Derive EOQ appllied to production order?

Answer 1

Q size to order : obej. to find best of Q to minimize the cost

K:setup cost

c:cost of one unit

h: holding cost for one unit per one unit period of time

landa = demand rate

T cycle length = Q/landa

The cost is = order cost + cost of all unit ordered + average holding cost

C=K+cQ+(ThQ)/2

we divided all over time to be per unit time

so the average cost is :

G= (K+cQ)/T + (hQ/2)

replace T=Q/landa

G= ((K+cQ) / (Q/landa)) + (Qh/2)

then by manipulating

G= ((K* landa )/Q) + ( landa* c)+ (hQ/2)

this formula represent period setup cost , period purchases cost and period holding cost respectively.

because we want to find the minimize this formula gives we need to take the derivative -using calculus- to respect of Q:

G' = (- k *landa / Q^2) + h/2 - give min and max -

taking 2nd derivative

G'' = (2*k*landa)/Q^3

for Q>0 => G''>0 => G' is the min

having G' = 0

G' = (- k *landa / Q^2) + h/2 = 0

( k *landa / Q^2) = h/2

=> Q^2= (2*k*landa)/h

by taking square root of both sides

Q# (EOQ)= sqrt [(2*k*landa)/h]