2. 2
Introduction
The objectives of inventory management are to provide the
required level of customer service and to reduce the sum of all costs
involved. To achieve these objectives, two basic questions must be
answered:
1. How much should be ordered at one time?
2. When should an order be placed?
Management must establish decision rules to answer these questions
so inventory management personnel know when to order and how
much. Lacking any better knowledge, decision rules are often made
based on what seems reasonable. Unfortunately, such rules do not
always produce the best results.
3. 3
Stock-Keeping Unit (SKU)
Control is exercised through individual items in a particular
inventory. These are called stock-keeping units (SKUs). Two white
shirts in the same inventory but of different sizes or styles would be
two different SKUs. The same shirt in two different inventories
would be two different SKUs.
Lot-Size Decision Rules
The eleventh edition of the APICS Dictionary defines a lot, or
batch, as “a quantity produced together and sharing the same
production costs and specifications.” Following are some common
decision rules for determining what lot size to order at one time.
4. 4
Lot-for-lot
The lot-for-lot rule says to order exactly what is needed – no
more – no less. The order quantity changes whenever
requirements change. This technique requires time-phased
information such as provided by a material requirements plan or
a master production schedule.
Since items are ordered only when needed, this system
creates no unused lot-size inventory. Because of this, it is the
best method for planning A items (see Chapter 9) and is also
used in a just-in-time environment.
5. 5
Fixed-order quantity
Fixed-order quantity rules specify the number of units to be
ordered each time an order is placed for an individual item or
SKU. The quantity is usually arbitrary, such as 200 units at a
time. The advantage to this type of rule is that it is easily
understood. The disadvantage is that it does not minimize the
costs involved.
A variation on the fixed-order quantity system is the min-
max system. In this system, an order is placed when the
quantity available falls below the order point (discussed in the
next chapter).
6. 6
Fixed-order quantity
The quantity ordered is the difference between the actual
quantity available at the time of order and the maximum.
For example, if the order point is 100 units, the maximum is 300
units, and the quantity actually available when the order is
placed is 75, the order quantity is 225 units. If the quantity
actually available is 80 units, an order for 220 units is placed.
One commonly used method of calculating the quantity to
order is the economic order quantity, which is discussed in the
next section.
7. 7
Order n periods supply
Rather than ordering a fixed quantity, inventory management can
order enough to satisfy future demand for a given period of time. The
question is how many periods should be covered? The answer is
given later in this chapter in the discussion on the period-order
quantity system.
Costs
As shown in Chapter 9, the cost of ordering and the cost of carrying
inventory both depend on the quantity ordered. Ideally, the ordering
decision rules used will minimize the sum of these two costs. The
best-known system is the economic-order quantity.
8. 8
ECONOMIC-ORDER QUANTITY (EOQ)
Assumptions
The assumptions on which the EOQ is based are as follows:
1. Demand is relatively constant and is known.
2. The item is produced or purchased in lots or batches and not
continuously.
3. Order preparation costs and inventory-carrying costs are
constant and known.
4. Replacement occurs all at once.
9. 9
ECONOMIC-ORDER QUANTITY (EOQ)
Assumptions
These assumptions are usually valid for finished goods whose demand
is independent and fairly uniform. However, there are many situations
where the assumptions are not valid and the EOQ concept is of no
use.
For instance, there is no reason to calculate the EOQ for made-to-order
items in which the customer specifies the order quantity, the shelf life
of the product is short, or the length of the run is limited by tool life
or raw material batch size.
In material requirements planning, the lot-for-lot decision rule is often
used, but there are also several rules used that are variations of the
economic-order quantity.
10. 10
EXAMPLE PROBLEM
The annual demand for an SKU is 10,075 units, and it is ordered in
quantities of 650 units. Calculate the average inventory and the
number of orders placed per year.
11. 11
Relevant costs. The relevant costs are as follows:
• Annual cost of placing orders.
• Annual cost of carrying inventory.
As the order quantity increases, the average inventory and the
annual cost of carrying inventory increase, but the number of
orders per year and the ordering cost decrease.
It is a bit like a seesaw where one cost can be reduced only at the
expense of increasing the other.
The trick is to find the particular order quantity in which the total
cost of carrying inventory and the cost of ordering will be a
minimum.
12. 12
Let,
A = annual usage in units
S = ordering cost in dollars per order
i = annual carrying cost rate as a decimal or a percentage
c = unit cost in dollars
Q = order quantity in units
Then,
Annual ordering cost = number of orders × costs per order
= A/Q × S
Annual carrying cost = average inventory × cost of carrying 1 unit for 1 year
= average inventory × unit cost × carrying cost
= Q/2 × c × i
Total annual costs = annual ordering costs + annual carrying costs
= A/Q × S + Q/2 × c × i
13. 13
EXAMPLE PROBLEM
The annual demand is 10,000 units, the ordering cost is $30 per order, the
carrying cost is 20%, and the unit cost is $15. The order quantity is 600 units.
Calculate:
a. Annual ordering cost
b. Annual carrying cost
c. Total annual cost
14. 14
Trial-and-Error Method
Consider the following example:
A hardware supply distributor carries boxes of 3-inch bolts in stock. The
annual usage is 1000 boxes, and demand is relatively constant throughout
the year. Ordering costs are $20 per order, and the cost of carrying inventory
is estimated to be 20%. The cost per unit is $5.
Figure 10.2 is a tabulation of the costs for different order quantities.
16. 16
Figures 10.2 and 10.3 show the following important facts:
1.There is an order quantity in which the sum of the
ordering costs and carrying costs is a minimum.
2.This EOQ occurs when the cost of ordering equals
the cost of carrying.
3.The total cost varies little for a wide range of lot
sizes about EOQ.
17. 17
Figures 10.2 and 10.3 show the following important facts:
The last point is important for two reasons:
First, it is usually difficult to determine accurately the cost
of carrying inventory and the cost of ordering. Since the
total cost is relatively flat around the EOQ, it is not critical
to have exact values. Good approximations are sufficient.
Second, parts are often ordered in convenient packages
such as pallet loads, cases, or dozens, and it is adequate to
pick the package quantity closest to the EOQ.
18. 18
Economic-Order Quantity Formula
The previous section showed that the EOQ occurred at an order
quantity in which the ordering costs equal the carrying costs. If these
two costs are equal, the following formula can be derived:
Carrying costs = ordering costs
19. 19
How to Reduce Lot Size
The EOQ formula has four variables. The EOQ will increase as the
annual demand (A) and the cost of ordering (S) increase, and it will
decrease as the cost of carrying inventory (i) and the unit cost (c)
increase.
The annual demand (A) is a condition of the marketplace and is
beyond the control of manufacturing. The cost of carrying inventory
(i) is determined by the product itself and the cost of money to the
company. As such, it is beyond the control of manufacturing.
The unit cost (c) is either the purchase cost of the SKU or the cost of
manufacturing the item. Ideally, both costs should be as low as possible.
In any event, as the unit cost decreases, the EOQ increases.
20. 20
How to Reduce Lot Size
The cost of ordering (S) is either the cost of placing a purchase
order or the cost of placing a manufacturing order. The cost of
placing a manufacturing order is made up from production
control costs and setup costs. Anything that can be done to
reduce these costs reduces the EOQ.
Just-in-time manufacturing emphasizes reduction of setup
time. There are several reasons why this is desirable, and the
reduction of order quantities is one. Chapter 15 discusses just-
in-time manufacturing further.
21. 21
VARIATIONS OF THE EOQ MODEL
There are several modifications that can be made to
the basic EOQ model to fit particular circumstances.
Two that are often used are
i. The monetary unit lot-size model;
ii. The non-instantaneous receipt model.
22. 22
Monetary Unit Lot Size
The EOQ can be calculated in monetary units rather than physical
units. The same EOQ formula given in the preceding section can
be used, but the annual usage changes from units to dollars.
AD = annual usage in dollars
S = ordering costs in dollars
i = carrying cost rate as a decimal or a percent
Because the annual usage is expressed in dollars, the unit cost is not
needed in the modified EOQ equation. The EOQ in dollars is:
23. 23
Monetary Unit Lot Size
EXAMPLE PROBLEM
An item has an annual demand of $5000, preparation costs of $20 per
order, and a carrying cost of 20%. What is the EOQ in dollars?
24. 24
Non-instantaneous Receipt Model
In some cases when a replenishment order is made, the order is not all
received at one time. The most common reason for this is that the
ordered material is being produced over an extended period of time, yet
material is received for the order as it is being produced.
In this case the EOQ is modified to reflect the rate of production as
related to rate of demand:
25. 25
QUANTITY DISCOUNTS
When material is purchased, suppliers often give a discount on orders over
a certain size. This can be done because larger orders reduce the supplier’s
costs; to get larger orders, suppliers are willing to offer volume discounts.
The buyer must decide whether to accept the discount, and in doing so
must consider the relevant costs:
• Purchase cost.
• Ordering costs.
• Carrying costs.
EXAMPLE PROBLEM
An item has an annual demand of 25,000 units, a unit cost of $10, an order
preparation cost of $10, and a carrying cost of 20%. It is ordered on the basis of an
EOQ, but the supplier has offered a discount of 2% on orders of $10,000 or more.
Should the offer be accepted?
26. 26
ORDER QUANTITIES FOR FAMILIES OF PRODUCT WHEN
COSTS ARE NOT KNOWN
The EOQ formula depends upon the cost of ordering and the cost of
carrying inventory. In practice, these costs are not necessarily known or
easy to determine. However, the formula can still be used to advantage
when applied to a family of items.
For a family of items, the ordering costs and the carrying costs are generally
the same for each item. For instance, if we were ordering hardware items –
nuts, bolts, screws, nails, and so on – the carrying costs would be virtually
the same (storage, capital, and risk costs) and the cost of placing an order
with the supplier would be the same for each item.
In cases such as this, the cost of placing an order (S) is the same for all
items in the family as is cost of carrying inventory (i).
27. 27
EXAMPLE PROBLEM
Suppose there were a family of items for which the decision
rule was to order each item four times a year. Since the cost
of ordering (S) and the cost of carrying inventory (i) are not
known, ordering four times a year is not based on an EOQ.
Can we come up with a better decision rule even if the EOQ
cannot be calculated?
28. 28
PERIOD-ORDER QUANTITY (POQ)
The economic-order quantity attempts to minimize the total cost of
ordering and carrying inventory and is based on the assumption that
demand is uniform.
Often demand is not uniform, particularly in material requirements
planning, and using the EOQ does not produce a minimum cost.
The period-order quantity lot-size rule is based on the same theory
as the economic-order quantity. It uses the EOQ formula to calculate
an economic time between orders.
This is calculated by dividing the EOQ by the demand rate. This
produces a time interval for which orders are placed.
29. 29
PERIOD-ORDER QUANTITY (POQ)
Instead of ordering the same quantity (EOQ), orders are placed to
satisfy requirements for the calculated time interval.
The number of orders placed in a year is the same as for an economic-
order quantity, but the amount ordered each time varies.
Thus, the ordering cost is the same but, because the order quantities are
determined by actual demand, the carrying cost is reduced.
EOQ
Period-order quantity = -------------------------------
Average weekly usage
30. 30
EXAMPLE PROBLEM
The EOQ for an item is 2800 units, and the annual usage is 52,000
units. What is the period-order quantity?
EXAMPLE PROBLEM
Given the following MRP record and an EOQ of 250 units, calculate
the planned order receipts using the economic-order quantity. Next,
calculate the period-order quantities and the planned order receipts. In
both cases, calculate the ending inventory and the total inventory
carried over the 10 weeks.
31. 31
Practical Considerations When Using the EOQ
Lumpy demand. The EOQ assumes that demand is uniform and
replenishment occurs all at once. When this is not true, the EOQ will
not produce the best results. It is better to use the period-order
quantity.
Anticipation inventory. Demand is not uniform, and stock must
be built ahead. It is better to plan a buildup of inventory based on
capacity and future demand.
Minimum order. Some suppliers require a minimum order. This
minimum may be based on the total order rather than on individual
items. Often these are C items where the rule is to order plenty, not an
EOQ.
32. 32
Practical Considerations When Using the EOQ
Transportation inventory. As will be discussed in Chapter 13, carriers give
rates based on the amount shipped. A full load costs less per ton to ship than a part
load. This is similar to the price break given by suppliers for large quantities. The
same type of analysis can be used.
Multiples. Sometimes, order size is constrained by package size. For example, a
supplier may ship only in skid-load lots. In these cases, the unit used should be the
minimum package size.
Order quantities and just-in-time. As will be discussed in Chapter 15, JIT
has a profound effect on the amount of inventory to be produced at one time. The
replenishment quantity of an item is adjusted to match the demand of the next
operation in the supply chain. This adjustment leads to smaller lot sizes and is often
determined by the frequency of shipments to a customer or the size of an easily
moved container rather than by calculation.
