Hamilton, Ontario

Manufacturers are making decisions all the time about what products to make and how best to make them. And, regardless of whether the products are chemicals, fuels, consumer products, or widgets, those decisions are incredibly important for the company’s bottom line and can make—or break—the business. For example, when manufacturing consumer electronics, planners continually search for the best deals on the different components, manage delivery times, and orchestrate their factories to ensure that demand is met on schedule. However, things can get complex very quickly, and with a global market that is always changing, it can be very difficult for planners and schedulers to determine the best courses of action. Fortunately, MACC researchers have come up with a new strategy to help. Professor Vladimir Mahalec and PhD student Pedro Castillo Castillo have developed a new decision support tool that is meant to help planners and schedulers orchestrate their operating decisions in a way that can improve their profits. Their tool is useful whenever a manufacturer uses the same piece of equipment for different purposes, such as making different kinds of products at different times, and the schedule for how to best use that equipment has to be determined in advance and updated frequently. In manufacturing, changing how a piece of equipment is used has an associated cost of that transition. For example, maybe there is time lost while waiting for the equipment to switch to a new mode, additional energy is required, or during the tradition it produces off-spec product that is wasted. Castillo and Mahalec’s tool is meant to help save on these costs by identifying clever ways of operating the process as a whole, which can add up to millions of dollars in savings each year.

Castillo demonstrated the tool for an example of a typical petrochemical refinery. Refineries separate raw crudes into different kinds of oils via distillation. After various treatment steps, those oils are then blended into different fuel products downstream, such as regular, mid-grade, and premium gasoline, trucking diesel, marine diesel, kerosene, jet fuel, and industrial lubricants. Every day, the refinery has to change how they operate the column to make different product blends in different amounts in response to market demands and prices for each and which kinds of crude oil they must make it from, which is complicated by always changing prices and chemical compositions of crude oils. For example, the refinery could incur losses if they make too much premium gasoline, and have to instead sell it off as mid-grade just to get rid of it.

*A simple model of a refinery which has to make many decisions each day about what raw material to use, how to process them, and how to blend the outputs into the final products.*

Currently, human operators in refineries make their daily operating schedules with the aid of simulation tools to predict how the distillation column might perform under different conditions. However, Castillo says that “although this approach is successful in making good schedules to use, the problem is extremely complex, and so even the most experienced planners will often miss finding a better schedule that is more profitable and less wasteful.” In fact, the current method leaves the operator wondering just how good their solution actually is. Fortunately, the MACC has created an algorithm to find a schedule mathematically proven to be the best and most profitable given the information currently available to the operators. Even if the algorithm cannot find the provable best, it is at least able to compute a number that represents the maximum possible profit that could ever be obtained, even if it cannot find the actual schedule that can achieve it. That way, the operators know just how good it could possibly get and decide whether they should keep looking for better schedules, or just get to work with what they have now. Although there have been previous attempts to solve this problem with mathematical programming in the past, even the very best state-of-the-art algorithms can only solve relatively small problems in a reasonable amount of time. However, industrial, everyday problems like the refinery blending problem (known to academics as the “pooling problem”) are very large and complex. Since refinery blending problems need to be solved over and over again every day, the existing methods simply cannot be used unless simplifying assumptions are made. Therefore, the MACC team created a new algorithm tailored to solve just this kind of difficult problem in only a few minutes.

*The algorithm makes decisions at three levels at different time scales and level of details. It can be used daily to create a detailed schedule for how to best produce gasoline that day.*

In order to tackle this problem, Castillo and Mahalec created a model of the refinery and blending processes that was not only simple and quick to solve, but also retained a high accuracy of the real process. Then, they took the pooling problem (which is a mathematical way of asking the question “what is the best way to mix different components today to try to make a certain set of products and what is the best way to schedule such blends?”) and studied its mathematical framework. They were able to identify trends and correlations within the mathematical equations themselves that allowed them to cleverly divide the problem into three, bite-sized pieces that have to be solved in a certain sequence in an iterative fashion. “By doing this,” says Castillo, “one huge problem that used to take hours to solve now can be solved in small pieces in a sequence, reducing run times to mere minutes.” Their approach contained two key contributions: 1) a novel solution strategy based on a model decomposition and a production-demand pinch concept, and 2) computation of optimal schedules with a reduced number of different operating conditions; therefore, smaller transition costs and less off-spec product.

The result? Mahalec and Castillo found that their tool produces schedules with operating costs 0.5-1% lower than those computed by previously published methods. That could save over $1 million per year for a refinery. That’s $1 million in savings just by changing the order in which the same products are made! Although this was successful for refineries, Castillo hopes to test the method on other industrial examples, since the algorithm is general and can be applied to many different kinds of processes. For now though, the value of one clever algorithm even in just one major industry is clear.

The results of their work have been published in the following research journal articles:

- Castillo, P., Mahalec, V. Improved continuous-time model for gasoline blend scheduling,
*Computers & Chemical Engineering,*,**84**627-646 (2016) [ Publisher Version| Open Access Version (free) ] - Castillo, P., Mahalec, V. Inventory pinch gasoline blend scheduling algorithm combining discrete- and continuous-time models,
*Computers & Chemical Engineering,*, (84) 611-626 (2016) [ Publisher Version| Open Access Version (free) ]