Formula Sheet: Inventory Control | Industrial Engineering - Mechanical Engineering PDF Download

 Page 1


F ormula Sheet: Inventory Control
Introduction to Inventory Control
• Definition : Inventory control involves managing stock levels to minimize
costs while meeting demand, optimizing ordering, holding, and shortage
costs.
• K ey Costs :
– Ordering Cost (C
o
): Cost per order (e.g., setup, paperwork).
– Holding Cost (C
h
): Cost per unit per time (e.g., stor age, insur ance).
– Shortage Cost (C
s
): Cost due to stock outs (e.g., lost sales).
– Purchase Cost (C
p
): Cost per unit of inventory .
Economic Order Quantity (EOQ)
• EOQ F ormula (Basic Model) :
Q
*
=
r
2DC
o
C
h
whereQ
*
= optimal order quantity ,D = annual demand,C
o
= ordering cost
per order ,C
h
= holding cost per unit per year .
• T otal Invent ory Cost (TIC) :
TIC =
DC
o
Q
+
QC
h
2
+DC
p
whereQ = order quantity ,C
p
= purchase cost per unit.
• Optimal O rder Cycle Time :
T
*
=
Q
*
D
• Number o f Orders per Y ear :
N =
D
Q
*
EOQ with Quantity Discounts
• T otal Cost with Discounts :
TIC =DC
p
(Q)+
DC
o
Q
+
QC
h
2
whereC
p
(Q) = unit cost depending on order size (discount applied).
• Procedure : Calculate Q
*
for each price break, evaluate TIC, and select Q
with minimum cos t.
1
Page 2


F ormula Sheet: Inventory Control
Introduction to Inventory Control
• Definition : Inventory control involves managing stock levels to minimize
costs while meeting demand, optimizing ordering, holding, and shortage
costs.
• K ey Costs :
– Ordering Cost (C
o
): Cost per order (e.g., setup, paperwork).
– Holding Cost (C
h
): Cost per unit per time (e.g., stor age, insur ance).
– Shortage Cost (C
s
): Cost due to stock outs (e.g., lost sales).
– Purchase Cost (C
p
): Cost per unit of inventory .
Economic Order Quantity (EOQ)
• EOQ F ormula (Basic Model) :
Q
*
=
r
2DC
o
C
h
whereQ
*
= optimal order quantity ,D = annual demand,C
o
= ordering cost
per order ,C
h
= holding cost per unit per year .
• T otal Invent ory Cost (TIC) :
TIC =
DC
o
Q
+
QC
h
2
+DC
p
whereQ = order quantity ,C
p
= purchase cost per unit.
• Optimal O rder Cycle Time :
T
*
=
Q
*
D
• Number o f Orders per Y ear :
N =
D
Q
*
EOQ with Quantity Discounts
• T otal Cost with Discounts :
TIC =DC
p
(Q)+
DC
o
Q
+
QC
h
2
whereC
p
(Q) = unit cost depending on order size (discount applied).
• Procedure : Calculate Q
*
for each price break, evaluate TIC, and select Q
with minimum cos t.
1
Reorder Point (R OP) and Safety Stock
• Reorder P oint (Constant Demand, No Lead Time V ariability) :
R OP =d·L
whered = demand r ate (units/time),L = lead time.
• Reorder P oint with Safety Stock :
R OP =d·L+SS
whereSS = safety stock.
• Safety St ock :
SS =z·s
L
where z = safety factor (z-score for desired service level), s
L
= standard
deviation of deman d during lead time.
• F or V ariable Demand:
s
L
=
q
L·s
2
d
wheres
d
= standard deviation of daily/weekly demand.
Inventory Models
• Production Order Quantity (POQ) :
Q
*
=
v
u
u
t
2DC
o
C
h

1-
d
p

wherep = production r ate,d = demand r ate.
• Economic P roduction Lot Size :
TIC =
DC
o
Q
+
QC
h
2

1-
d
p

+DC
p
• Periodic Re view S ystem :
Order Quantity =T ·d+SS-I
whereT = review period,I = current inventory level.
ABC Analysis
• Classification :
– A Items: High value, low quantity ( 10-20
– B Items: Moder ate value and quantity ( 20-30
– C Items: Low value, high quantity ( 50-60
• Annual Usag e V alue :
V alue = Unit Cost× Annual Demand
2
Page 3


F ormula Sheet: Inventory Control
Introduction to Inventory Control
• Definition : Inventory control involves managing stock levels to minimize
costs while meeting demand, optimizing ordering, holding, and shortage
costs.
• K ey Costs :
– Ordering Cost (C
o
): Cost per order (e.g., setup, paperwork).
– Holding Cost (C
h
): Cost per unit per time (e.g., stor age, insur ance).
– Shortage Cost (C
s
): Cost due to stock outs (e.g., lost sales).
– Purchase Cost (C
p
): Cost per unit of inventory .
Economic Order Quantity (EOQ)
• EOQ F ormula (Basic Model) :
Q
*
=
r
2DC
o
C
h
whereQ
*
= optimal order quantity ,D = annual demand,C
o
= ordering cost
per order ,C
h
= holding cost per unit per year .
• T otal Invent ory Cost (TIC) :
TIC =
DC
o
Q
+
QC
h
2
+DC
p
whereQ = order quantity ,C
p
= purchase cost per unit.
• Optimal O rder Cycle Time :
T
*
=
Q
*
D
• Number o f Orders per Y ear :
N =
D
Q
*
EOQ with Quantity Discounts
• T otal Cost with Discounts :
TIC =DC
p
(Q)+
DC
o
Q
+
QC
h
2
whereC
p
(Q) = unit cost depending on order size (discount applied).
• Procedure : Calculate Q
*
for each price break, evaluate TIC, and select Q
with minimum cos t.
1
Reorder Point (R OP) and Safety Stock
• Reorder P oint (Constant Demand, No Lead Time V ariability) :
R OP =d·L
whered = demand r ate (units/time),L = lead time.
• Reorder P oint with Safety Stock :
R OP =d·L+SS
whereSS = safety stock.
• Safety St ock :
SS =z·s
L
where z = safety factor (z-score for desired service level), s
L
= standard
deviation of deman d during lead time.
• F or V ariable Demand:
s
L
=
q
L·s
2
d
wheres
d
= standard deviation of daily/weekly demand.
Inventory Models
• Production Order Quantity (POQ) :
Q
*
=
v
u
u
t
2DC
o
C
h

1-
d
p

wherep = production r ate,d = demand r ate.
• Economic P roduction Lot Size :
TIC =
DC
o
Q
+
QC
h
2

1-
d
p

+DC
p
• Periodic Re view S ystem :
Order Quantity =T ·d+SS-I
whereT = review period,I = current inventory level.
ABC Analysis
• Classification :
– A Items: High value, low quantity ( 10-20
– B Items: Moder ate value and quantity ( 20-30
– C Items: Low value, high quantity ( 50-60
• Annual Usag e V alue :
V alue = Unit Cost× Annual Demand
2
Applications
• Used in supp ly chain management to optimize inventory levels.
• Helps minim ize costs while ensuring availability for production or sales.
• Critical for GA TE problems on EOQ , reorder points, and inventory models.
3