Economic Order
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Before 1913, factory managers across America decided how much to order based on gut feeling, custom, and the persuasion of salesmen. Then a young engineer at Westinghouse Electric published a two-page paper that would, quietly and permanently, change the logic of commerce.

A Problem as Old as Trade Itself

The tension at the heart of inventory management is ancient. Order too little, and you run out — halting production, losing sales, disappointing customers. Order too much, and capital sits frozen on shelves, slowly decaying in value. Merchants in ancient Mesopotamia faced this dilemma. So did the quartermasters of Roman legions.

But nobody had put a formula to it. The costs involved — the expense of placing an order versus the cost of holding stock — were understood intuitively, but never mathematically balanced.

Ford Harris and the Square Root Formula

Ford Whitman Harris, working at Westinghouse in 1913, was the first to formalise the trade-off. His insight was elegant: total inventory cost is the sum of two opposing curves — ordering cost falls as batch size grows (fewer trips to the supplier), while holding cost rises (more stock sitting in the warehouse). The optimum is precisely where they intersect.

The mathematics resolves to a square root, which is why EOQ scales sub-linearly with demand — double your sales volume, and your optimal order size only grows by roughly 41%, not 100%. This is a counter-intuitive but deeply important result for procurement strategy.

The Wilson Controversy

Harris’s formula was later popularised — and sometimes attributed to — R.H. Wilson, a consultant who applied it extensively in the 1930s. For decades it was called the Wilson Formula in European textbooks. Modern scholarship firmly credits Harris, though Wilson deserves credit for commercialising it.

World War II and the Logistics Revolution

The formula’s most consequential application came during the Second World War. The U.S. military’s operations research teams used EOQ-derived models to manage millions of SKUs across global supply chains — from Springfield rifles to aviation fuel. The results were staggering: the same mathematics that Harris had applied to factory components now coordinated the largest logistics operation in human history.

After the war, operations research — and EOQ as a core tool — migrated from military logistics into business schools and corporate planning departments. By the 1960s, it was standard curriculum at Harvard Business School.

The Digital Age: Still Relevant, Now Automated

One might expect that modern ERP systems and AI-driven demand forecasting would have made EOQ obsolete. They have not. Instead, EOQ has become the mathematical foundation on which more sophisticated models are built. Amazon’s warehouse replenishment algorithms, Walmart’s supplier ordering systems, and NHS pharmaceutical procurement all contain EOQ logic at their core — surrounded by layers of probabilistic demand modelling and real-time adjustment.

The formula is also used in reverse: given an observed order quantity and holding cost, procurement analysts can back-calculate the implicit ordering cost that a supplier is experiencing — a powerful tool in negotiation and should-cost modelling.

Limitations and Extensions

EOQ rests on assumptions that rarely hold perfectly: constant demand, fixed costs, instantaneous replenishment, no quantity discounts. Each of these has spawned an extension model — the Economic Production Quantity (EPQ) for gradual replenishment, the Quantity Discount Model, the News Vendor problem for perishables.

The formula is not a ceiling. It is a floor — the minimum standard of rigour that any serious procurement function should apply. Optimising EOQ alone reduces inventory cost by double digits for most recurring category spends. That is the commitment behind Metricon: better decisions should not be gated by software budgets or subscription contracts.