, scheduling operations when disturbances are or are not considered might be completely different from each other, which reinforces the importance of online scheduling strategies for process optimization purposes.