The encyclopedia · R&D & Science · Technical decision · 1913–1930s
Harris's 1913 square-root formula settled how many parts to make at once
A one-page 1913 formula balancing setup and holding cost became the foundation of inventory science.
Westinghouse Electric
the move
In February 1913, Ford Whitman Harris — an engineer who had spent 1904–1912 at Westinghouse Electric — published 'How Many Parts to Make at Once' in Factory, The Magazine of Management. It asked a question every factory faced: produce a part in many small batches or a few big ones?
Harris framed the trade-off: interest on capital tied up in wages, material and overhead sets a maximum limit to economical batch size, while set-up costs set the minimum. Balancing the two gives a square-root formula for the cheapest lot — later named the economic order quantity (EOQ), one of the most widely used formulas in operations.
The paper was lost from sight for many years before being rediscovered, after the formula had already become standard. Erlenkotter's centennial review, published in 2014, celebrates Harris's square-root derivation as 'one of the most widely used' results in the field and the foundation of inventory management.
why it works
- One page captured a trade-off every factory faced
- The square-root formula gave a number, not a judgment call
- It applied to any item with setup and holding costs
- Rediscovery only confirmed how standard the idea had become
what transfers
When two costs pull in opposite directions, the optimum is a formula, not a guess: name the trade-off and the best number falls out.
what came after
EOQ became the base of inventory theory — reorder points, safety stock, lot-sizing and whole enterprise systems descend from it. A reprint of Harris's 1913 essay ran in Operations Research in 1990, and the centennial was marked with a special issue of the International Journal of Production Economics in 2014.
references
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