# Improve Warehouse Productivity using Pathfinding Algorithm with Python

Implement Pathfinding Algorithm based on Travelling Salesman Problem Designed with Google AI Operation Research Libraries

Implement Pathfinding Algorithm based on Travelling Salesman Problem Designed with Google AI Operation Research Libraries

## I. Pathfinding Algorithm for Picking Route Creation

In the first articles, we built a model to test several strategies of Orders Wave Creations to reduce the walking distance for picking by

link each order line with the associated picking location coordinate (x, y) in your warehouse**Warehouse Mapping:**a function calculating walking distance from two picking locations**Distance Calculation:**functions grouping orders by waves using geographical (x, y) clusters to reduce the maximum distance between two locations in the same picking route**Picking Locations Clustering:**

At this stage, we have orders grouped by waves to be picked together. For each wave, we have a list of picking locations that need to be covered by the Warehouse Picker.

The next target is to design a function to find a sequence of locations that will minimize walking distance.

** Initial Solution:** Next Closest Location Strategy

In the first article, we presented an initial solution using ** Next Closest Location Strategy**.

This simple strategy does not require a high level of computation effort.

From a location ** j (xj, yj)**, this function will take as input a list of potential next locations

**.**

**[(xj, yj), (xk, yk), (xh, yh)]**The output will be the closest location, using a custom distance walking function, as the best candidate for the next location to cover.

Is it the most optimal solution for Picking Route Creation ?Question:

## II. Travelling Salesman Problem Applied to Warehouse Picking Route Design

Objective: find the optimal algorithm for picking route creation using the ** Single Picker Routing Problem (SPRP)** for a two-dimensional warehouse.

** SPRP** is a specific application of the general

**answering the question:**

**Traveling Salesman Problem (TSP)**“Given a list of

*and the*

*storage locations**, what is the shortest possible route that visits each storage location and returns to the depot ?”*

*distances between each pair of locations***Building a Travelling Salesman Model using Google AI’s OR-Tools**

** OR-Tools** is an open-source collection of tools for

*Out of a very large set of possible solutions, the objective is to find the best solution.*

*combinatorial optimization.*Here, we’re going to adapt their Travelling Salesman Problem use-case for our specific problem.

*You can find the full code in my GitHub repository: Link*### 1. Adapt Google-OR Model

The only adaptation we need to do

Input Data

- List of picking locations coordinates:
**List_Coord = [(xi, yi), (x2, y2), …, (x_n, y_n)]** - Walking Distance Function
**f: ((x_i, y_i), (x_j, y_j)) -> distance(i,j)**

**Code**

In Google OR’s example, a dictionary is created with:

- Distance Matrix:
**[distance(i,j) for i in [1, n] for j in [1, n]]** - Number of Vehicles:
**1 vehicle for our scenario** - Location for
start and*depot =*: start = end =*end***List_Coord[0]**

### 2. Simulation: OR-Tool Solution vs. Closest Next Location

The target is to estimate the impact on total walking distance if we use the ** TSP Optimized Solution of Google-OR **vs. our initial

**.**

**Closest Next Location Solution**We’re going to use the part 2 method to simulate scenarios

20,000 Lines**Order lines:**Maximum distance between two picking locations in each cluster (distance_threshold = 35 m)**Distance Threshold:**orders_number in [1, 9]**Orders per Wave:****3 Methods for Clustering**

Method 1:clustering is not applied

Method 2: clustering applied on single-line orders only;

Method 3: clustering on single-line orders and centroids of multi-line orders;

**Best Performance**** Method 3** for

**with**

**9 orders/Wave****reduction of Walking Distance**

**83%****Question**

How much can we reduce Walking Distance by applying ** TSP Optimized Solutions** of Google-OR on top of this?

**Code**

### 3. OR-Tool Solution vs. Closest Next Location

After running Waves using these three methods, we build picking routes using:

distance_init**Next Closest Location:**distance_or**TSP Optimized Solution of Google-OR:**100 * (distance_init-distance_or)/distance_init**Distance Reduction (%):**

Few Insights

when orders number per wave OR-Tools is more impactful**Orders per Wave:**when clustering for Wave Processing is added OR-tools impact is lower**Methods:**

**Best Scenario Result**

Method 3 (Clustering for all orders) impact is ** -1.23 %** of the total Walking Distance.

**Learn more about Voice Picking Systems to implement this solution**

## III. Understand TSP Solution

For Method 3 (Clustering for all orders) OR-Tool TSP Solution reduce the total Walking Distance by ** 1.23 % **— let’s have a look at a specific example to understand.

### Highest Gap: 60 m for 21 Picking Locations

A specific example, is one picking wave with 21 Locations covered:

Distance = 384 m**OR-Tool TSP:**Distance = 444 m**Next Closest Location:**60 m**Distance Reduction:**

### Limits of Next Closest Location (NCL) Algorithm

**TSP Point 2 (Point A)**

In this specific example, we can see the benefits of the TSP Optimization Solution for the second point (19.5, 21)

Starting at Point 1, the three closest points are {A, B, C}

- The closest point from Point 1 is A
- NCL Point is going directly to C, TSP starts from A
- TSP covers {A, B, C} covers in one time while NCL only covers {B, C} and lets A for later

### NCL Point 21

In the example above, after Point 20 (Point A) Warehouse Picker still needs to cover Point 21 (Point D) before going to Depot (Point 1). This extra distance greatly impacts NCL efficiency for this Wave.

## IV. Conclusion

Applying Travelling Salesman Problem Solution to the Picking Route Creation can reduce total Walking Distance and improve the overall productivity.

Coupled with smart Order Wave Processing, it can optimize the sequence of picking for waves with a high number of picking locations to cover by finding the shortest path to cover a maximum number of locations.

## References

[1] Google OR-Tools, Solving a TSP with OR-Tools, Link

[2] Samir Saci, Improve Warehouse Productivity using Order Batching with Python

[3] Samir Saci, Improve Warehouse Productivity using Spatial Clustering for Order Batching with Python Scipy