Joint Order Batching and Picker Routing Problem in Warehouse Operations

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Effective warehouse operations depend heavily on enhancing the order picking process, which accounts for a considerable portion of operational expenses. In extensive e-commerce and grocery fulfillment centers, where orders frequently consist of many items, the complexities of order batching and picker routing become even more pronounced. Without adequate optimization, poorly organized batch grouping and inefficient routing can result in unnecessary picker travel distances, escalated labor costs, and delayed fulfillment times.

In this blog, we will explore the Joint Order Batching and Picker Routing Problem (JOBPRP). We will discuss the current challenges businesses face, the complexities involved in addressing this issue, and how optimization strategies can improve warehouse efficiency.

Problem Description: The Challenges of JOBPRP.
JOBPRP is primarily consist of two interconnected decisions:

Order Batching: This involves consolidating several customer orders into groups to be picked simultaneously.
Picker Routing: This pertains to determining the most efficient path for each picker to gather all designated items within a warehouse configuration.

Warehouses are organized with aisles and cross-aisles, requiring pickers to move through various sections to retrieve products. The complexity of the problem arises from several factors:

Varied Item Characteristics: Items differ in size, weight, and storage location, complicating the batching decisions.
Warehouse Layout Limitations: Certain routes may experience higher congestion, which influences optimal routing choices.
Picker Capacity Restrictions: Each picker has a maximum number of items that can be carried per trip.
Minimizing Travel Distance: Reducing unnecessary travel is crucial for enhancing efficiency and lowering costs.

Example: Inefficient vs Optimized Picking

Consider a warehouse with four orders containing different SKUs, as shown below:

Order ID	SKU ID	Description	Dimension (LxBxH))	Quantity
01	S1	Laptop	15″x 10″ x1″	1
01	S2	Wireless Mouse	5″x 3″x 2″	1
02	S3	Printer	20″x 15″x10″	1
02	S4	Notebook	8″x 6″x 1″	2
03	S5	Headphoones	8″x 8″x 5″	1
03	S6	Coffee Mug	4″x 4″ x 4″	2
04	S7	Office Chair	40″x 30″ 30″	1

When processing each order in isolation, pickers would need to navigate the warehouse multiple times, which greatly increases the distance traveled. In contrast, consolidating compatible orders and streamlining the picker’s route can help minimize overall travel time.
### Current Business Challenges
Numerous warehouses are hindered by operational inefficiencies due to:

*Ineffective Batching Techniques**: Orders are frequently grouped in a way that isn’t optimal, causing excessive movement by pickers.

*Manual Route Planning**: In the absence of algorithm-based routing, pickers may follow inefficient routes, leading to longer labor hours.

*High Congestion and Delays**: Poor order assignment can result in multiple pickers scrambling for the same items in busy aisles.

*Lack of Real-Time Optimization**: Fluctuations in incoming orders or item availability can interfere with current batch arrangements.

### Example: Impact of Suboptimal Batching

Consider a scenario in a warehouse where three orders include overlapping SKUs. If batching isn’t properly managed, each picker must collect the items for these orders separately:

Order O1 consists of a laptop and a wireless mouse, while Order O2 includes a printer and a notebook, and Order O3 has headphones and a coffee mug. Instead of optimally grouping O1 and O3 together, which contain smaller and lighter items, a suboptimal batching approach may pair O1 with O2. This would lead to one batch containing the bulky printer and another batch being underused, ultimately causing inefficient carton utilization and unnecessary travel for the picker.

What Makes This Issue Challenging to Address?Resolving the JOBPRP optimally is computationally demanding because of:

● Exponential Increase in Constraints: The potential batches grow exponentially as the number of orders rises.

● Shifting Routing Constraints: Routes are influenced by real-time conditions like congestion levels, resource availability, and the picker’s position.

● Conflicting Multi-Objective Decisions: The challenge entails reducing travel distance while simultaneously enhancing batch efficiency, often resulting in competing optimization objectives.

How Optimization Can Solve JOBPRP

In an Integer Programming (IP) Model, constraints play a fundamental role in ensuring that the optimization process aligns with the practical limitations of a warehouse while aiming to reduce travel distances. Below are the essential constraints taken into account in this scenario:

Order Assignment Constraint

Guarantees that each order is allocated to precisely one picker. To prevent overlapping efforts and confusion, every order must be handled by a single picker.

Picker Capacity Constraint

Limits the number of items a picker can transport in a single trip. Each picker has a defined weight or volume threshold that must not be exceeded during transportation.

Route Continuity (Flow Conservation) Constraint

Mandates that pickers maintain a continuous route without any abrupt jumps. If a picker enters a particular location, they are required to exit from it, except when reaching the final destination.

Start and End Constraint

Requires each picker to begin and conclude their journey at the depot (warehouse entry). A picker cannot depart from or return directly to any location other than the depot.

Distance Reduction Requirement

Guarantees that pickers take the most efficient routes while accessing all designated locations. This requirement aids in reducing the overall distance traveled or walked.

Unified Order Picking Requirement

Ensures that a single picker is responsible for collecting all items in an order. This prevents the fragmentation of orders among different pickers, eliminating the need for redundant repacking activities.

Enhancing Order Batching and Routing in a Compact Warehouse

Warehouse Configuration:

Picture a warehouse featuring five distinct zones: Picker operations commence and conclude at the Depot (O), collecting items from various locations along the way.

Orders Acquired:

Order ID	Items	Weight
01	Laptop, Mouse	3kg
02	Printer, Paper	7kg
03	Phone, Charger	2kg

Picker Constraints:

2 Pickers available
Max weight per picker = 10 kg

Distance Matrix (in meters):

From → To	O	A	B	C	D
O	0	10	15	20	25
A	10	0	5	5	10
B	15	5	0	10	5
C	20	5	10	0	5
D	25	10	5	5	0

Streamlined Order Allocation and Navigation

Batching Approach:

– Picker 1 → Responsible for O1 & O3 (Combined weight: 5 kg) → Route: Depot → A → C → D → Depot

– Picker 2 → Responsible for O2 (Weight: 7 kg) → Route: Depot → B → D → Depot

Overall Distance Traveled Calculation.

Picker 1’s Route

– O → AO → AO → A = 10 meters

– A → CA → CA → C = 5 meters

– C → DC → DC → D = 5 meters

– D → OD → OD → O = 25 meters

Total: 45 meters

Picker 2’s Route

– O → BO → BO → B = 15 meters

– B → DB → DB → D = 5 meters

– D → OD → OD → O = 25 meters

Total: 45 meters

Total Optimized Travel Distance = 90 meters

Without the optimization, the travel distance would exceed 125 meters due to less efficient picking routes.

Advantages of Employing Integer Programming for Optimization

Decreased Travel Time: Pickers cover less distance, enhancing productivity.
Lowered Picker Fatigue: Intelligent batching minimizes redundant movements.
Enhanced Order Accuracy: Guarantees that orders are fulfilled in the most efficient manner.
Increased Warehouse Throughput: Accelerated order processing boosts overall operational capacity.

Machine Learning-Driven Predictions: Utilizing Historical Order Trends for Dynamic Batch Assignments

One of the most effective strategies for enhancing order batching and optimizing picker routing is to harness the power of machine learning (ML) in the analysis of historical order trends. By drawing insights from previous orders, ML models can anticipate which items are commonly ordered together, allowing them to be grouped into efficient batches proactively.

Scenario: Anticipating Future Order Combinations for Streamlined Batching

Consider an e-commerce warehouse that processes orders on a daily basis. Over time, the system accumulates data about items that are often purchased together. By using this historical information, we can train a machine learning model (such as association rule mining or clustering algorithms) to forecast likely order combinations effectively.

Step 1: Historical Order Data

Consider a dataset of past 10 orders from a warehouse:

Order ID	Item Purchased
01	Laptop, Wireless Mouse, Keyboard
02	Printer, Ink Cartridge, Paper
03	Phone, Phone Case, Screen Protector
04	Wireless Mouse, Keyboard
05	Laptop, USB Hub, HDMI Cable
06	Printer, Paper, Ink Cartridge
07	Phone, Earbuds, Screen Protector
08	Wireless Mouse, Keyboard
09	Laptop, Wireless Mouse
10	Printer, Ink Cartridge

The table above highlights following observations:

Wireless mouse and keyboards are often ordered alongside laptops
Similarly, cartridge and paper are frequently purchased with printer
While, phones accessories such as phone cases and screen protectors are purchased under single order id

Step 2: Predicting Future Orders

Advanced probability concepts such as bayesian algorithms can help to predict the following relationships using the concepts such as a priori:

IF a Laptop is ordered, THEN a Wireless Mouse is likely included (90% confidence).
IF a Printer is ordered, THEN Ink and Paper are also likely included (95% confidence).
IF a Phone is ordered, THEN a Screen Protector is likely included (85% confidence).

Step 3: Applying Predictions for Dynamic Batching

Now, a new batch of 5 orders comes in:

New Order ID	Items Purchased
NO1	Laptop
NO2	Printer
NO3	Phone
NO4	Laptop, HDMI Cable
NO5	Printer, Ink Cartridge

Using ML predictions, we anticipate missing items and optimize batch assignments:

NO1 → Likely needs a Wireless Mouse, Keyboard → Batch with NO4.
NO2 → Likely needs Paper, Ink Cartridge → Batch with NO5.
NO3 → Likely needs a Screen Protector, Earbuds → Hold for completion or suggest.

Step 4: Benefits of ML-Based Batching

Reduces Picker Travel Distance → Orders with common SKUs are picked together.
Minimizes Partial Orders → Reduces the need for multiple trips for a single order.
Increases Fulfillment Speed → Predictive batching ensures faster processing.

Since orders are real-time information and vary in their shape, volume, etc depending on the seasons and offers, applying ML can improve the predictions of order processing and batch creation process.

Final Thoughts: Why Every Warehouse Needs Optimization

Without optimization, pickers waste valuable time, labor costs rise, and fulfillment slows down. Combining Integer Programming for route planning and Machine Learning for predictive batching can revolutionize warehouse efficiency.

Companies like Amazon, Walmart, and DHL use these techniques to stay ahead in logistics efficiency. If you manage a warehouse, now is the time to start integrating these strategies. If your companies solve a very large problems like these then optimization packages such as Gurobi, Pulp can come handy to optimize the solution efficiency and implementation.

REFERENCES:

Cristiano Arbex Valle, John E. Beasley, and Alexandre Salles da Cunha. Optimally solving the joint order batching and picker routing problem. European Journal of Operational Research, 262(3):817 – 834, 2017.