Chapter 11. Order Point Inventory Control Methods
Homework problems: 1, 2, 3, 5.
Order Point Inventory Control Methods
Order point methods are used to determine
appropriate order quantities and timing for
individual independent-demand product items
that are characterized by random customer
Performed well, these inventory management
functions can provide appropriate levels of
customer service without excess levels of
inventory and/or cost.
1. Basic Concepts
Independent Demand
When item’s demand is influenced by market conditions and is
not related to (i.e., is “independent” of) production decision for
any other item.
Wholesale and retail merchandise (finished goods), service
industry inventory, end-item and replacement-part inventories,
spare-parts, MRO (maintenance, repair, and operating)
Demand must be forecast
Dependent Demand
When item’s demand derives from (i.e., “depend” on) the
production decisions for its parents.
All intermediate and purchased items in manufacturing.
Demand must be derived.
Functions of the 4 Types of Inventory
Cycle Stock/Inventory
Created when we place orders LESS frequently.
The longer the cycle, the bigger the Q (order quantity).
Helps with customer service, ordering cost, setups,
transportation rates, and material costs.
Equal to Q/2, when demand rate is constant and uniform.
Safety Stock/Inventory
Created when we place an order sooner than when it is
needed, or more than the expected demand during lead time. .
Protects against three types of uncertainty: demand, lead time,
and supply.
Helps with customer service and missing parts.
Functions of Inventory
Anticipation Stock/Inventory
Created by overproducing during the slack season or
overbuying before a price increase or capacity shortage.
Helps absorb uneven rates of demand and supply.
Pipeline (transit) Stock/Inventory
Created by the time spent to move and produce materials.
Can be in any of three stages:
 Inbound, within the plant, outbound
Equal to d x L, where,
 d: avg. demand per period
 L: the # of periods in the lead time to move between two
Functions of Inventory Example
Management has decided to establish three distribution centers
(DCs) in different region of the country to save on transportation
costs. For one of the products, the average weekly demand at
each DC will be 50 units. The product is valued at $650 per unit.
Average shipment sizes into each DC will be 350 units per trip.
The average lead time will be two weeks. Each DC will carry one
week’s supply as safety stock, since the demand during the lead
time sometimes exceed its average of 100 units (50x2).
Anticipation inventory should be negligible.
How many dollars of cycle inventory will be held at each DC, on
the average?
How many dollars of safety stock will be held at each DC?
How many dollars of pipeline inventory will be in transit for each
DC, on the average?
How much inventory, on the average, will be held at each DC?
Which type of inventory is your first candidate for reduction?
Functions of Inventory Example
Cycle Inventory = (350/2)($650)=$113,750.
Safety stock = (1)(50)($650)=$32,500.
Pipeline inventory = (2)(50)($650)= $65,000
Inventory at DC = cycle + safety + pipeline =
Cycle inventory
Inventory Reduction
Primary Lever
Reduce Q
Reduce ordering and setup
Place orders closer
to the time when
they must be received
Improve forecasting.
Reduce lead time.
Reduce uncertainty.
Vary production rate
to follow demand rate
Level out demand rates.
Cut productiondistribution lead time
Forward inventory positioning.
Selection of suppliers and
Reduce Q.
Where are the Inventories?
Inventories are held in: manufacturing
(36%), retail trade (25%), wholesales
trade (23%), farm (8%), other (8%).
Inventory Total:
3.6 monthly sales in 1970s
3.1 monthly sales in 1980s
2.7 monthly sales in 1990s (> $1 trillion)
2. Management Issues – Two Fundamental
Inventory Questions/Decisions
1. How Much?
2. When?
See. Figure 11.2 for models
Inventory System Performance
Inventory Measures
Start with physical count in units, volume, or weight.
Average aggregate inventory value (total value of
all items held in inventory)
Weeks of Supply. Divide average aggregate
inventory value by weekly sales (at cost, i.e., cost of
goods sold) of finished goods.
Inventory Turnover (turns). Divide annual sales
(at cost, i.e., cost of goods sold) by average
aggregate inventory value.
Fill Rate. The % of units immediately available
when requested by customers, measuring
customer service level.
Inventory System Performance Example
 A recent accounting statement showed average
aggregate inventories (RM+WIP+FG) to be
$6,821,000. This year’s cost of goods sold is $19.2
million. The company operates 52 weeks per year.
How many weeks of supply are being held? What is
the inventory turnover?
Weeks of supply= ($6,821,000)/($19,200,000)/52=18.5 weeks.
Inventory turnover= ($19,200,000)/($6,821,000)= 2.8 turns.
Inventory Costs =
Ordering costs: physical counting, paperwork, fax/phone,
receipt verification, etc. e.g., $95/order vs.
+Holding/carrying costs: cost of capital (5~35%), taxes,
insurance, obsolescence, warehousing, etc.
Typically annual holding costs = 20~40%.
+Stockout/shortage costs: back order, lost sales, lost
goodwill. Customer service level ↔
inventory investment
+ Cost of items
Five Assumptions of EOQ
Demand is known and constant
Whole lots ordering
Only two relevant costs
Item independence
Certainty in lead time and supply
Economic Order Quantity (EOQ)
A: annual demand
Q: order quantity
CP: ordering (preparation) cost per order
CH: carrying cost per unit per year
Annual inventory carrying cost= (Q/2)·CH
Annual ordering cost= (A/Q) ·CP
Total annual cost (TAC) = (A/Q)·CP + (Q/2)·CH
Finding the optimal order quantity that minimizes TAC using
Observation (Fig 11.4)
Economic time between order (TBO) in weeks = EOQ/(A/52)
EOQ Sensitivity
What happens to cycle inventory if the demand rate
What happens to lot sizes if setup/ordering cost
What happens to lot size if interest rates drop?
How critical are errors in estimating A, CP, CH ?
Overestimate A by 300% → overestimate EOQ by 100%
Total cost curve is relatively “flat” around the minimum cost
ordering quantity, implying total cost performance is
relatively insensitive to small changes in order quality around
the optimal order quantity.
EOQ is robust.
When setup cost → 0, EOQ → small → small lot production
in JIT.
Reorder Timing Decisions
Under the (Q,R) rule, an order for a fixed quantity (Q)
is placed whenever the stock level reaches a reorder
point (R).
Reorder point = average demand during the average
replenishment lead time + safety stock.
R= d + S
Reorder point is influenced by demand, lead time,
demand uncertainty, and lead time uncertainty.
When both demand and lead time are constant,
reorder point = expected demand during lead time,
and no safety stock is needed.
Reorder Point Decisions:
Discrete Distribution of Demand during Lead Time
Safety Stock can be determined using (1) stockout risk or
probability or (2) customer service level (fill rate).
Stockout Risk: the probability of not meeting demand
during ANY given replenishment order cycle.
e.g., 5% stockout; See Figure 11.5.
Fill Rate (Customer Service Level): the % of demand,
measured in units, that can be supplied directly
out of inventory. See Fig. 11.7
Normal Distribution provides a close approximation to a
given discrete distribution, facilitating and simplifying the
reorder point (and thus safety stock) calculations.
Reorder point and Stockout Probability
Reorder point of 7
units will provide
5% chance of
stockout during a
one day lead time
With a lead time
of one day, 95%
of cycles will
demand for 7 or
fewer units
Sum of demand
probability is 0.05 (5%)
Introducing Safety Stock for variable demand
Lead time=
1 day
During the replenishment lead time (1 day), demand can range from 1 through 9 units.
If demand during lead time is less than 5 units, inventory reaches a point between b and c.
If demand during the 1 day lead time exceeds 5 units, inventory level
reaches a point between c and e.
Fig. 7 Determining safety stock for specified service levels
Know how
to construct
this table
* Calculated by
d Max
 P(d )( d  R )
ⱡ Assuming order quantity (Q) is 5 units; annual demand=1,250
d  R 1
P(d) = probability of a demand of d units during the replenishment lead time
dMax = maximum demand during the replenishment lead time
SL  100 (100/ Q )
d Max
 P(d )(d  R)
d  R 1
Reorder Point Decisions:
Continuous Distribution of Demand during Lead Time
Note. Service level is
defined differently with
continuous demand.
The ROP based on a Normal
distribution of lead time demand
Reorder Point Decisions:
Continuous Distribution of Demand during Lead Time
Reorder Point Decisions:
Continuous Distribution of Demand during Lead Time
Probability of Stocking Out Criterion
Constant demand and variable lead time
R= d x LT + Z·d·σLT
Variable demand and constant lead time
R= d x LT + Z· √LT · σd
(cf. equation 11.18)
Variable demand and variable lead time
R= d x LT + Z·√LT· σd2 + d 2 · σ2LT
(cf. equation 11.20)
Where d= average daily or weekly demand,
σd = standard deviation of demand per day or week,
σLT = standard deviation of lead time per day or week
Reorder Point Decisions: Continuous Demand Example
The injection molding department of a company uses 40 ponds of a
powder a day. Inventory is reordered when the amount on hand is
240 pounds. Lead time averages 5 days. It is normally distributed
and has a standard deviation of 2 days.
a). What is the probability of a stockout during lead time?
b). What reorder point would provide a 5% stockout?
Reorder Point Decisions
Note that while discrete demand distributions (e.g.,
Figure 11.5) can be approximated by the continuous
Normal distribution for reorder point decisions (e.g.,
discussions in the section of Continuous Distribution on
page 433 and Customer Service Criterion on page 435),
the results won’t be optimal.
Thus, when demand is discrete, equation 11.8 should
be used. When demand is continuous, the formulas on
slide 21 should be used.
The difference between dependent and independent
demand must serve as the first basis for determining
appropriate inventory management procedures.
Organizational criteria must be clearly established
before we set safety stock levels and measure
Savings in inventory-related costs can be achieved by a
joint determination of the order point and order quantity
The functions of inventory are useful principles to apply
in determining whether or not inventory reductions can
be made.
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