Chapter 6
Inventory Control Models
Types of Inventory
2
Uses of Inventory
 As
a buffer to decouple
suppliers and users,
– manufacturers and customers,
– two workstations in a workshop.
–
3
Costs Related to Inventory
 Carrying
(holding) cost
 Ordering cost
 Stockout cost
 Purchase (material) cost
4
Carrying Cost
 Includes:
–
–
–
–
–
Capital cost
Opportunity costs,
Storage space rental, and labor and
facilities for storage,
Cost of obsolescence and damage,
Insurance.
 Varies
with the amount of inventory.
5
Ordering Cost

Includes:
–
–

Shipping and handling cost,
Cost of processing orders, such as forms,
papers, labor.
Typically, this cost varies with number of
orders, not with number of units in an order.
6
Stockout Cost
 Includes:
–
–
–
Lost profit,
Expediting and back ordering expenses,
Cost of reputation and goodwill
7
Inventory Profile
8
Average Inventory
 Inventory
level changes everyday.
 Average inventory is often used to
measure inventory level
 Average daily inventory level
number of units in an order Q


2
2
9
Some Basic Calculations (1 of 2)
D=annual demand in units
Co=ordering cost per order
Ch=carrying cost per unit per year
Q=order quantity = number of units in an order.

Number of orders required in a year
annualdemand in units
D


number of unitsin an order Q
10
Some Basic Calculations (2 of 2)
 Total
annual holding cost
Q
= Ch
2
D
 Total annual ordering cost  Co
Q
 Total
annual inventory cost
Q
D

C h  Co
2
Q
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Economic Order Quantity
(EOQ)
 EOQ
is the order quantity at which the
total annual cost (annual holding cost +
annual ordering cost) is minimized.
12
EOQ Total Costs
Total annual costs
= annual ordering costs + annual holding costs
13
Formula for EOQ
Let Q* be Economical Order Quantity (EOQ):
2 DCo
Q* 
Ch
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Simco Pump Example (p.197)
Annual demand = 1,000 units
 Ordering cost = $10 / order
 Annual holding cost = $0.5 / unit


What is the best order quantity?
15
Simco Pump Example (p.197)
With order quantity Q*=200 units,
(a) How many orders would be made
annually?
(b) What is the total annual ordering cost?
(c) What is the average daily inventory?
(d) What is total annual holding cost?
(e) What is the total annual inventory cost?
16
Simco Pump Example (p.197)
We have found the EOQ is 200 units per
order, and the associated total annual
inventory cost is $100.
 If the company orders 250 units each
time, what is total inventory cost then?
 If the company orders 100 units each
time, what is total inventory cost then?
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Purchase Cost, C
Purchase cost, C, of inventory items is not
in the EOQ formula, since the order
quantity Q does not affect the annual
purchase cost, DC. That is, C is not
relevant in determining the order quantity.
 Sometime, unit carrying cost is a percent, I,
of the purchase cost of the item, i.e., Ch=IC.

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Reorder Point
 Reorder
point is in terms of number of
units on hand, at which an order should
be placed.
 Reorder point must be at least the
demand during the lead time (delivery
time).
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Safety Stock
 Safety
stock is the extra stock to help
in avoiding stockout, when there exist
uncertainties in demand and lead time.
20
Safety Stock and Uncertainties
21
Formula for Reorder Point
 Reorder
Point
= dL + SS
where
d = average daily demand in units
L = lead time in days
SS = safety stock in units
22
Example (p.201 extended)
 Procomp’s
annual demand is 8,000
units. There are 200 work days per
year. So, daily demand is 40 units.
 Lead time = 3 days
 Safety stock = 20 units
 What is the reorder point (ROP)?
23
How Does EOQ Work in
Inventory Control?
 For
each item k, calculate its economic
order quantity Qk* and its reorder point
ROPk.
 Keep watching the inventory on hand.
If the stock of item k drops to ROPk,
order Qk* units of item k.
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EOQ Assumptions (p.193)
 Demand
rate is constant.
 The ordered units are delivered in a
single shipment (instantaneous).
 No quantity discount is available
 All demand is satisfied (no shortages)
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EOQ without Instantaneous
Receipt Assumption (p.201)
The ordered units arrive piece by piece.
 Application example:

–
A company's finished good inventory that is
supplied by its production department.
It is called Production Run Model
 The best order quantity is called Optimal
Production Quantity (OPQ).

26
OPQ Formula
d = daily demand in units,
p = daily production capacity in units,
Cs = setup cost (similar to Co)
D and Ch are defined same as before,
then
2 DC
Q 
*
s
d
Ch (1  )
p
27
Meaning of Q* in OPQ:
 Q*
here is still the “order quantity”
(number of units in an order), but
the order is issued to the production
department of the same company.
 Therefore, Q* can also be
understood as the production batch
size.
28
Formulas in Production Run Model

Maximum Inventory Level
d
 Q (1  )
p

Average Inventory Level
Q
d
 (1  )
2
p
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Formulas in Production Run Model
D
Cs
 Total annual ordering cost =
Q
(same as for EOQ)
Q
d
 Total annual holding cost  (1 ) Ch
2
p
 Total annual inventory cost
D
Q
d
 Cs  (1 ) C h
Q
2
p
30
Example of Brown Manuf. (p.203)
Annual demand = 10,000 units;
Setup (ordering) cost = $100/order
Carrying cost = $0.50/unit/year
Daily production rate = 80 units
Daily demand rate = 60 units.
Once a unit is finished, it is counted into the
inventory.
31
To Find EOQ under Quantity
Discount (p.206 – 209)
 Trial-and-error
method in general
 May develop a spreadsheet that
calculate the total cost for each
possible order quantity. Then, pick up
the order quantity with the lowest total
cost. (See class demonstration)
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