Model
Formula
2DS
H
EOQ = Q* =
1. Basic EOQ
Q* = Economic order quantity
Q
D
H+ S
2
Q
TC =
Number of Orders =
Symbols
D = Annual demand
D
Q*
S = Ordering cost per order
H = Annual holing cost per unit
Q*
Length of order cycle =
D
2DS
p
H p−d
Q* =
Q* = Optimal run or order quantity
p = production rate
I
D
TC = max H + S
2
Q
2. Economic production quantity (EPQ)
Cycle length =
Run length =
3. Quantity discounts
Q
d
d = Usage or demand rate
Imax = Maximum inventory level
Q
p
I max =
Q
(p − d)
p
TC =
Q
D
H + S + RD
2
Q
⎛ H ⎞
Qb = Q ⎜
⎝ H + B ⎟⎠
4. Planned shortage
R = Unit price
Qb = Quantity backordered in an order cycle
B = Annual backorder cost per unit
2DS ⎛ H + B ⎞
Q=
H ⎜⎝ B ⎟⎠
5. Reorder point under:
ROP = Quantity on hand at reorder point
a.
Constant demand and lead time
ROP = d × LT
b.
Variable demand rate
ROP = d × LT + z × LT × δ d
c.
Variable lead time
ROP = d × LT + z × d × δ LT
d.
Variable lead time and demand
2
ROP = d × LT + z LT × δ d2 + d 2 × δ LT
d = Demand rate
LT = Lead time
d = Average demand rate
δ d = Standard deviation of demand rate
z = Standard Normal deviate
LT = Average lead time
δ LT = Standard deviation of lead time
Q = Imax – Amount on hand
OI = Order interval
I max = d × (OI + LT) + z × δ d × OI + LT
Imax = Maximum inventory (target level)
6. Fixed- order interval
7. Single period
SL =
Cs
Cs + C e
SL = Service level
Cs = Shortage cost per unit
Ce = Excess cost per unit
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