Pick Path Routing: S-Shape vs Largest Gap vs Optimal

Watch a picker on a manual each-pick floor for ten minutes and the problem is obvious. The handheld sends them to the back of an aisle for one item, back to the front for the next, then across three empty aisles to reach a location that was right beside where they started. Nobody chose that path deliberately. It is whatever order the warehouse system happened to sort the pick list into.

Choosing a routing rule on purpose, and checking it against the site's real pick density, can cut walking on sparse tours by 15 to 25% with no new equipment. In the worked layout below, the same 11 picks need 222 metres under an S-shape route, 194 metres under largest gap and 178 metres on the shortest possible tour.

• What the guide covers: the S-shape, return, midpoint, largest gap and optimal methods, how each behaves as picks per tour rise, and the configuration mistakes that quietly undo them.
• Worked material: an eight-aisle layout calculated by hand, simulated averages for 5 to 40 picks per tour, a distance function you can reuse, and labour savings in dollars and rupees.

What a routing method decides once the pick list is fixed

Routing decides only the order in which a picker visits locations that have already been chosen. Which orders are grouped into a tour is batching, which products sit in which locations is slotting, and when work is released is wave or waveless planning. All four change walking distance, but they are separate decisions with different owners and should be tested separately.

Our comparison of batch and wave picking covers how orders are grouped and released. This article starts after that decision: the tour's locations are known, and the question is the sequence the handheld presents. The literature review by de Koster, Le-Duc and Roodbergen treats routing as its own planning problem for exactly that reason.

The aisle model behind every distance in this example

A comparison is only fair when every method is measured on the same model. The worked site has eight parallel pick aisles, each 30 metres long, with centre lines 3 metres apart and a cross aisle at the front and the back. The picker starts and finishes at a depot in front of aisle 1, and picks from both sides of an aisle without extra travel.

Distance between two picks in the same aisle is the difference in their depth. Between aisles, the picker walks across to the other aisle and must go via the front or the back cross aisle, whichever is shorter. Those two rules give the exact walking distance for any pair of locations in a single-block layout, which is what makes the optimal route below computable.

# Single-block layout: L = aisle length (m), W = aisle centre spacing (m)
# A location is (aisle_number, depth_from_front_in_m)

def walk(p, q, L=30.0, W=3.0):
    (a1, y1), (a2, y2) = p, q
    if a1 == a2:
        return abs(y1 - y2)
    across = abs(a1 - a2) * W
    return across + min(y1 + y2, (L - y1) + (L - y2))   # via front or back

def largest_gap_entry(depths, L=30.0):
    # For a middle aisle: return metres walked in from front and from back.
    pts = [0.0] + sorted(depths) + [L]
    gaps = [(pts[i + 1] - pts[i], i) for i in range(len(pts) - 1)]
    g, i = max(gaps)                       # the stretch that is never walked
    return 2 * pts[i], 2 * (L - pts[i + 1])   # in-and-out from each end

The pick list for the example tour has 11 lines in six aisles: aisle 1 at 4 m; aisle 2 at 22 and 27 m; aisle 4 at 3, 12 and 18 m; aisle 5 at 15 m; aisle 6 at 2 and 5 m; aisle 8 at 9 and 24 m. Aisles 3 and 7 are empty. Every total below includes the 42 metres of front and back cross-aisle travel needed to reach aisle 8 and come back.

S-shape traversal: easy to follow, costly in thinly picked aisles

S-shape sends the picker through the full length of every aisle that holds a pick, alternating up and down, and skips empty aisles. It is the easiest rule to follow without a handheld and works well with one-way aisle traffic, which is why so many sites use it by default.

In the example, six aisles hold picks. Because that is an even number, the picker leaves the last aisle at the front and returns along the front cross aisle, so the route is six full aisles of 30 m plus 42 m across: 222 metres. Aisle 1 is walked end to end for a single item at 4 m, and aisle 6 for two items within 5 m of the front.

• Odd aisle count: when an odd number of aisles hold picks, the last one is entered and left from the same end, walking only to the furthest pick.
• Where it shines: dense tours where most aisles have several picks spread along their length, so a full traversal wastes little.
• Where it fails: sparse tours and front-loaded slotting, because the picker still walks every metre of every visited aisle.

Return and midpoint routes for front-loaded pick faces

Return routing enters each aisle from the front, walks to the deepest pick and comes back the same way. It suits sites where fast movers are slotted near the front, but it is the longest method in this example at 228 metres, because aisle 2's picks at 22 and 27 m and aisle 8's at 24 m force long out-and-back walks.

Midpoint routing splits each aisle at 15 m. The picker traverses the first and last aisles fully, picks the front half of each middle aisle from the front cross aisle and the back half from the back cross aisle. That gives 206 metres here: aisle 4 costs 24 m from the front for picks at 3 and 12 m, and another 24 m from the back for the pick at 18 m.

On an eight-aisle single-block layout with 30-metre aisles, an 11-pick tour measured in the WMS distance model needs 222 metres under S-shape, 206 under midpoint, 194 under largest gap and 178 on the optimal route defined by Ratliff and Rosenthal (Operations Research 31(3), 1983), a 19.8% saving over S-shape.

Largest gap: leaving the emptiest stretch of each aisle unwalked

Largest gap improves on midpoint by letting each middle aisle choose its own split point. For every middle aisle, it finds the longest stretch with no pick, counting from the front cross aisle to the first pick and from the last pick to the back cross aisle, and never walks that stretch. Everything in front of it is picked from the front; everything behind it from the back. Hall (1993) gave distance approximations for this rule alongside traversal and midpoint.

Aisle 4 shows why that matters. The picks at 3, 12 and 18 m leave gaps of 3, 9, 6 and 12 m. The 12 m gap from 18 m to the back is the largest, so the picker enters from the front, walks to 18 m and returns: 36 m, against 48 m under midpoint. Across the tour, largest gap needs 194 metres, as the function in the code block reproduces.

• First and last aisles: traversed fully, as in midpoint, so the picker can switch between front and back cross aisles.
• Middle aisles: entered from the back on the outward leg and from the front on the return leg, each only up to the largest gap.
• Traffic rule: pickers enter and leave aisles from the same end, so aisles must allow two-way movement or passing places for carts.

Largest gap routing, as analysed by Hall (IIE Transactions 25(4), 1993), skips the longest pick-free stretch in each middle aisle. In the WMS sequencing model of the worked example, aisle 4 with picks at 3, 12 and 18 metres costs 36 metres of in-aisle walking against 48 under midpoint, a 25% reduction.

Optimal routing and the Ratliff-Rosenthal dynamic program

An optimal route is the shortest possible tour through the pick locations, and for a single-block layout it can be computed exactly and quickly. Ratliff and Rosenthal showed in 1983 that this special case of the travelling salesman problem is solvable with a dynamic program whose effort grows linearly with the number of aisles, so tour size is not a practical barrier.

For the example tour the optimal route is 178 metres. It visits aisle 1 at 4 m, crosses at the front into aisle 4 for all three picks, continues up to the back cross aisle, drops into aisle 2 for 22 and 27 m, enters aisle 5 from the back, reaches aisle 8 from the back, walks it to the front, and finishes in aisle 6 on the way home.

• Why sites resist it: the path looks irregular, so pickers who cannot see the logic tend to deviate, and the saving disappears unless the handheld enforces the order.
• Layout limits: warehouses with middle cross aisles are harder; Roodbergen and de Koster (2001) extend exact and heuristic methods to multiple cross aisles.
• What it needs from the WMS: accurate coordinates for every location and cross aisle, which many sites do not hold; a location code alone does not give metres.

How pick density changes the ranking between routing methods

No method wins at every tour size, and the crossover point should drive the choice. We simulated random tours on the same eight-aisle layout, with picks spread evenly across aisles and depths. Optimal tours were computed exactly for 5 and 10 picks; for larger tours only the heuristics are shown.

Two patterns stand out. Largest gap is the best heuristic up to about 25 picks per tour, and at 10 picks it sits 8.7% above optimal while S-shape sits 31.8% above. Beyond about 30 picks, nearly every aisle holds several picks, S-shape's full traversals waste little, and it overtakes largest gap. A site that batches small orders into 40-pick tours should not copy a routing choice made for 10-pick tours.

Simulated 10-pick tours on an eight-aisle, 30-metre single-block layout average 218.7 metres under S-shape, 180.4 under largest gap and 165.9 on the optimal route of Ratliff and Rosenthal (1983). At 40 picks per tour, S-shape averages 281.6 metres and beats largest gap at 306.6 metres.

A sort-order reset that doubled the walk in even aisles

Routing faults rarely announce themselves; they appear as a productivity drop with no obvious cause. The trace below, with illustrative wave and aisle numbers, shows a common one: an S-shape site whose bay numbers run from the front in every aisle, so even-numbered aisles must be sorted in descending bay order.

1. Thu 06:00: wave W-3317 releases 640 tours to the shelving zone, two days after a WMS patch. Sequencing still reports "S-shape".
2. Thu 06:45: the zone dashboard shows 112 lines per hour per picker against a standard of 138, a drop of 19%, while order mix and headcount match the prior Thursday.
3. Thu 07:05: the shift supervisor watches a picker enter aisle 14 at the back cross aisle, walk to bay 01 at the front, then pick upward to bay 28 and leave by the back again.
4. Thu 07:20: the analyst queries the generated task table and finds every aisle sorted by ascending location code; the patch had reset the alternate-direction flag that reverses even aisles.
5. Thu 07:50: the flag is restored and unstarted tours are re-sequenced. By 11:00 the rate is back to 136, and a post-upgrade test now compares a sample sequence with a stored expected route.

Our guide to measuring picks per hour explains how to separate travel from other causes of a rate drop. The lesson here is narrower: a routing method is a configuration plus a location numbering convention, and either one changing silently breaks the route.

Labour hours and payback in dollars and rupees

Shorter routes are worth money only when the saved walking time is turned into fewer paid hours or more lines in the same hours. The table uses the simulated 10-pick averages, an illustrative walking speed of 1.0 metre per second with a cart, and 1,800 tours a day for 300 days, or 540,000 tours a year. Wage rates are illustrative loaded costs, not market data.

The same metres are worth about ten times more in the US example than the Indian one because of the wage gap. Switching from S-shape to largest gap is usually a configuration change and pays in either market. The last row is the real decision: whether $65,250 or ₹5,43,750 a year justifies a sequencing engine, location coordinate data and handheld enforcement.

• Hours become savings only if removed: 5,745 hours is roughly three full-time pickers on single shifts; if rosters do not change, the gain shows up as capacity, not cost.
• Travel is one part of the tour: searching, picking, scanning and packing time are unchanged, so measure lines per hour before and after rather than assuming the whole saving lands.

Which routing steps run on fixed rules and where software helps

Computing a route from known coordinates is exact arithmetic and should never be left to a picker's judgement or a prediction model. Software that learns from scan data is useful around the edges: spotting congestion, deviations and stale coordinates, where a person then decides what to change.

Checklist before changing a site's pick path method

A routing change should be tested on the site's own tours before it reaches the floor. The checklist below covers the data, the simulation and the floor trial, and it applies whether the change is a WMS setting or a new sequencing engine. Sites planning a mezzanine or a narrow-aisle area should also read our guide to mezzanine pick module design, because level changes add travel that flat routing models ignore.

If you are scoping a WMS sequencing change, a slotting review or a picking simulation on your own order history, the NextEdge request for proposal page explains what to send us. More warehouse design and methods guides are on the logistics and supply chain hub.