08-20-2026, 04:54 PM
Algebra: the maths working to solve the UK’s supply chain crisis
Author: Michael Brooks
Source:The Guardian / The Observer
Published: 12 September 2021
Area: Applied mathematics, linear algebra, operations research and optimisation
The article explains how the apparently abstract algebra learned at school forms the mathematical foundation of modern logistics and supply-chain management. Supermarkets and delivery companies must constantly decide how much stock to order, where to store it, how to minimise waste and how to satisfy changing customer demand. These problems begin with linear algebra, where relationships such as $y=4x$ are represented through systems of equations involving many variables. In real applications, those systems may contain enormous datasets describing inventory, warehouse capacity, delivery times, vehicles and customer orders.
Modern logistics extends this basic algebra into linear programming, mixed-integer programming, combinatorial optimisation and heuristic algorithms. Companies such as Ocado use these techniques to decide how products should be packed, which route warehouse robots should follow, how orders should be allocated to vans and in what sequence deliveries should occur. The difficulty is that the number of possibilities grows extraordinarily quickly: even delivering to only 12 locations can produce about 479 million possible routes. For a driver making 60–70 deliveries, checking every possible route is computationally impossible. Consequently, algorithms use heuristics—methods that search intelligently for solutions that are very close to optimal rather than examining every possibility.
A classic example is the travelling salesman problem: finding the shortest route that visits a collection of locations. Similar optimisation problems occur not only in supermarkets and parcel delivery but also in airline scheduling, Google searches and internet routing. Airlines, for instance, must simultaneously optimise aircraft, crews, passengers, departure times and connecting flights. The article's central message is therefore that school algebra is far from useless: the simple idea of representing unknown quantities by variables ultimately develops into the sophisticated mathematical machinery that keeps modern supply chains functioning.
Key takeaways
ARTICLE
Author: Michael Brooks
Source:The Guardian / The Observer
Published: 12 September 2021
Area: Applied mathematics, linear algebra, operations research and optimisation
The article explains how the apparently abstract algebra learned at school forms the mathematical foundation of modern logistics and supply-chain management. Supermarkets and delivery companies must constantly decide how much stock to order, where to store it, how to minimise waste and how to satisfy changing customer demand. These problems begin with linear algebra, where relationships such as $y=4x$ are represented through systems of equations involving many variables. In real applications, those systems may contain enormous datasets describing inventory, warehouse capacity, delivery times, vehicles and customer orders.
Modern logistics extends this basic algebra into linear programming, mixed-integer programming, combinatorial optimisation and heuristic algorithms. Companies such as Ocado use these techniques to decide how products should be packed, which route warehouse robots should follow, how orders should be allocated to vans and in what sequence deliveries should occur. The difficulty is that the number of possibilities grows extraordinarily quickly: even delivering to only 12 locations can produce about 479 million possible routes. For a driver making 60–70 deliveries, checking every possible route is computationally impossible. Consequently, algorithms use heuristics—methods that search intelligently for solutions that are very close to optimal rather than examining every possibility.
A classic example is the travelling salesman problem: finding the shortest route that visits a collection of locations. Similar optimisation problems occur not only in supermarkets and parcel delivery but also in airline scheduling, Google searches and internet routing. Airlines, for instance, must simultaneously optimise aircraft, crews, passengers, departure times and connecting flights. The article's central message is therefore that school algebra is far from useless: the simple idea of representing unknown quantities by variables ultimately develops into the sophisticated mathematical machinery that keeps modern supply chains functioning.
Key takeaways
- School algebra is the starting point of logistics optimisation.
- Linear algebra and operations research allow companies to manage thousands or millions of interacting variables.
- Many logistics problems are too large to solve exhaustively, so heuristics and optimisation algorithms search for near-optimal solutions.
- The travelling salesman problem is a fundamental mathematical model behind delivery-route planning.
- Mathematics can have substantial economic consequences: improved optimisation can save companies millions while reducing wasted fuel, storage and food.
ARTICLE
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