Computes s (stock), i.e., the EOQ, "economic order quantity" or "order size" (replenishment) that minimizes the expected (management only) cost, z, in inventory management, under random demand, with holding cost, c_s, and shortage cost, c_p. The demand is random, with either Poisson (mean, μ) or given probabilities.

The parameters μ and σ are computed for probabilities given (from the definition) as well as √μ (which is σ for Poisson) and it over σ (which is 1 for Poisson).

If probabilities are given and do not add up to 1, a warning is issued (and uncorrected results are produced).

(Too large a Poisson μ will eventually cause overflow, due to the factorial in the formula.)

¹ Subscripts: s, holding (stock, armazenagem); p, shortage (penúria), both $/unit-T.
"Order size": stock máximo, reaprovisionamento.

• Sapra, A., V.-A. Truong, R. Q. Zhang, 2010, "How much demand should be fulfilled", Operations Research, 58(3), pp 719–733 (terminology).

• Weisstein, Eric W., "Stirling's Approximation." From MathWorld--A Wolfram Web Resource (search "double inequality").

• Google "inventory management"

• 1713-05-07: Clairaut, Alexis Claude (1765-05-17).