  # Mathematics in the Supply Chain

In a recent article in The Guardian by Michael Brooks, “Algebra: the math’s working to solve the UK’s supply chain crisis,” several knowledge experts were asked how mathematics is used to solve supply chain issues. One of the experts, Ravi Ahuja, founder and CEO of Axele, shared his expertise in the article by saying, “Mathematics gives us the confidence that we are close enough to the best option.”

Transportation management systems, supply chain network design solutions, and logistics optimization apps utilize an optimization engine to solve supply chain problems. The optimization engine, or solver, can sort through tens of thousands of variables in seconds to return the optimal answer to a problem, whether it is determining the best load for a truck driver or the location of a distribution center.

### Optimization engines and algorithms

An optimization problem involves maximizing or minimizing a real function based on variables or constraints. Optimization engines use different types of algorithms to solve the problem. Optimization algorithms are executed iteratively by comparing various solutions till an optimum or satisfactory solution is found.

As mentioned, these optimization engines, based on mathematics, are used within supply chain solutions because supply chain problems are very challenging. For example, in the airline industry, variables include flight paths, how many planes per flight path and at what intervals, and how to schedule passengers to maximize profit.

Per Ravi, “Timing is everything for airlines, as that enables inbound planes to connect with outbound planes, crews to go from one flight to another, passengers to fly when they want to and make flight connections. For a large passenger airline that flies thousands of flights a day, it is a massive and tremendously complex mathematical problem.”

### How this works in the supply chain

Axele and its parent company, Optym, use various algebraic techniques to solve supply chain and scheduling challenges. These include:

• Greedy heuristics – defined by Wikipedia as: “A greedy algorithm is an algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time.

For example, a greedy strategy for the traveling salesman problem (which is of high computational complexity) is the following heuristic: “At each step of the journey, visit the nearest unvisited city.” This heuristic does not intend to find the best solution, but it terminates in a reasonable number of steps; finding an optimal solution to such a complex problem typically requires unreasonably many steps. In mathematical optimization, greedy algorithms optimally solve combinatorial problems having the properties of matroids and give constant-factor approximations to optimization problems with the submodular structure.”

• Mixed-integer programming is a problem where some decision variables are constrained to be integer values at the optimal solution. The use of integer variables dramatically expands the scope of practical optimization problems you can define and solve.

Ravi used his algebra skills to find an optimal solution for a massive set of equations for an airline company, which resulted in profits rising by several million dollars annually. The Optym optimization engine is the heart of the Axele TMS. Users can search through all connected load boards to find the best load for each driver by considering their hours of service availabilities and personal preferences.​

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