Warehouse Order Batching & Picking
TSP-Based Pick Path — Nearest Neighbor / 2-opt
In a fulfillment warehouse, a picker walks 12–15 km per shift. Optimizing the pick sequence through a 6×5 aisle grid reduces walking distance by 20–40%, equivalent to €80,000–€200,000 annual savings per warehouse.
Where This Decision Fits
Supply chain operations — the highlighted step is what this page optimizes
The Problem
From warehouse aisles to optimization theory
A fulfillment warehouse is arranged as a 6×5 aisle grid — 6 parallel aisles with 5 pick bays per side. A single order batch contains 8 pick locations scattered across the grid. The picker starts at the I/O point (depot), visits every pick location, and returns. The objective is to minimize total walking distance — this is the Traveling Salesman Problem (TSP).
Unlike outdoor routing, warehouse TSP operates on a rectilinear grid with cross-aisles only at the top and bottom, making Euclidean shortest paths unavailable. The picker must traverse aisles and cross-aisles, giving the problem a distinct Manhattan-like distance metric.
subject to
Σj xij = 1 ∀ i // leave each location exactly once
Σi xij = 1 ∀ j // arrive at each location exactly once
ui − uj + n · xij ≤ n − 1 // subtour elimination (MTZ)
xij ∈ {0, 1} // binary routing variables
Where dij is the rectilinear walking distance between pick locations i and j (through aisles and cross-aisles), and xij indicates whether the picker walks directly from i to j.
With 8 pick locations, TSP has 7! = 5,040 possible tours — tractable by enumeration, but real batches of 20–40 items make exact methods impractical, motivating heuristic approaches.
See full TSP theory and all algorithmsTry It Yourself
Optimize pick paths through the warehouse grid
Pick Path Optimizer
6×5 Grid · 8 PicksReady. Click “Solve & Compare All Algorithms” to run.
| Algorithm | Distance (m) | Aisle Traversals | % vs S-Shape |
|---|---|---|---|
| Click Solve & Compare All Algorithms | |||
The Algorithms
From simple traversal to local search improvement
S-Shape Traversal
O(n log n)The industry standard baseline. The picker enters an aisle from one end, walks to the last pick in that aisle, exits from the other end, and enters the next aisle containing picks from the opposite side — creating an S-shaped serpentine path. Simple to implement and understand, but traverses entire aisles even when only one pick is near the entrance.
Nearest Neighbor
O(n²)From the current position, always walk to the closest unvisited pick location (using rectilinear aisle distance). Greedy and fast, it avoids full aisle traversals when picks are sparse, but can produce poor solutions when the last few picks are far apart. Typically 15–25% better than S-shape for scattered picks.
2-Opt Improvement
O(n²) per iterationStart with a Nearest Neighbor tour, then iteratively try reversing every sub-segment of the path. If reversing a segment between positions i and j shortens the total tour, accept the swap. Repeat until no further improvement is found. Typically shaves another 5–15% off the NN solution, approaching near-optimal for small batches.
Real-World Complexity
Why warehouse picking goes beyond the basic TSP
Beyond Standard TSP
- Order batching — Grouping multiple orders into a single pick wave to amortize travel time; the batch composition itself is an NP-hard problem
- Multi-level racking — Pick locations at different heights require vertical travel time (reach truck, mezzanine) that varies by bay
- Congestion and aisle blocking — Multiple pickers in the same aisle create delays; stochastic travel times depend on warehouse traffic
- Weight and fragility sequencing — Heavy items must be picked first (bottom of cart), fragile items last; this adds precedence constraints
- Zone picking — Large warehouses are divided into zones with dedicated pickers; inter-zone handoffs add coordination complexity
- Dynamic arrivals — New orders arrive continuously; re-optimizing mid-wave changes the pick list while the picker is in motion
- Returns and restocking — Combined pick-and-put-away tours require visiting both pick and storage locations in one trip
Key References
Foundational works in warehouse order picking
- (1983). “Order-picking in a rectangular warehouse: a solvable case of the traveling salesman problem.” Operations Research, 31(3), 507–521.
- (2007). “Design and control of warehouse order picking: a literature review.” European Journal of Operational Research, 182(2), 481–501.
- (2001). “Routing methods for warehouses with multiple cross aisles.” International Journal of Production Research, 39(9), 1865–1883.
- (1997). “An evaluation of order picking routeing policies.” International Journal of Operations & Production Management, 17(11), 1098–1111.
- (1973). “An effective heuristic algorithm for the traveling-salesman problem.” Operations Research, 21(2), 498–516.
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