Running a business involves navigating a variety of challenges, many of which can be tackled effectively through mathematical optimization. Yet, without recognizing these challenges as such, business experts may get sidetracked by less effective methods, ultimately going down technological rabbit holes.
Even when optimization is identified as the right approach, translating a business problem into a mathematical model can be intimidating, adding another layer of complexity. After all, implementing an optimization problem is no simple task. Alright, so how do we get past these roadblocks?
This article will explore how emerging tools are simplifying these traditionally complex processes, making optimization more accessible and practical for everyone.
What mathematical optimization actually is, why it is important for companies, and why it’s so damn complicated
Optimization is the process of enhancing operational efficiency and performance by identifying the best-fit solution for a specific business scenario. It typically involves setting a well-defined goal, such as reducing operational costs or increasing revenue, while considering many factors and navigating multiple constraints.
In the context of logistics, for example, a company must determine the optimal combination of shipments while considering factors such as delivery times, costs, and availability of drivers and goods. Constraints can be soft, such as preferable delivery dates, which may allow flexibility albeit with penalties, or hard, such as insufficient inventory levels, which cannot be violated.
There are many ways these factors can be combined to reach the desired outcome, and optimization tools aim to find the optimum, or near-optimum, solution in order to maximize efficiency.
Modeling
This phase involves translating the business problem into mathematical formulas, which are then converted into a constraint matrix for the solver algorithm to process and find the optimal solution. Formulating business problems mathematically is a highly complex and time-consuming task. Additionally, transforming these formulas into a constraint matrix generally requires programming skills.
Solving
At this stage, the solver algorithm attempts to find an optimal feasible solution based on the constraints defined earlier. However, in most real-world problems, current solver algorithms on the market can take hours or even days to find a solution – and sometimes, they don’t succeed at all. This often happens when there are too many hard constraints, making an “optimal” solution virtually unattainable.
The most frustrating part is that when a feasible solution cannot be found, these algorithms provide no explanation, offering no insight into which constraints could be adjusted to achieve a solution. They operate like a “black box” that simply rejects the input, leaving us to start over from scratch.
How Rulex revolutionizes mathematical optimization
Rulex has just released a new advanced optimization tool that revolutionizes the traditional approaches, reducing time and complexity in both the modeling and solving phases. A part of Rulex Platform’s suite, Build & Solve is a powerful optimization task where business experts can define the problem along with its hard and soft constraints (Build), then apply an advanced algorithm to find a solution (Solve), all within a reasonable time frame and without the need for advanced technical skills.
In the Modeling (or Build) phase, no mathematical formulas are needed. Users can define problems using logical syntax within familiar spreadsheets, while the Build & Solve task itself automatically generates the constraint matrix from the business data and spreadsheets.
This is already a significant advantage. But there’s more.
In the Solving phase, the Build & Solve algorithm is extremely rapid. While traditional tools may take hours or even days, Rulex can find a feasible solution within seconds or minutes. If a solution is not found on the first attempt, the tool identifies which specific constraints are preventing a feasible solution, thus allowing experts to quickly assess and address the issue. This approach significantly reduces the need for repeated, time-consuming calculations and accelerates the path to a viable solution.
In addition to offering all the essential tools for gathering and pre-processing data, Rulex Platform also provides comprehensive capabilities for post-processing and visualization, allowing results to be presented to end-users exactly as and where they need them.
Real-world applications of Build & Solve
Build & Solve is not some future proof-of-concept; it’s already in production at numerous global companies, particularly in supply chains and manufacturing, where it is efficiently optimizing processes as we write. One of its most successful applications is in scheduling, ensuring that tasks and actions within a plan align with specific business objectives.
Scheduling optimization:
The tool was used to develop a solution for a Fortune 50 company, optimizing production efficiency by simultaneously tackling both product and packaging planning. This was a highly complex challenge, given the diverse constraints – ranging from managing different batch sizes to coordinating multi-stage orders and machines that cannot operate simultaneously.
The company’s experts were able to define the problem using logical syntax in spreadsheets, avoiding the need for complex mathematical formulas. Thanks to the tool’s user-friendly interface and rapid processing, the solution was deployed in under a month. Now, production planning can be optimized in less than 10 minutes, significantly outperforming traditional manual methods in both speed and accuracy, resulting in a threefold increase in production efficiency.
More in-house optimization tools
While Build & Solve serves as a general purpose optimization tool, Rulex also offers specialized tasks for specific supply chain and logistics challenges, including warehouse and transport optimization. With these tools, the problem framework is already established; users simply need to customize it with their specific case details and data.
Avoid getting stuck down rabbit holes
Tailored around business needs, Build & Solve offers extremely rapid and efficient problem resolution, so you don’t get stuck down rabbit holes.
Do you have a business challenge that feels insurmountable? Bring your case to us, and together we’ll find a solution. Schedule a free consultation with one of our experts today!
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