Why the terminology “pricing” in the Simplex algorithm?

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In the Simplex algorithm, the task of finding a variable with negative reduced cost is often referred to as “pricing”. What is the origin of/intuition behind this terminology?

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Fundamentally, a big reason for this is because Simplex is largely used in contexts where the goal is to generate income, or save money, for a business/individual. The field of Operations Research (OR) is predominantly used by big corporations in order to maximize profit, or maximize savings, and for them the amount they are required to pay for something is the cost of it leveraged against how actually useful it is to the model. In other words, most of the problems we will be facing in OR will be economic problems where everything is predominantly about cost and behaviors tied to it, and the Simplex method is a tool to measure these behaviors.

It shouldn’t come to a surprise once we realize that the Simplex method came about in a military setting (these are two links, look to the History section in the former link), specifically one where the optimization of battle planning and reductions of cost were at an all-time high in World War II. However, it probably did not get as developed or nuanced around that time to be what it is today, it took people years of planning/figuring out applications before businesses found out its applications.

One thing that is pretty common to hear about in terms of the Simplex Method is “Shadow Prices”, the amount of profit we would get from a resource by increasing the amount of that resource by one singular unit. From here, there are loads of terms to denote the acceptable amounts of change the tableau is allowed to have before the basis completely changes (this is called Sensitivity Analysis).