Simplex

The word Simplex has two separate meanings in technology that have nothing to do with each other. The more common one refers to a computational method for planning: one searches for the best solution to a problem in which there are fixed limits. An example: A factory wants to make as much profit as possible, but has only limited material, machines, and working time. Simplex calculates how much of each product should be produced. The second meaning comes from radio technology and describes a connection over which data travels in only one direction. This entry deals primarily with the first meaning, because it constantly appears in business and computer science.

Why planning problems would be unsolvable without Simplex

Problems of this kind are called linear optimization. Linear means: all relationships are simple proportions. Twice as many chairs need twice as much wood. Optimization means: there is a clear goal, such as maximum profit or minimum cost. Such tasks are embedded in timetables, shift schedules, supply chains, and power grids.

One might think you could simply try out all combinations. With three products, that’s still feasible. But real problems have thousands or millions of variables being decided on. The number of combinations then grows so fast that no computer in the world could calculate through them all. Simplex still finds the best solution in a manageable amount of time.

The algorithm was developed in 1947 by the American George Dantzig. It ranks among the most influential methods of the 20th century. Airlines use it for aircraft and crew deployment plans. Refineries use it to divide up crude oil in the most profitable way possible. The economic value of these calculations runs into the billions.

The path via the corners

Every constraint, such as “at most 500 kilos of wood,” cuts away part of the possibilities. What remains is a region of permissible solutions. With two variables, you can draw it on paper: it forms a polygon. With many variables, it is a solid with a huge number of corners and edges that one can no longer visualize.

The decisive mathematical finding is: the best solution always lies at a corner of this region. Never in the middle. Simplex therefore only needs to check corners, not the entire space. The procedure starts at some corner and then moves along an edge to the next one. In doing so, it always chooses the direction in which the result improves the most.

When no neighboring corner is any better, the algorithm stops. That corner is then guaranteed to be the best solution. You can picture it like a mountain climber who always walks uphill on a cut crystal. A common misconception is that Simplex only delivers a good approximation. It actually finds the exact optimum, provided one exists.

From logistics software to the radio device

You almost never see Simplex directly. It’s built into programs that companies use for logistics and production planning. Spreadsheet programs like Excel contain it too: the “Solver” function uses exactly this method. In business and computer science degree programs, it belongs to the required curriculum.

In the world of AI, Simplex tends to appear more at the margins. Neural networks are trained with other methods, above all with so-called gradient descent. But Simplex remains important wherever rules must be strictly adhered to. A data center must not exceed its power budget, not even by a little. Such rigid limits are the home turf of linear optimization.

The second meaning is encountered in radio technology. A radio station transmits in simplex operation: it broadcasts, the radio only receives. A telephone call, on the other hand, runs in duplex operation, meaning in both directions simultaneously. Anyone who comes across the word in network technology datasheets is usually looking at this meaning.