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Packing algorithms sound intimidating and for good reason. In popular culture, we associate algorithms with complex, advanced technology.<\/p>\n
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In reality, an algorithm is just a means of solving problems really quickly. In the world of supply chain management, packing algorithms help warehouse managers address what\u2019s known as the bin packing problem\u2014 the issue of packing multiple items of various sizes into a finite number of bins (in this case, shipping boxes).<\/p>\n
Today, the computational complexity of the bin packing problem is quite high, due to the large number of resources like time and storage. This means that it takes a lot of effort to solve through algorithms. As a result, most bin packing solutions come in the form of 3D bin packing software\u2014 tools that allow customers to visualize their items and digitally pack them\u2014rather than software with fancy algorithms.<\/p>\n
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BONUS:<\/strong> Before you read further, download our Warehouse Management Software Whitepaper to see how Logiwa uses real-time data to help you get up to 100% inventory accuracy and execute advanced fulfillment strategies like wave planning.<\/a><\/p>\n Nevertheless, it\u2019s important to understand what packing algorithms are, because if someone ever cracks this puzzle, it\u2019ll have huge implications on the warehouse industry. In addition to that, understanding these algorithms will give you ideas for optimizing your warehouse packing methods in your day-to-day operations.<\/p>\n If you\u2019ve been avoiding the words \u201cpacking algorithm\u201d during your continuous improvement efforts, now\u2019s the time to make their acquaintance. Take a breath, settle in, and let\u2019s break down this concept together.<\/p>\n An algorithm is simply a set of instructions one follows in order to complete a task or solve a problem. It\u2019s a \u201csequence of instructions telling a computer what to do<\/a>\u201d according to Pedro Domingos, author of The Master Algorithm.\u00a0<\/i><\/p>\n We build algorithms on three logical operations: \u201cand,\u201d \u201cor,\u201d and \u201cnot.\u201d While algorithms can become complicated, conceptually they\u2019re quite simple.<\/p>\n Today, tech marketers use the term to make their products seem more sophisticated and mysterious<\/a>. At the end of the day though, an algorithm is just a set of sequenced instructions and every company creates different instructions for different tasks they want to complete.<\/p>\n Algorithms exist in our everyday life, even if we aren\u2019t using machinery. Baking a cake or getting dressed in the morning could be considered algorithms. There are specific steps and the sequence matters. You wouldn\u2019t put your shirt over your jacket, and you wouldn\u2019t frost a bag of flour.<\/p>\n In the marketplace, we find algorithms all over. They facilitate trading in the financial industry, curate our newsfeed on social media, and help us to decide what to buy next on ecommerce sites like Amazon.<\/p>\n The \u201cbin packing problem\u201d refers to the issue of packing multiple items of various sizes into a finite number of bins, or shipping boxes. It\u2019s an optimization problem in math and computer science: it\u2019s about \u201cfinding the best possible solution from all feasible solutions<\/a>.\u201d When it comes to bin packing, the best solution can be one of two things:<\/p>\n Both objectives are meant to serve one overarching objective: cost savings. Inefficient packing methods lead to excess shipping costs.<\/p>\n In some cases, shipping companies use dimensional weight pricing, meaning that even if you\u2019re shipping something light, it\u2019ll get charged for the amount of space it takes up. This further increases the incentive to optimize your packing methods.<\/p>\n In addition, using more packaging than necessary leads to higher packaging material costs. Moreover, inefficient packing methods take up more space on transport trucks, limiting a warehouse\u2019s shipping capacity and jeopardizing their ability to deliver products to customers on time.<\/p>\n While this is a less-pressing packing concern for warehouses, it is related to the overall concept of packing algorithms. Imagine you\u2019ve got several items. Each item has a dollar value and a weight. How do you decide which items to pack into a knapsack so that (a) the total weight is less than or equal to what the knapsack can handle and (b) the most valuable items are packed. It\u2019s a resource allocation problem faced by several industries.<\/p>\n A problem\u2019s computational complexity refers to how many resources, such as time (e.g., labor hours) and space (e.g., data storage), it will take to solve a problem. Some computer scientists use this classification system to identify the difficulty level of certain algorithms and choose a less difficult algorithm to keep the project efficient.<\/p>\n As a decision problem, where the answer you\u2019re looking for is a \u201cyes\u201d or a \u201cno,\u201d the bin packing problem and the knapsack problem are both considered \u201cNP-Complete\u201d problems. That means there is no known way to find a solution quickly.<\/p>\n As optimization problems, they are both considered \u201cNP-hard.\u201d<\/p>\n For those interested in computer science, this is an opportunity to dive into the difficult P versus NP problem (whether problems that are quick to verify are also quick to solve). For the purposes of this article, let\u2019s keep it simple. If you\u2019re ever reading about packing algorithms, come across the term \u201cnondeterministic polynomial time\u201d and consider throwing in the towel, remember that all you need to know is this:<\/p>\n With today\u2019s technology, packing algorithms may be able to tell you how to optimize your packing efforts, but they can\u2019t definitely tell you that a specific packing solution exists.<\/p>\n In other words, they\u2019ll help you find the best way to pack your packages (solution to an optimization problem), but you can\u2019t find out whether there is <\/i>a solution to your packing problem by simply turning to an algorithm (decision problem).<\/p>\n After all of that, you may think this all sounds like a lot of work for very little reward. Well, you\u2019d only be half right. It\u2019s a lot of work, but the potential reward is huge!<\/p>\n Almost any warehouse manager will tell you that bin selection is a pain . Oftentimes, warehouse workers don\u2019t bother trying to find the best-sized bin (shipping box)\u2014they just pick the largest one and proceed with the task at hand. This is incredibly inefficient and unnecessarily expensive in terms of energy, boxes, and additional packing materials to avoid damage to the product. It\u2019s like using express mail for a package that doesn\u2019t need to arrive for another three weeks.<\/p>\n One manual solution to the bin packing problem is rotating each object to determine if it fits in a bin before retrieving a larger one. The drawback of this is time. In order to make the most of the shipping box, you\u2019d need to do this for every item you suspect might <\/i>fit into it. That\u2019s a lot of items and rotations. It would take forever and customers would never receive their products.<\/p>\n This is why an algorithm that speeds up the process and limits the amount of analysis = would be a big day for warehouse efficiency efforts. For now warehouses simply make do with what they have.<\/p>\n Overview of Standard Bin Packing Algorithms<\/strong><\/p>\n Bin packing algorithms are categorized by the specific bin packing strategy they facilitate.<\/p>\n Next Fit<\/strong><\/p>\n The worker checks if an item fits in the bin they\u2019re currently filling. If it does fit, they place it in. If it doesn\u2019t, they close that box and use the next one. With this strategy, a worker never returns to a previous bin. For instance, if they can\u2019t fit an item in Bin 4, they don\u2019t return to Bin 3. They simply grab a new one.<\/p>\n The benefit of this method is that you don\u2019t need a lot of dedicated warehouse space. The minute additional items cannot fit into the bin, it\u2019s shipped off to the end customer.<\/p>\n First Fit<\/strong><\/p>\n When packing an item, start with the earliest bin. For instance, if you have a row of boxes partially filled with various items, check to see if it fits in the very first box you packed (Bin 1). If it doesn\u2019t move on to Bin 2, and down the row until you find one that works.<\/p>\n Best Fit<\/strong><\/p>\n With this approach, a worker looks for the bin with just enough room to pack an item. The goal is to use as much of that bin\u2019s space as possible and get the bin shipped out as quickly as possible.<\/p>\n Worst Fit<\/strong><\/p>\n If you\u2019ve got an item, and several partially filled bins, try and put the item into the bin with the least amount of items, working your way up. You can think of it as evening the weight between each of the shipping boxes. If there are two boxes tied for \u201cemptiest\u201d or \u201clightest,\u201d choose the one that was opened or started earliest.<\/p>\n The Decreasing Variation on Standard Packing Algorithms and the Difference Between Algorithms<\/strong><\/p>\n All of these algorithms, or instructions, if you will, have decreasing variations. All the items to be packed are lined up, decreasing in size and then those items are packed using the next fit, first fit, best fit, or worst fit system.<\/p>\n Furthermore, bin packing algorithms are classified into two categories: online algorithms and offline algorithms. If an algorithm must pack items in a fixed order, such as the order they arrive in, it\u2019s an online algorithm. If the algorithm can rearrange the order and find the most optimal packing scenario, then it\u2019s an offline algorithm.<\/p>\n Ideally, these algorithms would be built into a company\u2019s warehouse management system<\/a>. Even companies who create 3D bin packing software could build these algorithms into their solutions to help businesses come up with the most optimized manner of packing their goods.<\/p>\n Current solutions prompt the warehouse to input the number of goods and dimensions of each of their goods into the system. The software then analyzes these variables and suggests the best way to pack these goods so that warehouses can make the most of their bins and pallets. In some cases, they could provide step-by-step assistance, guiding the worker through the packing process.<\/p>\n In addition to guiding workers on the best way to pack their bins, 3D bin packing software also helps workers find the exact shipping container they need for their items, so they don\u2019t simply reach for the nearest box, regardless of its suitability.<\/p>\n But, what is 3D bin packing software?<\/p>\n Imagine a game of tetris, where you\u2019re quickly fitting blocks together. 3D bin packing is like a more forgiving game of tetris, but in 3D. The pieces don\u2019t have to fit in perfectly together, but they should fit in as best as possible, and you can digitally pack your bins, or shipping boxes,\u00a0 in 3D. This way, your workers don\u2019t have to go through the process of manually rotating items and checking to see which boxes they fit best in. They can quickly and easily review a simulation based on previously conducted analysis.<\/p>\n Keep in mind, though, that not all 3D shipping software will necessarily have reliable packing algorithms.<\/p>\n A frustrating part of the online shopping experience is being hit with unexpected shipping charges. In some cases, if customers knew how much they\u2019d be charged, they wouldn\u2019t have bought the product. Furthermore, it\u2019s frustrating for businesses that want to be upfront, but don\u2019t know exactly how much they\u2019ll spend on shipping until later.<\/p>\n 3D shipping software helps businesses do this. For instance, Shopify offers intelligent 3D packing that allows product and box dimensions to digitally find the smallest box and provide the dimensional weight pricing in real time. As a result, customers know exactly what they\u2019ll pay for shipping up front.<\/p>\n Customers aren\u2019t surprised and businesses eager not to anger customers don\u2019t have to swallow unexpected shipping fees. The process becomes transparent, and both companies and customers are happy. The Shopify solution integrates with popular carriers like Purolator, UPS, and the United States Postal Service (USPS).<\/p>\n While packing algorithms present exciting possibilities, there aren\u2019t a lot of reliable, advanced solutions on the market that allow customers to rapidly come up with the most efficient way to pack boxes.<\/p>\n Not surprising, considering that the bin packing problems and the knapsack problem are extensions of the \u201cP versus NP problem,\u201d one of the big unsolved computer science Millenium Problems. (If you\u2019re wondering how tough and important these problems are, there\u2019s a $1 million USD prize for solving them<\/a>.)<\/p>\n In the meantime, 3D packing tools are the most feasible option. Nevertheless, it\u2019s important for warehouse operators to understand and keep an eye on the world of 3D packing algorithms. While they\u2019re currently a bit of a holy grail for warehouse owners, they will still inform and guide how warehouse operations are run and improved.<\/p>\nWhat is an Algorithm?<\/h2>\n
What Kinds of Problems do Warehouse Packing Algorithms Try to Solve?<\/h2>\n
The Bin Packing Problem<\/h3>\n
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The Knapsack Problem<\/h3>\n
The Computational Complexity of These Problems<\/h3>\n
Why Does Solving Packing Problems Even Matter?<\/h2>\n
How Are Algorithms Applied to the Warehouse Management Process?<\/h2>\n
How 3D Shipping Software Provides Optimal Solutions For Your Customers<\/h2>\n
So Will Packing Algorithms Achieve Widespread Usage?<\/h2>\n