How do you derive the formula for the simple EOQ model?

Answer 1

The simple, or basic, economic order quantity (EOQ) is a special case of the continuous rate EOQ, which can be derived from the equation of total cost as follows.

Here is the equation for total cost (TC) as a function of run size (q):

TC(q) = K*D/q + P*D + q*H(r - D)/(2r), where:

K = Fixed cost per order

D = Annual Demand of product

q = run size

P = Purchasing cost per unit

H = Annual holding cost per unit

r = Production rate

K*D/q = Setup cost

P*D = Purchasing cost

H(r - D)/(2r) = holding cost.

To find the maximum value of q, you take the derivative, d[TC(q)]/dq, set it equal to zero, and solve for q.

First, take the derivative:

d[TC(q)]/dq = -K*D/q2 + H(r - D)/(2r).

Then, to maximize, set this equal to zero, and solve for q:

H(r - D)/(2r) - K*D/q2 = 0,

q2 = (2*r*K*D)/[H(r - D)],

q = √((2*r*K*D)/[H(r - D)]).

That's the formula for the continuous rate EOQ.

Basic EOQ is the special case of r >> D, which means r - D pretty much equals r, which allows you to cancel the r's in the above equation, giving you the formula:

q = √((2*K*D)/H).

This is the formula for basic EOQ.