Tag: LOGOS

Solving the Interdependent Challenges of Packing Fitness and Delivery Distance

In global distribution, operational efficiency is a balancing act between conflicting physical realities. To maximise margins, supply chain leaders are constantly caught between two critical metrics: packing fitness (how densely items are secured within a vehicle) and delivery distance (the total mileage of the transportation route).

For any commercial fleet, the core objective is simple: deliver inventory from a central hub to multiple destinations at the absolute lowest total cost. Yet, when executed on an enterprise scale, material costs (pallets, vehicle overheads) and transport costs (fuel, driver hours) frequently pull operations in opposite directions.

To achieve true capital efficiency, decision-makers can no longer afford to evaluate packing and routing in isolation. They must be solved simultaneously.

The Costly Reality of Fragmented Models

Traditionally, logistics architecture has relied on the Separated Packing and Routing (SPR) model. This legacy approach treats the Bin Packing Problem (BPP) and the Vehicle Routing Problem (VRP) as two entirely independent workflows managed by separate teams.

While the SPR model offers administrative simplicity, it introduces two critical operational flaws:

• Conflicting Corporate Objectives: Packing teams focus entirely on minimising fixed asset and pallet usage, while dispatch teams focus solely on reducing mileage. Without a unified framework, these goals directly undermine each other.
• The 20% Cost Penalty: Because packing configurations are finalised before routing algorithms begin, vital destination and drop-off sequence data are completely excluded from the initial loading phase. This structural blind spot creates systemic delivery bottlenecks and highly sub-optimal routes.

The Computational Bottleneck

The obvious alternative is an integrated model powered by Mixed Integer Programming (MIP). When paired with advanced mathematical solvers like Gurobi, MIP models can guarantee a mathematically flawless, optimal solution.

However, exact mathematical modeling suffers from exponential computational scaling. For an enterprise fleet managing 1,000 boxes across 100 destinations, calculating a perfect MIP solution could literally take years of computing time. In live logistics environments where windows are tight, this approach is commercially unfeasible.

Introducing LOGOS+: Next-Generation Hyper-Heuristics

To bridge the gap between mathematical idealism and real-world operational velocity, Decision Lab developed LOGOS+ (Logistics Optimisation System — Two-Level Capacitated Vehicle Routing Problem, or LOGOS-2S-CVRP).

LOGOS+ is a proprietary hyper-heuristic framework that bypasses exponential computing delays. By combining two distinct algorithmic classes, it delivers near-optimal operational plans in seconds.

1. Constructive Heuristics

This layer builds a highly viable, baseline operational solution from scratch using two distinct, configurable strategies:

• Volume-Driven (VD) Heuristics: Prioritises the minimisation of material and pallet costs. Items are systematically sorted and packed into vehicles based on customisable, high-scoring geometric constraints.

• Destination-Driven (DD) Heuristics: Prioritises transportation efficiency. The engine automatically clusters items by geographic proximity or pre-loads containers to perfectly align with the intended multi-drop sequence.

2. Perturbative Heuristics

Once the initial solution is constructed, LOGOS+ deploys advanced local search and hill-climbing algorithms to eliminate hidden inefficiencies. The engine continuously optimises the fleet layout via four core operators:

Packing Swap: Exchanging assets between two vehicles to achieve a superior volumetric fit.

Packing Insert: Shifting an individual item to an alternative vehicle to maximise space utilisation.

Degrading: Completely unloading a under-utilised vehicle and resetting its contents across the remaining fleet.

Destination Swap: Altering the drop-off sequence within a single vehicle’s manifest to uncover a shorter, faster transit path.

The system iterates automatically, accepting a new layout only if it actively reduces total operational expenditure, until a refined local optimum is achieved.

Proven Performance and Speed

Through rigorous benchmarking against randomised enterprise datasets scaling up to 80 variables and 50 destinations, LOGOS+ demonstrated a massive leap forward in computational and financial performance.

Optimisation Method	Solution Quality	Computation Time	Operational Viability
Separated Packing & Routing (SPR)	Poor (Up to a 20% cost penalty vs integrated models)	Very Fast (Seconds)	High administrative ease, but poor financial efficiency.
Mixed Integer Programming (MIP)	Perfect (100% mathematically optimal)	Extremely Slow (30+ mins for just 10 boxes)	Commercially unfeasible for live, large-scale operations.
LOGOS+ (Hyper-Heuristic)	Excellent (Averages within 10% of true mathematical optimum)	Instantaneous (Processes 1,000 boxes across 100 drops in 6.52 seconds)	Ideal for real-time, large-scale enterprise logistics.

Strategic Business Impact

LOGOS+ represents a significant paradigm shift for enterprise supply chains. Rather than breaking logistics challenges apart (packing individual pallets, loading vehicles, and planning routes in silos) our engine processes them within a single, unified pipeline.

By eliminating the traditional 20% cost penalty associated with fragmented planning, LOGOS+ allows organisations to tailor their optimisation core to match specific corporate KPIs:

• Decarbonisation & Sustainability: Configure the system to explicitly minimise total CO₂ emissions, automatically influencing optimal vehicle selection and routing configurations.
• Bottom-Line Maximisation: Dynamically balance fuel consumption variables against fluctuating driver labor rates, clean-air zone fees, and service level agreements (SLAs).

What’s Next: The AI Frontier

While we are actively expanding our suite of heuristics, our next frontier is total intelligent automation. Decision Lab is currently developing an Artificial Neural Network (ANN) layer designed for automatic algorithm selection. Once deployed, this AI capability will instantly evaluate incoming logistics profiles and automatically select the absolute best heuristic combination for that specific dataset, unlocking true hyper-optimality without human intervention.

LOGOS+ is architected to serve as the high-performance optimization engine powering modern supply chain and enterprise resource planning software.

To learn how to integrate this capability into your logistics ecosystem, contact us.

Solving the 3D Bin Packing Problem with AI and MILP

The relatable anxiety of trying to fit an entire holiday wardrobe into a single 23kg suitcase mirrors one of the most financially demanding challenges in global supply chain logistics: the 3D Bin Packing Problem (3D BPP).

While a consumer might face an extra airline fee for poor packing, the stakes for commercial shipping are exponentially higher. A single poorly allocated item on a pallet can force the use of an additional container, instantly doubling transport costs for that consignment.

Despite these high stakes, human operators fill only 50% to 60% of available space on average, often requiring multiple manual attempts to achieve higher efficiency. To solve this, Decision Lab developed LOGOS (Logistics Optimisation System). By leveraging two distinct computational paradigms (mathematical optimisation and deep reinforcement learning) LOGOS consistently outperforms human capabilities in both speed and spatial utility.

Defining the 3D Bin Packing Challenge

To evaluate the effectiveness of different digital solutions, we established a standardised testing environment. The core objective is to pack a varied sequence of cuboid items into the minimum number of containers while maximising spatial utility.

For our baseline study, we used a 5x5x5 container environment packed with items ranging in dimensions from 1x1x1 to 3x3x3. Container efficiency is precisely calculated using the following utility formula:

To find the optimal operational approach, we developed and compared three distinct computational methods:

• Mathematical Optimisation (LOGOS-OPT): A deterministic approach that searches the entire problem space to calculate an absolute mathematical optimum.
• Deep Reinforcement Learning (LOGOS-RL): An AI-driven approach where an autonomous agent learns highly adaptive packing strategies through continuous trial and error.
• Rules-Based Algorithm: A standard procedural heuristic used as a comparative baseline for traditional industry software.

Approach 1: Mathematical Optimisation (LOGOS-OPT)

Our mathematical framework formulates the 3D BPP as a Mixed Integer Linear Programming (MILP) problem. This method assumes full information is available upfront, allowing the system to map out the entire packing sequence simultaneously.

Driven by the commercial Gurobi solver, LOGOS-OPT maximises total container utility while strictly enforcing real-world physical constraints:

• Spatial Boundaries: Items must remain entirely within the physical dimensions of the container.
• Volumetric Integrity: No physical overlap between items is permitted.
• Rotational Logic: Items can be orthogonally rotated, though specific orientation restrictions can be applied to individual assets.
• Vertical Stability: To prevent damage or structural collapse, the bottom face of every item must be structurally supported by the container floor or the flat surface of items beneath it, verified across all four base vertices.

Approach 2: Deep Reinforcement Learning (LOGOS-RL)

In real-world logistics hubs, operations are rarely static. Items arrive sequentially on a conveyor belt, demanding immediate, real-time placement decisions with highly imperfect future data. This dynamic, stochastic environment is where Deep Reinforcement Learning (DRL) excels.

Unlike LOGOS-OPT, LOGOS-RL does not have an upfront list of items; it evaluates items sequentially, holding visibility of only one step ahead on the conveyor line.

The AI Training Architecture

To build a highly capable neural network, we paired advanced simulation with automated cloud training:

• Simulation Environment: Built using AnyLogic, the model tracks advanced states, including a dynamic height map matrix, container utility trends, and real-time feasibility maps that serve as an action mask.
• AI Training Engine: We utilised machine teaching hosted on Azure to scale training across millions of parallel iterations. The system automatically selected the optimal deep reinforcement learning algorithms (such as SAC, Apex DQN, or PPO) based on environmental feedback.
• Reward Function: Rather than relying on a delayed end-of-game reward, the agent received immediate positive reinforcement proportional to the change in container utility, alongside a steep penalty and immediate episode termination for invalid placements.

Continuous curriculum learning allowed the agent to master basic 1x1x1 packing across 318,000 iterations before successfully mastering highly variable multi-dimensional item packing over 7 million training iterations. Once fully trained, the brain is exported into a lightweight Docker container for instant, on-site deployment.

Benchmarking Performance: Human vs. Machine

To validate LOGOS in practice, we executed two series of rigorous live trials comparing manual human efforts against our automated systems.

Trial 1: Standard Pallet Allocation (17 Items)

• LOGOS-OPT: Generated an optimal packing configuration in 13 seconds, achieving a 75.8% packing density. Using the LOGOS Visual Assistant (a digital guidance system that projects exact placement instructions), the physical packing took just 40 seconds.
• Unassisted Human: Averaged 90 seconds across multiple attempts, only managing to load 12 to 15 of the items, resulting in a significantly lower spatial density between 55% and 70%.

Trial 2: High-Complexity Pallet Allocation (19 Items)

• LOGOS-OPT: Calculated a complex packing arrangement in 105 seconds, yielding a 73.5% packing density that allowed the physical operator to safely pack all 19 items in 50 seconds.
• Unassisted Humans: The increased complexity highlighted a severe performance gap. One experienced packer gave up entirely after 5 minutes. A second achieved only 60% density, leaving 5 critical items completely unpacked. The final human packer managed to fit all items but required 10 full minutes, which is four times longer than the combined computing and packing time of LOGOS.

Comparative Results: Finding the Operational Sweet Spot

When evaluating the three algorithmic models across multiple randomised arrival sequences, Deep Reinforcement Learning proved to be an incredibly formidable alternative to perfect mathematical models.

Metric	Mathematical Optimisation (LOGOS-OPT)	Deep Reinforcement Learning (LOGOS-RL)	Standard Rules-Based Heuristic
Exp 1: Packing Density	93.5%	83.2%	75.0%
Exp 1: % of Theoretical Max	100%	89.0%	80.0%
Exp 2: Packing Density	88.35%	80.4%	74.8%
Exp 2: % of Theoretical Max	100%	91.0%	84.0%
Exp 3: Packing Density	93.6%	80.5%	71.8%
Exp 3: % of Theoretical Max	100%	86.0%	77.0%

Key Strategic Insights

1. The DRL Advantage: Despite having no knowledge of future item arrivals, LOGOS-RL consistently achieved 86% to 91% of the mathematical gold standard, comfortably outperforming standard rules-based algorithms. In fact, during Experiment 2, the RL agent matched the absolute mathematical optimum a staggering 55% of the time.
2. Infinite Scalability: Traditional mathematical optimisation complexity scales exponentially, often requiring complex problem decomposition to avoid computation time explosion when managing large fleets. Conversely, LOGOS-RL delivers near-instantaneous decision-making responses and scales linearly across an infinite number of containers without any added computational overhead.
3. Real-Time Resilience: Because the DRL framework processes decisions item-by-item, it is uniquely suited for live logistics environments where orders change mid-route, or stock availability suddenly shifts.

Transforming Fleet Economics

By bridging the gap between theoretical data science and warehouse floor execution, the LOGOS framework provides logistics enterprises with a tangible path toward maximising fleet utilisation, reducing fuel consumption, and eliminating systemic supply chain waste.

To learn more about deploying LOGOS within your logistics infrastructure, contact us.