Using Math to Minimize Resource Waste

Lately, I’ve had many conversations about 𝘇𝗲𝗿𝗼 𝘄𝗮𝘀𝘁𝗲 𝗽𝗮𝘁𝘁𝗲𝗿𝗻 design, so I thought I’d lay out the math behind it. Let’s begin with the first part of the problem: 𝘰𝘱𝘵𝘪𝘮𝘪𝘻𝘪𝘯𝘨 𝘧𝘢𝘣𝘳𝘪𝘤 𝘶𝘴𝘢𝘨𝘦 given a fixed set of pieces. As suggested, this is a classic mathematical optimization problem. To formulate it, we need a few core components:  • 𝗢𝗯𝗷𝗲𝗰𝘁𝗶𝘃𝗲 𝗳𝘂𝗻𝗰𝘁𝗶𝗼𝗻: In our case, this is the total area of fabric consumed. The goal is to minimize this area.  • 𝗩𝗮𝗿𝗶𝗮𝗯𝗹𝗲𝘀 (𝗱𝗲𝗴𝗿𝗲𝗲𝘀 𝗼𝗳 𝗳𝗿𝗲𝗲𝗱𝗼𝗺): These include the position, rotation, and flipping of each piece. Each piece contributes a 6-dimensional vector: 2 for displacement, 2 for rotation, and 2 for flipping.  • 𝗖𝗼𝗻𝘀𝘁𝗿𝗮𝗶𝗻𝘁𝘀: The most obvious one is no overlap between pieces. This can be handled using collision detection, often made more efficient through techniques like hierarchical trees to reduce the number of checks. Other constraints include grainline alignment (some pieces must follow the fabric's grainline, some others are diagonal. Note that some cheaper production completely drop this constraint to save more fabric), and specific rules about whether certain pieces can be flipped. The naïve approach would be to try every valid arrangement, calculate the fabric usage, and select the layout with the minimum area. But this would take forever to compute. And I don’t mean that metaphorically. Optimization tasks suffer under a problem called the curse of dimensionality. Even though the problem seems easy to solve (it’s just an area calculation), finding the optimal solution becomes exponentially difficult with the number of pieces added to the system. Instead, we resort to approximations. Approximation algorithms do not guarantee the absolute best solution to the system, but they give a good enough solution in a reasonable amount of time. The trade-off is usually between solution quality and runtime. Some popular approaches:  • 𝗦𝗶𝗺𝘂𝗹𝗮𝘁𝗲𝗱 𝗔𝗻𝗻𝗲𝗮𝗹𝗶𝗻𝗴: Inspired by physics, this technique treats each layout as an energy state. It perturbs the system in search of lower energy (better solutions) and eventually settles into a stable, near-optimal configuration.  • 𝗚𝗲𝗻𝗲𝘁𝗶𝗰 𝗔𝗹𝗴𝗼𝗿𝗶𝘁𝗵𝗺𝘀: Mimic natural selection, evolving better solutions over generations based on fitness criteria. They literally simulate the survival of the fittest concept and give the solution that has the best “genes”.  • 𝗔𝗜-𝗯𝗮𝘀𝗲𝗱 𝗠𝗲𝘁𝗵𝗼𝗱𝘀: While the algorithms above incur a similar computational cost every time you run them, AI can shift that cost to the training phase. Once trained, a model can instantly generate optimal or near-optimal layouts. Inference is fast, and the heavy lifting is done only once during training. Now, when we move from optimizing fixed patterns to generating patterns that are inherently zero-waste by design, AI becomes the only scalable solution. Let's talk about that in a different post!

Last month, we saved 5 lakhs in just 10 minutes by doing one thing. Let me tell you about this small adjustment that made a huge impact at Go Zero. Here's how our packaging works: → Ice cream goes into plastic cups → 12 cups go into cartons → Cartons go into crates for storage and transport And the cartons we were buying were the standard size in the market. So, each crate held 5 cartons = 60 cups total. One day, someone walked out of our cold room carrying these crates. And I noticed something - there was empty space in each crate. It got me thinking how we can fit one more carton in here. Tried it. Didn't fit. It was just 10mm short. Instead of accepting it, I did the math. We already had 5 cartons in the crate. If I reduced each carton's height by just 2mm, I'd free up exactly the 10mm needed for the 6th carton. The impact was immediate: 5 cartons per crate became 6 cartons per crate. Scale that up - every 100 crates now carry 600 cartons instead of 500. Same truck. Same storage space. 20% more product. All because of 2mm. Sometimes the biggest breakthroughs come from the smallest observations. You just have to be willing to question what everyone else accepts as "standard."

Most companies operate on gut feel and spreadsheets. The best companies use Operations Research (OR); the math behind smarter decisions. Here’s a quick way to think about OR: Imagine you run a delivery fleet. You have 50 trucks, hundreds of orders, and traffic delays. What’s the best way to deliver everything on time and at the lowest cost? 👉 A basic approach: Assign routes manually → Expensive and slow 👉 A data-driven approach: Use past data to plan better → Better, but not optimal 👉 An OR approach: Build a routing optimization model → Finds the best possible plan in seconds Real-world OR impact: ✅ Airlines schedule flights to minimize delays and costs ✅ Retailers optimize inventory to reduce stockouts and waste ✅ Automakers balance supply and demand to maximize profits If you’re working with complex decisions, constraints, and trade-offs, OR is the tool you need. Curious about how OR can help your business? Let’s discuss in the comments!

🧠 𝐖𝐡𝐲 𝐢𝐬 𝐓𝐞𝐭𝐫𝐢𝐬 𝐒𝐨 𝐒𝐚𝐭𝐢𝐬𝐟𝐲𝐢𝐧𝐠? 𝐂𝐨𝐮𝐥𝐝 𝐌𝐚𝐧𝐮𝐟𝐚𝐜𝐭𝐮𝐫𝐢𝐧𝐠 𝐋𝐞𝐚𝐫𝐧 𝐟𝐫𝐨𝐦 𝐈𝐭? 🎮🏭 𝐄𝐯𝐞𝐫 𝐧𝐨𝐭𝐢𝐜𝐞𝐝 𝐡𝐨𝐰 𝐟𝐢𝐭𝐭𝐢𝐧𝐠 𝐩𝐢𝐞𝐜𝐞𝐬 𝐩erfectly in Tetris sparks joy? It's more than a game—it's a lesson in efficiency! The principles of Tetris mirror strategies in modern manufacturing: optimize space, resources, and workflows to achieve maximum output while minimizin𝐠 𝐰𝐚𝐬𝐭𝐞. 𝐋𝐞𝐭’𝐬 𝐛𝐫𝐞𝐚𝐤 𝐢𝐭 𝐝𝐨𝐰𝐧. ⬇️ 📊 𝐓𝐡𝐞 𝐓𝐞𝐭𝐫𝐢𝐬 𝐄𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐜𝐲 𝐅𝐨𝐫𝐦𝐮𝐥𝐚 𝐉𝐮𝐬𝐭 𝐥𝐢𝐤𝐞 𝐜𝐥𝐞𝐚𝐫𝐢𝐧𝐠 𝐚 𝐥𝐢𝐧𝐞 𝐢𝐧 𝐓𝐞𝐭𝐫𝐢𝐬 𝐫𝐞𝐪𝐮𝐢res strategic placement, manufacturing efficiency thrives on smart planning. Here's the basic formula: ME = (Resource Utilization ÷ Available Capacity) × 100 Where ME = Manufacturing Efficiency, Resource Utilization = How much you use, and Available Capacity = Total resources you have. 💡 Why It Works in Manufacturing 1️⃣ Maximizing Space Usage: Tetris = No wasted blocks.  Manufacturing = Lean operations, maximizing storage, and production areas.  Impact: Businesses report a 30% reduction in inventory costs with optimized layouts. 2️⃣ Resource Allocation: Tetris = Use every piece.  Manufacturing = Properly align raw materials and labor to minimize downtime.  Stat: Companies using advanced resource planning see 20% increased productivity. 3️⃣ Reducing Waste: Tetris = Avoid "holes."  Manufacturing = Eliminate inefficiencies and material waste.  Fact: Lean manufacturing processes can reduce waste by 50%.  🔮 The Future of Manufacturing by 2030 🚀 Automation Meets Optimization: AI-driven resource planning tools will integrate Tetris-like logic to reduce downtime and errors by up to 70%. 🌍 Sustainable Manufacturing: Optimizing layouts and resources could cut global manufacturing waste by 45%, supporting sustainability goals. 🔧 How You Can Apply This Today ✅ Audit Your Space: Map out your physical and digital layouts for efficiency gaps. ✅ Use Smart Tools: Explore tech like 3D inventory mapping or automated planning software. ✅ Adopt a “Tetris Mindset”: Always ask, “How can we fit this better?” 📖 A Real-Life Example Think of Amazon's fulfillment centers: They mirror Tetris with automated shelving and dynamic space optimization. Result? Faster deliveries, lower costs, and satisfied customers. 🎯 Your Takeaway Challenge 🔲 What’s one area in your work or daily life where you could "clear the line" by optimizing resources or space? Share your thoughts in the comments below! 👇 📚 Credits 🌟 All research and write-up by me (P.S. Mahesh). Visuals belong to respective owners.