Chapter 13 - Inventory Management
Inventory - stock or store of goods
Type of Inventories
1. Raw Materials (RM) and purchased parts
2. Partially completed goods (WIP)
3. Finished goods inventory (FG)
4. Replacement parts, tools, supplies
5. Goods in transit to warehouse or customer
* A typical firm has about 30% of its current assets and as much as 90% of its working capital invested in
inventory.
Assume your company manufactures and sells Snickers candy bars. List all items you have in inventory.
____________
____________
_____________
____________
____________
____________
____________
____________
Estimate the total dollar value of your inventory ($_______________) on any given day, if you produce
250,000 candy bars per day.
What happens to production AND sales if you don=t have the inventory you need?
Imagine what your production process looks like. Imagine where the WIP inventory is located. Imagine the
WIP inventory replaced with $ representing the total dollar value of the inventory.
How important is good inventory management? Good inventory management is essential to the success of the
organization because (1) the amount of $ inventory represents, and (2) the impact on daily operations.
Independent vs. Dependent Demand
Dependent demand: inventory items that are components of FG. Demand is derived from # of desired Fgs.
Independent demand: FGs. How do we estimate the demand for FG? Hint (chapter 3)
Functions of Inventory
(1) to meet anticipated customer demand.
FG: Aanticipation stocks@
(2) to smooth production requirements
FG: Aseasonal inventories@
(3) to decouple operations, we use buffers of inventory between successive operations to maintain continuity
of production.
WIP. (JIT philosophy argues strongly against using WIP this way. WHY?)
(4) to protect against stockouts
FG and RM: Asafety stock@
(5) to take advantage of order cycles. This is when we buy quantities of inventory that exceed our need to
minimize purchasing costs and inventory costs. Example: shopping at Sams
(6) to hedge against price increases
RM
(7) to permit operations
WIP
Inadequate control of inventory results in
(1) understocked items, and/or
(2) overstocked items
Problems with understocking. Understocking inventory results in :
1.
2.
Problems with overstocking. Overstocking inventory causes problems with:
1.
2.
Inventory Management attempts to balance the issues.....to have enough inventory on hand to satisfy the
customer, while minimizing inventory so as not to unnecessarily use $ or space. To balance these issues we
make decisions (1) regarding the timing of orders (when) - Reorder Point decisions
(2) regarding the size of orders (how much) - Economic Order Quantity decisions (EOQ)
To make these inventory decisions effectively, we must have
(1) a system to track inventory
(A) periodic systems - physical count
(B) perpetual systems - continual system, usually on-line. E.g. scanning UPC codes
1. Advantages: real time totals of inventory
2. Disadvantages: expensive and you still need a periodic system. Why?
(2) forecast of demand - must have reliable estimates of amount and time of demand.
(3) knowledge of lead times - time interval between ordering and receiving the order.
(4) estimates of holding costs, ordering costs, and shortage costs
(A) Holding costs - how much does it cost to store inventory? Costs include interest, insurance, taxes,
obsolescence, deterioration, spoilage, heat, light, security, and opportunity costs for not being able to spend $
elsewhere.
- stated as either a % of unit price or as $/unit price.
- typical annual holding costs range from 20-40%.
- If our Snickers Bar costs $1, holding cost, can then range from $____ to $______.
- If we warehouse 200,000 bars, holding cost would be ______________.
- If we warehouse 1,000,000 bars, holding cost would be __________________.
(B) ordering costs - cost of ordering and receiving inventory. Includes preparing invoices, shipping
costs, inspection costs.
(C) shortage costs - costs that result when we fail to meet demand, including the cost of NOT making a
sale, loss of customer good will, etc.
(5) classification systems - we need to classify inventory on the basis of relative importance. The ABC
approach classifies inventory according to annual dollar usage (dollar value/unit * annual usage rate).
A items:
very important items
60-70% of dollar usage
approx. 15-20% of # of items
B items:
moderately important items
C items:
least important items
10% of dollar usage
approx. 60% of number of items
Therefore, A items should receive close attention through frequent reviews and control. C items can be more
loosely controlled.
Work Problem 1, page 602/362
The manager of an automobile repair shop hopes to achieve an improved allocation of inventory, by adopting
an ABC approach. Given the following inventory data, classify the items as ABC according to dollar usage.
Item
Usage
Unit cost
4021
50
$1,400.00
9402
300
12.00
4066
40
700.00
6500
150
20.00
9280
10
1,020.00
4050
80
140.00
6850
2000
15.00
3010
400
20.00
4400
7000
5.00
TOTALS
Usage (% of totals)
A: ____________________% of total items
B: ____________________% of total items
C: ____________________% of total items
Annual $ value
(usage * unit cost)
Classification
A, B, or C
Annual Dollar Value (% of totals)
A: ____________________% of total dollars
B: ____________________% of total dollars
C: ____________________% of total dollars
Which categories need tighter inventory controls? Why?
EOQ and ROP Models
1. How much to order? Economic Order Quantity Models (EOQ)
(a) Basic EOQ
(b) EOQ with quantity discounts
2. When to order? Reorder Point Models (ROP)
(a) ROP with demand and lead time constant
(b) ROP with safety stock
(c) ROP with service level (risk)
1. How much to order? Economic Order Quantity Models (EOQ)
(a) Basic EOQ
EOQ Models identify optimal order quantity by minimizing the sum of certain annual costs that vary with
order size. The Basic EOQ model is used to identify the order size that will minimize the sum of the annual
costs of holding inventory and ordering inventory.
Assumptions:
(1) only one product is involved
(2) annual demand requirements are known
(3) demand is spread evenly, i.e., the demand rate is reasonably constant
(4) lead time does not vary
(5) each order is received in a single delivery
(6) no quantity discounts are given
The optimal order quantity reflects a trade-off between carrying costs and ordering costs.
Large Order - lower ordering cost, but higher carrying cost. WHY?
Small Order - higher ordering cost, but lower carrying cost. WHY?
An ideal solution is an order size that is neither too large (increased carrying cost) or too small (increased
ordering cost).
Annual Carrying Cost = Q/2(H)
Q=order quantity in units
H=holding(carrying)cost/unit
TC= annual carrying cost
Q/2(H)
Annual Ordering Cost = D/Q (S)
D=demand (Units/year)
S=ordering cost
+
+
annual ordering cost
D/Q (S)
EOQ = square root of 2DS
H
Length of order cycle = EOQ
D
D=demand (units/yr)
S=ordering cost
H=holding(carrying) cost
EXAMPLE
A local distributor sells 9600 tires per year. Annual carrying costs are $16 per tire and ordering costs is $75
per order. The store operates 288 days a year.
D=9,600 tires
H=$16/tire
S= $75
(a) what is EOQ?
EOQ = square root of
2DS
H
(b) how many times per year does the store order?
D =
EOQ
(c) what is length of order cycle?
Length of order cycle = EOQ
D
(d) what is total annual cost if EOQ quantity is ordered?
TC= annual carrying cost
Q/2(H)
TC=
+
+
annual ordering cost
D/Q (S)
*Note that TC for the EOQ is where carrying cost = ordering cost. WHY?
Now, try your hand at an EOQ problem. For homework :
A bakery buys flour in 25 lb bags. They use 4,860 bags per year on average. Ordering costs are $4 per order
and carrying costs are $30 per bag.
(a) determine EOQ
EOQ = square root of 2DS
H
D=demand (units/yr)
S=ordering cost
H=holding(carrying) cost
(b) Average number of bags on hand?
(c) how many orders will there be?
Length of order cycle = EOQ
D
(d) total cost of carrying and ordering
TC= annual carrying cost
Q/2(H)
TC=
+
annual ordering cost
D/Q (S)
+
(e) If annual ordering cost were to increase by $1/order, how much would that affect the minimum total
annual cost?
S=$5
D=4860
H=$30
1. How much to order? Economic Order Quantity Models (EOQ)
(b) EOQ with quantity discounts
Quantity discounts are price reductions for large orders offered to customers to induce them to buy in large
quantities (like shopping at SAM=s). If customer discounts are offered, the customer must weigh the
potential benefits of reduced purchase price and fewer orders (because we will buy in large quantities) against
the increase in carrying cost caused by higher average inventories.
Goal of buyer: select and order quantity that will minimize total cost, where
TC= Q/2 (H)
+
H= holding cost
S= ordering cost
P= price per unit
D= annual demand
D/Q (S)
+
P(D)
Procedure for EOQ with quantity discount:
(1) Compute the common EOQ.
(2) Only one unit price will have the feasible EOQ included. Identify that range.
A. if EOQ is in the lowest price range, that is EOQ.
B. if EOQ is in any other range, compute the total cost for EOQ and the TC for all lower price breaks.
Compare total costs. Select EOQ that yields lowest TC.
EXAMPLE:
The maintenance department at a mall uses about 816 cases of cleanser per year. Ordering costs are $12 and
carrying costs are $4 per case. Pricing is:
Discounts:
1-49
50-79
80-99
100-over
$20/case
$18
$17
$16
D= 816 cases
S= $12
H= $4
What is EOQ and TC?
(1) compute common EOQ.
EOQ =
Square root of 2DS
H
(2) What price range does EOQ fall in? ___________________
a. is this the lowest price range? __________________
b. compute TC for EOQ and other lower price ranges.
TC= Q/2 (H)
+
H= holding cost
S= ordering cost
P= price per unit
D= annual demand
EOQ TC =
TC for 80 cases =
D/Q (S)
+
P(D)
TC for 100 cases =
Which TC is lower? So what is my best EOQ? _______________________________
Now, you try one on your own, for homework. Problem:
A catalogue retailer uses 18,000 boxes per year. Holding costs are $.20 per box and ordering
costs are $32. Pricing is as follows:
1,000-1,999 boxes
2,000-4,999
5,000-9,999
10,000 or more
$1.25 per box
$1.20
$1.18
$1.15
(a) Determine EOQ
TC= Q/2 (H)
+
H= holding cost
S= ordering cost
P= price per unit
D= annual demand
D/Q (S)
+
P(D)
Is EOQ in the lowest price range? If not, computer TC for other lower ranges. What is lowest TC and order
quantity? _______________________________
(b) number of orders/year?
2. When to order? Reorder Point Models (ROP)
(a) ROP with demand and lead time constant
(b) ROP with safety stock
(c) ROP with service level (risk)
EOQ tells us how much to order and the number of orders, BUT, not WHEN to order. ROP models tell us
WHEN to order. The ROP occurs when inventory on hand drops to a predetermined amount. ROP requires
a perpetual inventory.
Determinants of ROP quantity:
1. Rate of demand
2. Lead time
3. Demand and/or lead time variability
4. Degree of stockout risk acceptable
If demand and lead time are constant:
ROP = d x LT
d=demand rate (units/ some period of time)
LT= lead time in days or weeks.
If you use 15 ink cartridges/week, and it takes 2 weeks to get a new shipment, when should you re-order?
ROP = d x LT
d= 15/wk
LT=2 weeks
ROP = _________________________________
When variability is present in demand or LT.
When variability is present in demand or LT, variance creates RISK that demand will exceed expected
demand, leaving us with not enough materials on hand. To reduce the risk of running out of inventory, we
sometimes carry excess inventory called SAFETY STOCK. ROP then increases by the amount of desired
safety stock.
ROP = expected demand during LT
+
Safety stock
safety stock = 10 ink cartridges
d= 15/wk
LT = 2 weeks
ROP = ( d x LT)
+
SS
ROP = ___________________________
Service Level and Risk
Our customer service level increases and risk of stockout decreases. WHY? The order cycle service level is
the probability that demand will not exceed supply during LT. A service level of 97% implies a 97%
probability that demand will NOT exceed supply during LT. Alternatively a service level of 97% implies a
RISK of 3%. The amount of safety stock that is appropriate then depends on:
a. average demand rate and average LT
b. demand and LT variability
c. desired service level
ROP = expected demand during lead time
+
Z
z= standard deviate (number of standard deviations)
= standard deviation of lead time demand
Value of z depends on the stock-out RISK you are willing to accept. Generally, the smaller the risk, the
greater the value of z. WHY? Use appendix B or the back inside cover of your book to obtain values of z for
a given service level.
EXAMPLE:
Demand for sand at a local construction company is 50 tons during lead time. Demand during lead time is
normally distributed with a mean of 50 tons and a standard deviations of 5 tons. The manger is wants a
stockout risk of no more than 3%
demand during LT = 50 tons
 = 5 tons
stock out risk = 3%
(a) what value of z represents 3% stock our risk? (See Appendix B, page 881).....you want 97% of the area
under the normal curve)
for .9699 (really close to 97%), the z value = 1.88
(b) how much safety stock would be held?
SS = z 
SS = 1.88 (5 tons)
SS = ______________
(c) What is ROP?
ROP = expected demand during lead time
+
Z
ROP =
Homework:
Expected demand during LT = 300 units
= 30 units
(a) what is ROP with stockout risk of 1%?
Z for an area under the normal curve of 99% = ____________________
ROP = expected demand during lead time
ROP =
(b) safety stock at 1% risk?
SS =
Z
SS = ____________________
+
Z
(c) would a 2% stockout risk require more or less SS? WHY?
Would ROP be larger or smaller? WHY?