Warehouse Optimization  Algorithms For Picking Path Optimization
Managing a warehouse in the 21st century is a whole new ballgame.
In the past, it was enough to keep a clean, wellorganized facility and schedule a decent number of pickers.
Now, warehouses stay competitive by optimizing every possible area of work—from picking to packing to shipping. With new warehouses cropping up every day, and customer demand for speedy deliveries rising, distribution centers don’t have the option of phoning it in. They must analyze their warehouses from top to bottom to look for inefficiencies and nip them in the bud.
One warehouse process that’s ripe for warehouse optimization is the pick path. According to some estimates, picking takes up over 50% of a warehouse’s labor efforts. This isn’t surprising considering that, despite warehouse technological advancements in areas like automated storage and retrieval systems, picking is still a largely humanled process.
Nevertheless, it’s possible to further optimize picking and, more specifically, the pick path. Oftentimes, the biggest cause of inefficiency during the picking process is motion waste  the unnecessary movement that makes a given task take longer than it should.
Walking path optimization—or picking path optimization, depending on who you talk to—is the process of finding the fastest way to navigate the warehouse in order to pick products quickly, accurately, and efficiently by using various picking methods such as wave picking, zone picking.
In this article, we will walk you through some methods for walking path optimization for pickers.
BONUS: Before you go any further, download our Order Picking Strategies guide where we compare orderbased, cluster, and batchpicking methods to see which method leads to the highest productivity.
What Is A Heuristic and How Does It Apply To Walking Path Optimization for Pickers?
If you research algorithms to optimize any area of warehouse management, you’ll likely hear the word “heuristic” a lot. It’s one of those words tossed in to confuse readers into throwing their hands up in the air and giving up on the entire endeavor.
In the context of warehouse optimization, a heuristic or heuristic technique is a method of accomplishing a specific goal that is suitable for practical purposes, but isn’t guaranteed to be perfect.
For example, when you apply a rule of thumb or make an educated guess, you’re using a heuristic technique.
When talking about warehouse management, researchers come up with processes and algorithms designed to address warehouse inefficiencies without necessarily producing a perfect approach. This is because at the core of many warehouse management problems are difficult math problems that are still being worked out by academics.
If the warehouse industry waited for a perfect solution to every math problem at the foundation of warehouse management problems, (see: bin packing and knapsack problem) we’d be working in very inefficient warehouses for a very long time!
So, whenever you hear someone use the word “heuristic,” remember that they’re just referring to an “okay for now” method. It’s a way of saying the solution isn’t perfect. In fact, you can probably ignore the term altogether whenever you see it.
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What Is An Algorithm and How Does It Apply To Walking Path Optimization?
“Algorithm” is another word that’ll pop up often when you read about topics like walking path optimization. It sounds complicated, but it’s not.
An algorithm is just a sequenced list of instructions. When you bake a cake, you use a recipe and that recipe can be considered an algorithm. If you were to build a machine that created a cake for you from scratch, and all you needed to do was upload the recipe, you’d essentially be feeding your “cakemaking machine” an algorithm that it would use to make a dessert.
The algorithm would let the machine know that it needs to crack the eggs before putting them in the bowl.
In warehouse optimization scenarios, there are algorithms for any number of processes. In the case of walking path optimization, a warehouse manager may have an algorithm where he or she can plug in certain variables and obtain an optimized pick path.
Order picking accounts for 60% of your warehouse operational costs. Make sure you’re using the most costeffective order picking strategy by reading our detailed guide where we compare the 3 most common order picking methods.
The Two Problems at the Center of the Picking Path Optimization Process
Remember when we mentioned that larger math problems sit at the center of many warehouse optimization problems? The same idea applies to the walking path optimization process. In this area, we’re faced with two big algorithmic problems:
 The Traveling Salesman Problem
 The Shortest Path Problem
Both problems are tricky algorithmic problems to solve when faced with a large data set. This is why industry professionals devise “heuristics” to provide workable solutions in a warehouse management context.
The Traveling Salesman Problem
While the traveling salesman job may be dying out, the traveling salesman problem is still alive and kicking.
Suppose you’re a traveling salesman with several locations to visit. How do you take the shortest (quickest) route to visit all of these destinations once and ultimately wind up back in your starting city?
Now, you could figure this out through trial and error, which is known as the “brute force” method. If you’re only hitting four or five locations, you map out every possible route and pick the shortest route.
But what if you’re hitting up dozens of locations spread out across a large geography? In the time it takes you to map out every possible route and pick the best one, you could’ve completed your trip.
Normally, this is where algorithms come in to make life easier. You’ve got a problem. You plug in the variables. The algorithm does the timeintensive number crunching quickly and boom, you’ve got an answer.
But the traveling salesman problem is classified as an NPhard problem, which means it’s rather difficult to solve in a reasonable amount of time. This is why “heuristics” exist. They’re our “good enough” solutions to keep things moving.
The Shortest Path Problem
As the name implies, the shortest path problem is about finding the shortest path between two points, also known as “nodes” or “vertices” as they’re referred to in graph theory. Connecting these vertices are lines or “edges.”
The shortest path problem finds the shortest path between two nodes in a weighted graph—a graph where the edges (the lines between two points) have a specific value. That value could be the distance or even the cost.
In other words, a weighted graph represents the labor cost associated with moving through your warehouse, and the shortest path problem is about finding the quickest, cheapest way to move from one point to the next.
When the values are positive, the shortest path problem is considered solvable in a reasonable amount of time, unlike the traveling salesman problem. Since most warehouse managers aren’t in the habit of labeling graphs with negative dollar values or negative measurements, that’s good news.
In fact, a number of algorithms exist for tackling the shortest path problem.
Which Algorithms Are Available for Walking Pick Path Optimization?
As you can probably tell by now, walking path optimization requires warehouses to address both the traveling salesman problem and the shortest path problem.
 You must solve the traveling salesman problem for all storage spots in a warehouse order. The start and end point is the shipping area.
 Simultaneously, as you move through the traveling salesman problem while filling the order, you also must address the shortest path problem while moving from a given item location (node or vertices) to all other item locations.
In other words, you need to find the shortest point between all the nodes before you’re able to find the shortest path through all the nodes.
This is because there’s no guarantee that every node is connected with one edge, which is necessary for a standard approach to the traveling salesman problem. As a result, you must find the shortest distance between each node first.
There are a number of different algorithms for each problem.
Traveling Salesperson Problem 
Shortest Path Problem 
Exhaustive Search Algorithm This approach considers every possible tour path. If the exhaustive search method is completed, it will definitely find the shortest route, but it is highly complex and unviable with a large amount of data. The exhaustive search method is not considered an efficient algorithm for picking path optimization. 
Dijkstra’s Algorithm The shortest distance between a select number of starting points and all other vertices is found. It’s a useful and popular starting point for picking path optimization. As a result, there has been an extensive amount of research on this algorithm resulting in enhancements like:

Nearest Neighbor Algorithm This is a straightforward approach in which you start at the point closest to your starting point and continue through your path by moving to the nearest item. Naturally, there’s no guarantee that you’re going to take the best route this way. It just eliminates having to think about the process. This is not a recommended approach for warehouse picking path optimization. 
Floyd’s Algorithm The optimal distance between all points is found. While allowing a person to quickly move on to solving the traveling salesperson part of the problem, Floyd’s algorithm isn’t considered as efficient as Dijkstra’s algorithm for picking path optimization. 
MultiFragment Heuristic Algorithm This algorithm considers the edges of a graph (or distances in the warehouse layout) rather than the vertices (points or storage locations in a warehouse layout). It sorts the edges by their weightings to find the shortest distance. While the multifragment heuristic algorithm is considered a better approach than the nearest neighbor strategy, it doesn’t promise any accuracy. This is not a recommended approach for warehouse picking path optimization. 

Ant Colony Optimization Algorithm Ants take off in random directions to find a food source, leaving behind pheromones as they travel to and from the source. The more pheromones, the better the travel route, so more ants use this path. In a warehouse, if workers first take off in random directions and then communicate the results of their path in real time, the optimal pick path can be found in a reasonable time frame. This is a recommended approach in terms of its accuracy, but there are reservations because of how difficult it can be to execute. 

Twice Around the Tree Algorithm This algorithm uses a spanning tree to find an optimal route by generating a list of vertices while walking around the spanning tree. It’s a recommended approach for picking path optimization due to the amount of time it takes and its accuracy level. 

Christofides’ Algorithm An enhancement of the twice around the tree algorithm that uses a minimum spanning tree to create a Hamiltonian circuit (a path that visits every point once). 
What Is A Spanning Tree?
A spanning tree connects all the points (or vertices) in a graph while using the minimum number of edges. Meanwhile, a minimum spanning tree considers a graph’s weight and creates a spanning tree with the minimum total weight.
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Can I Run These Algorithms Automatically For My Picking Path Optimization?
Researchers at the Edinboro University of Pennsylvania have outlined a small case study of how these algorithms can be applied to a pick path optimization project.
Using a C# Windows application, a warehouse manager can create a graph representing the warehouse layout. They’d then ask the application to use the nearest neighbor approach to solve for the traveling salesman challenge and then use Dijkstra’s algorithm to solve for the shortest path part of the challenge.
The problem with using this application is that it doesn’t employ the recommended algorithms. As explained earlier, the nearest neighbor algorithm is not the most accurate way to determine the shortest route.
Pick Path Optimization Is A MathBased Approach To An Old Problem
Pick path optimization can be a lot of work, particularly for those who aren’t a fan of algorithms. But, understanding algorithms can help you understand “heuristics” or rulesofthumb for optimizing your warehouse.
While easytouse applications for these algorithms may be hard to come by, it is possible to start applying tactics inspired by these methods. As the warehouse industry becomes more competitive, continually acquiring knowledge about optimization techniques is a nonnegotiable.
Logiwa optimizes the directed putaway and picking path, saving your workers effort and speeding up your warehouse operations. Schedule a WMS demo of Logiwa today.
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Written by Ruthie Bowles
Ruthie is a content marketing consultant for Logiwa. Her specialties include small business development and inventory management.