Quantum Optimization Is Tested on a Real Warehouse Planning Problem

Warehouses are designed to move products efficiently.

Every product stored inside a distribution center occupies a particular location, and that location can affect how far workers or automated systems must travel when fulfilling orders.

Products that are frequently ordered together may benefit from being positioned relatively close to one another.

High-volume products may also need to be placed in locations that reduce the distance required for repeated picking operations.

Determining the best arrangement is known as the warehouse layout problem, or warehouse slotting.

It is a difficult optimization problem because changing the location of one product can affect the overall efficiency of the warehouse.

A new peer-reviewed study published in Scientific Reports on August 15, 2026, examined whether quantum optimization could be used to address this problem. The researchers, Kumar Gosh and Haitao Li, developed a quantum-optimization formulation of the warehouse layout problem and evaluated it using D-Wave's Leap Hybrid solver.

The study is relevant to logistics because warehouse slotting is directly connected to order-picking efficiency.

It is also notable because the researchers compared the quantum-hybrid approach with IBM CPLEX, a classical optimization solver, rather than evaluating the quantum approach by itself.

The results provide evidence that hybrid quantum-classical optimization can be competitive on the specific test cases studied.

They do not establish that quantum computing is already superior for warehouse operations generally.

That distinction is important.

What is warehouse slotting?

Warehouse slotting is the process of deciding where products should be stored.

The objective is often to reduce the amount of travel required to pick products for customer orders.

Consider a warehouse containing hundreds or thousands of products.

Some products may be picked very frequently.

Others may be picked only occasionally.

Some products may commonly appear together in the same order.

If products that are frequently picked together are placed far apart, workers or automated equipment may need to travel additional distances to complete an order.

If high-volume products are positioned strategically, picking operations can potentially require less travel.

The challenge is determining the best overall arrangement.

The researchers describe the warehouse layout problem as a combinatorial optimization problem and note that finding high-quality solutions for medium and large instances remains computationally challenging.

This makes warehouse slotting an interesting application for optimization research.

Why warehouse layout is an optimization problem

The number of possible product-to-location assignments can become very large as the number of products and storage locations increases.

Changing one assignment can influence the value of the entire solution.

For example, moving Product A closer to Product B may reduce travel for orders containing both products.

But that same storage location may have previously been used for Product C, which may have an even stronger relationship with another group of products.

The optimization system therefore needs to consider many relationships simultaneously.

This is different from simply placing the most popular products closest to the warehouse entrance.

The objective is to find an arrangement that performs well across the overall order profile.

The study approaches this problem mathematically using a formulation based on the Quadratic Assignment Problem, or QAP.

The researchers then transform the problem into a Quadratic Unconstrained Binary Optimization, or QUBO, formulation suitable for the quantum-hybrid solver they tested.

From classical optimization to QUBO

QUBO formulations are commonly used when applying quantum annealing and related optimization technologies.

The basic idea is to express the optimization problem using binary variables and a quadratic objective function.

In the warehouse study, the researchers formulate binary decision variables representing product-to-storage-location assignments.

Their formulation is designed to avoid the need for additional slack variables that can increase the size of a conventional QUBO representation.

The researchers state that this reduces some of the additional overhead associated with a typical QUBO reformulation and makes the problem suitable for the D-Wave Leap Hybrid solver.

This modelling step is important.

Quantum optimization is not simply a matter of taking an existing warehouse-management problem and sending it to a quantum computer.

The original business problem must first be translated into a mathematical form that the selected optimization technology can process.

That translation can affect computational performance.

What the researchers tested

The study examined a warehouse-layout scenario involving:

• 30 stock-keeping units, or SKUs

• 32 storage locations

• 960 binary decision variables

The researchers then tested the resulting QUBO formulation using the D-Wave Leap Hybrid solver.

The results were compared with IBM CPLEX using a mixed-integer quadratic programming, or MIQP, formulation.

This comparison is important because classical optimization remains the standard technology for many industrial optimization problems.

A quantum or quantum-hybrid system needs to demonstrate value relative to a capable classical alternative.

The researchers therefore did not simply ask whether the D-Wave system could find a feasible warehouse arrangement.

They compared the quality of the resulting solutions with those produced by CPLEX under the experimental conditions.

The reported comparison

For the base scenario, the D-Wave Leap Hybrid solver found a better solution than the exact CPLEX MIQP solver within the time limits used in the experiment.

The D-Wave hybrid solver was given a 60-second wall-clock limit.

CPLEX was given a 600-second budget.

The researchers therefore emphasize that the comparison was conducted under a specific experimental design rather than as a general measurement of the two technologies.

The researchers then conducted a sensitivity analysis involving 30 scenarios.

These scenarios combined:

• five annual pick-volume profiles

• six co-picking matrix density levels ranging from 0.5 to 1.0

The D-Wave hybrid solver produced better solution quality than CPLEX in 26 of the 30 scenarios.

The reported improvements in solution quality ranged from 0.4% to 12.1%.

The study also reports that the advantage generally increased as the density of the co-picking matrix decreased.

These are the central numerical findings of the research.

They should be presented exactly in this context rather than generalized into claims about all warehouse operations.

What the results mean

The findings provide evidence that a hybrid quantum-classical solver can produce competitive solutions for the particular warehouse-layout formulation studied.

That is potentially significant because warehouse slotting is a genuine logistics optimization problem rather than a purely theoretical mathematical exercise.

However, the results do not mean that warehouses can automatically expect a 0.4% to 12.1% improvement by adopting quantum computing.

Those percentages describe the difference in solution quality observed across the researchers' 30 experimental scenarios.

They are not measurements of actual warehouse productivity.

They do not represent reductions in labor costs.

They do not represent reductions in delivery times.

They do not represent increases in warehouse revenue.

And they do not demonstrate a production deployment.

Keeping these distinctions clear is essential.

Why the hybrid approach matters

One of the most interesting aspects of the study is that the technology tested is a hybrid solver.

The D-Wave Leap Hybrid approach does not mean that every component of the warehouse optimization process is performed by quantum hardware.

Hybrid quantum-classical systems combine quantum optimization resources with conventional computing.

This approach can be useful because modern quantum systems remain subject to technical constraints.

Instead of requiring a quantum processor to perform an entire industrial optimization workflow, a hybrid system can allocate different parts of the calculation to different computational resources.

For warehouse optimization, this means that classical systems can remain responsible for data preparation, modelling and other conventional computational tasks while quantum optimization is used for the relevant combinatorial component.

The August study provides an example of this architecture being applied to a logistics problem.

Why warehouse slotting matters to logistics

Warehouse layout decisions can have operational consequences.

If picking distances are reduced, workers or automated equipment may spend less time traveling between storage locations.

That can affect the efficiency of order fulfillment.

Warehouse slotting can also influence how products are organized around demand patterns.

Frequently ordered products may require different placement strategies from products with low or irregular demand.

Products that are frequently ordered together may also benefit from being positioned according to their co-picking relationships.

The research focuses specifically on minimizing total travel distance for picking operations.

It does not claim to optimize every component of warehouse performance.

For example, a real warehouse may also need to consider labor availability, congestion, safety requirements, storage equipment, replenishment activities and other operational constraints.

Those factors would need to be incorporated into a broader optimization model before a quantum-based approach could be evaluated for a particular facility.

The size of the experiment matters

The researchers' experiment involved 30 SKUs and 32 storage slots.

That is useful for testing the optimization methodology.

However, it is smaller than many commercial warehouse environments.

Large fulfillment centers can contain substantially more products, locations and operational constraints.

This creates an important question for future research:

• Does the observed performance remain useful as the problem becomes larger and more complicated?

• The study itself identifies the need for further investigation of hybrid quantum-classical methods at industrial-strength scales.

That means the research should be viewed as an important experimental result rather than a final demonstration of commercial scalability.

Why classical optimization remains important

The study also illustrates why classical optimization remains an essential benchmark.

IBM CPLEX was used as the comparison solver.

This is significant because any proposed quantum advantage needs to be evaluated against established optimization technology.

The fact that the D-Wave hybrid solver produced better results under the study's particular time budgets is noteworthy.

But the comparison does not establish universal superiority.

Different time limits, formulations, hardware configurations or problem instances could produce different outcomes.

The correct conclusion is therefore that the D-Wave hybrid approach performed better under the conditions tested by the researchers.

That is a defensible scientific statement.

A broader claim that quantum optimization is now better than classical optimization for warehouse management would not be supported by this study alone.

What could this mean for warehouse operators?

The research suggests that warehouse optimization is an area worth monitoring as quantum computing develops.

Warehouse operators already use software to manage inventory, storage locations and picking processes.

Quantum optimization could eventually become another computational option for particularly difficult optimization problems.

Potential applications could include:

• product-to-location assignment

• warehouse slotting

• picking-route optimization

• resource allocation

• scheduling

• distribution-center network planning

However, these applications should not be treated as commercially proven quantum use cases simply because they can be expressed as optimization problems.

Each application would need to be tested using realistic data and compared with the classical systems already used by the operator.

What businesses should watch next

The next stage of research should focus on several areas.

Larger warehouse problems

Future studies using substantially larger numbers of products and storage locations will help determine whether the observed results scale.

More operational constraints

Real warehouses involve more than product placement and picking distance.

Future models incorporating congestion, replenishment, labor and equipment constraints could provide a more complete picture.

Stronger classical comparisons

Quantum-hybrid methods should continue to be compared with strong classical optimization systems.

The comparison should use clearly defined time limits, hardware resources and solution-quality measurements.

Real warehouse pilots

The strongest evidence would eventually come from controlled tests using actual warehouse operations.

A real-world pilot could measure practical indicators such as picking travel, throughput, labor requirements or other operational metrics.

That evidence would be more directly useful to warehouse operators than a simulation alone.

The broader significance for quantum logistics

The warehouse study is important because it moves quantum logistics beyond vehicle routing.

Warehouses are another major component of modern supply chains.

Products must be stored, picked and prepared for transportation before they reach customers.

Optimization at this stage can influence how efficiently goods move through a distribution network.

The research therefore illustrates a broader point about quantum logistics.

The potential applications of quantum optimization are not limited to trucks and transportation routes.

They can also involve the decisions that take place inside logistics facilities.

At the same time, the study demonstrates why evidence needs to remain specific.

The researchers tested one warehouse-layout formulation under defined experimental conditions.

The results are promising within that scope.

They are not proof that quantum optimization is ready to replace existing warehouse-management systems.

Conclusion

A peer-reviewed study published in Scientific Reports on August 15, 2026, provides one of the clearest recent examples of quantum optimization being applied directly to a warehouse logistics problem.

Researchers Kumar Gosh and Haitao Li formulated the warehouse layout problem as a QUBO and evaluated it using the D-Wave Leap Hybrid solver. Their experimental case involved 30 SKUs, 32 storage locations and 960 binary decision variables.

In the reported experiments, the D-Wave hybrid solver produced a better solution than IBM CPLEX's MIQP solver for the base scenario under the specified time limits. Across 30 sensitivity-analysis scenarios, the D-Wave approach produced better solution quality in 26 cases, with reported improvements ranging from 0.4% to 12.1%.

These findings are relevant to logistics because warehouse slotting directly affects the travel required to pick products.

But the results should be interpreted carefully.

The study does not establish that quantum computing will deliver the same improvements in every warehouse. It does not report a commercial warehouse deployment, and its experimental problem is smaller and more controlled than many real-world warehouse environments.

The most important next step is therefore scalability and operational validation.

If future research can reproduce these results on larger warehouse problems with realistic operational constraints and demonstrate consistent advantages against strong classical optimization systems, quantum-hybrid technology could become increasingly relevant to warehouse planning.

For now, the August 2026 study provides credible evidence that quantum-hybrid optimization is being tested on a concrete logistics problem—and that warehouse optimization is emerging as another area where quantum computing deserves careful, evidence-based attention.