Planning the shelves of a supermarket
Which products go on which shelf and at which height, and where do this week’s non-food offers stand, so that the store sells more without slowing down the quick shop or crowding the aisles?
Drag to rotate, scroll or pinch to zoom. The schedule below plays the plan; hover a bar for details. Plan computed with a Timefold model.
The planning question
A supermarket of about 1,300 m² with ambient shelves, refrigerated walls, freezer chests, produce tables and three checkouts. Every Monday and Thursday new non-food offers arrive (garden, kitchen appliances, kids’ clothing), and on Thursday morning the offer hunters wait at the door at opening. Over the day about 1,400 shoppers come in, from the quick lunch shop with five items to the weekly family shop with forty. Where a product stands decides who passes it, at which height it is seen and how long the walk to the checkout takes.
How we plan it
Three methods work together.
Market basket analysis: FP-Growth, an alternative to the Apriori algorithm that needs only two passes over the receipts, finds which products are often bought together. Beer and nappies is the textbook example; the simulated receipts of this store yield 29 such pairs. For complements the model shortens the walk between them: ketchup and grill sausages move from 16 to 7 metres apart, jam and toast from 11 to 7, beer and crisps from 26 to 15. For two frequent destination items the model can also reward distance, so the shopper walks through more of the store. Here that applies to minced meat and pasta, but the plan hardly moves them: the meat counter is fixed, and the pasta stays next to the pasta sauces, which 184 shoppers a day buy with it.
Shelf space as a knapsack: the shelf space is limited and forms the capacity of the knapsack. The model decides how many shelf compartments each product group gets (a compartment is a 1.25 m section of one shelf level) and maximises the contribution margin within the physical dimensions of the packages. Package width, depth and height give the number of packs per compartment. The shelves are refilled at opening and once at midday, so a group can sell at most twice its shelf stock per day. If demand is higher, the shelf is empty until the next refill and the sale is lost.
Placement: the Timefold model plans compartments, shelf levels and offer spots in one run and weighs margin against walking, crowding and the work of moving goods. Shelf traffic and receipts come from the shoppers of one Thursday, simulated from five basket profiles. The same shoppers walk through both layouts, so the comparison is like for like.
What the plan shows
| KPI | Optimized plan | Comparison: Current layout (store sketch) |
|---|---|---|
| sales per day | 52,443 € +2,986 | 49,457 € |
| sales lost to empty shelves | 484 € −372 | 856 € |
| impulse sales | 5,246 € +989 | 4,257 € |
| non-food offers | 7,280 € +1,626 | 5,654 € |
| quick shop, time in store | 5.5 min | 5.5 min |
| weekly shop, time in store | 20.2 min | 20.2 min |
| crowded aisle minutes | 54 min −21 | 75 min |
| compartments rearranged | 263 +263 | 0 |
Decisions
- how many shelf compartments each of the 93 product groups gets (shelf space as a knapsack; a compartment is a 1.25 m section of one shelf level)
- shelf bay and level (bottom, grip, eye, top) for every compartment
- spot for every facing of the 9 weekly non-food themes
Constraints
- shelf space is limited: every compartment filled, packages must fit width, depth and height
- shelves are refilled at opening and once at midday
- refrigerated, frozen and produce furniture stays where it is
- heavy goods (water, beer crates, detergent, pet food) not above grip height
- no cleaning chemicals above food
- product groups and departments stay together
Objective
more contribution margin: no empty shelves, impulse sales at eye level and on the busy paths, short walks for quick shoppers, fewer crowded aisles at rush hour and at the new offers, with few compartments rearranged
Questions
Where do the shopper data come from?
Here from basket profiles with assumptions (shares, basket sizes, arrival times, typical co-purchases). In a project we use receipts, footfall counters and the planogram data of the store.
Why not mine all receipts?
Big weekly shops contain almost everything, which makes rare products look related. The rules are therefore mined on shopping missions (baskets of up to 16 items), where buying together carries information.
Does it change the whole store?
No. Moving goods costs work, so every moved facing counts against the plan; refrigerated and frozen furniture stays where it is. The model can also be limited to one department or one weekly offer change.
Does it work for more than one store?
Yes. Each store has its own layout and customers; the model runs per store, for example before each offer week.
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