OVERVIEW
Objective
¾
To understand the costs and benefits of holding inventory and determine the Economic Order Quantity (EOQ) which minimises costs.¾
To appreciate other possible inventory control systems.INVENTORY CONTROL
OTHER INVENTORY
SYSTEMS EOQ MODEL
¾ Definition
¾ Reasons for holding inventory ¾ Costs associated with inventory
¾ Definition
¾ Determination of EOQ
¾ Complications
¾ Quantity discounts
RE-ORDER LEVEL
¾ Definitions
¾ Constant demand
during lead time
¾ Uncertain demand
during lead time ¾ Service levels
¾ Periodic review system
¾ ABC system
¾ Just-in-time (JIT) ¾ Perpetual inventory
1
INVENTORY CONTROL
1.1
Definition
The systematic regulation of inventory levels.
¾
If inventory is too high Inefficient ⇒ profit reduced¾
If inventory is too lowInsufficient to satisfy customers ⇒ profit reduced.
1.2
Reasons for holding inventory
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To meet demand by acting as a buffer in times of unusually high consumption, i.e. to reduce the risk of stockouts.¾
To ensure continuous production.¾
To take advantage of quantity discounts.¾
To buy in ahead of a shortage or ahead of a price rise.¾
For technical reasons (e.g. maturing whisky in casks or keeping oil in pipelines).¾
To reduce ordering costs.1.3
Costs associated with inventory
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Purchase price;¾
Holding costs: cost of capital tied up; insurance;
deterioration, obsolescence and theft; warehousing;
stores administration.
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Re-order costs: transport costs;
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Shortage costs: production stoppages caused by lack of raw materials;
stockout costs for finished goods – anything from a delayed sale to a lost customer; emergency re-order costs.
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Systems costs – people and computers.The benefits of holding inventory must outweigh the costs.
2
EOQ MODEL
2.1
Definition
¾
The Economic Order Quantity (EOQ) is the quantity of inventory that should be ordered each time a purchase order is made.¾
EOQ aims to minimise the costs which are relevant to ordering and holding inventory.2.2
Determination of EOQ
x = order quantityCH = cost of holding one unit for one year D = annual demand
CO = cost of placing an order
¾
The total annual relevant cost to be minimised= annual holding cost + annual order cost
= the cost of holding one unit in inventory for one year × the average number of units held
+ the cost of an order × the number of orders in a year
=
2 x C
H + DCo
x
The total cost is minimized when:
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EOQ graph $Cost
Total cost
holding cost
ordering cost
EOQ
x Order quantity
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Assumption of EOQ: purchase price per unit is constant; constant demand;
no risk of stockouts.
Example 1
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Using the following data calculate the EOQ D = 40,000 unitsCO = $2 CH = $1
Solution
2.3
Complications
2.3.1
Warehouse rental
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The EOQ model assumes that holding costs vary with the average inventory level.¾
However if a warehouse is rented on a long-term contract (rather than daily) then itneeds to be large enough to hold the maximum level of stock, rather than the average.
must rent sufficient floor space to meet this quantity rather than
2
x
(x/2)
x
¾
deal with this by doublingthe floor space used by one unit when calculating holding cost, and then use the normal EOQ formulaExample 2
Annual demand = 3,000 units Reorder cost = $5
Holding cost = $3.33 per unit + rental of warehouse
Each unit occupies 3m2 rented on annual contracts for $5 per m2
Solution
D = CO = CH =
3,000 5
2.3.2
Cost of capital
¾
Inventory, like any other asset, must be matched by a liability. Therefore there must be a cost of financing inventory.¾
This is a type of holding cost.Illustration 1
Cost of Capital = 10% Price per unit = $100
∴ Holding cost = $100 × 0.1 = $10
This is in addition to any other holding costs you are given.
2.4
Quantity discounts
¾
The supplier may offer a “bulk-buying” discount on each unit purchased for specified quantities above the EOQ¾
In this case the purchase price obviously becomes a relevant factor in the decision¾
To deal with this, calculateTotal annual cost =
cost purchase
Annual cost
order Annual cost
holding Annual
+ +
for each order quantity where discounts are available and at the order level calculated by the EOQ.
Example 3
Annual demand = 5,000 Holding cost = $7.50 Reorder cost = $30 Purchase price = $1.10
A discount of 3% is available on orders of 300 units or more.
Required:
Determine whether or not the discount is worthwhile.
Solution
EOQ =
Total cost at EOQ $
Holding 2 xC
H =
Reorder x
D CO = Purchase cost Total
_____
–––––
Total cost at order quantity = 300 units
Holding 2
x C
H = Reorder
x
D CO =
Purchase cost _____
–––––
3
RE-ORDER LEVEL
3.1
Definitions
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Re-order level (ROL) is the level to which inventory should fall before a purchase order is made.¾
Lead time is the time between placing and receiving an order.¾
There are two possible situations to be dealt with:(1) Constant demand in lead time (2) Uncertain demand in lead time
3.2
Constant demand during lead time
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Re-order level (ROL) = lead time (days) × demand per day¾
For example if demand is 40 units per day and lead time is two days - when inventory levels fall to 80 units then inventory would be re-ordered. This can be showngraphically:
INVENTORY LEVEL
ROL
TIME
{
Lead time
3.3
Uncertain demand during lead time
¾
There will be an expected level of demand, not a known level of demand.Method
(1) Calculate expected demand in the lead time. Expected lead time demand = ∑xi p(xi) where
xi = level of demand
p (xi) = probability of level of demand
(2) Take each level of demand ≥ expected lead time demand as a possible reorder level and calculate the expected annual stockout cost.
(3) For each possible ROL calculate the expected annual buffer holding cost.
(4) Choose the ROL with the lowest sum of stock out and holding cost.
Example 4
The following information relates to inventory levels of component XL5: Holding cost = $8
Stockout cost = $3 Lead time = 1 week
EOQ = 150
The company operates for 50 weeks per annum and weekly demand is given by:
xi p(xi)
Demand Probability
40 0.1
50 0.2
60 0.4
70 0.2
80 0.1
Solution
Average demand in the lead time = Average annual demand =
orders per annum =
ROL Buffer Demand Units
short Probability units Ave short
The optimum ROL is therefore
3.4
Service levels
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Setting a “service level” of 98% implies that the firm accepts a 2% chance of a stock-outExample 5
Average weekly demand for an item of inventory is 300 units with a standard deviation of 40 units. The lead time is one week.
Required:
4
OTHER INVENTORY SYSTEMS
4.1
Periodic review system
The inventory levels are reviewed at fixed time intervals, and variable quantities will be ordered as appropriate.
The order size made is sufficient to return inventory levels to a pre-determined level. A very simple method of inventory control – ideal where inventory control is only one of a person’s responsibilities.
4.2
ABC system of inventory control
The aim is to reduce the work involved in inventory control in a business which may have several thousand types of inventory items.
The inventory is categorised into class A, B or C according to the annual cost of the usage of that inventory item, or the difficulty of obtaining replacements, or the importance to the production process.
Class A will then take most of the inventory control effort, Class B less and Class C less still.
Commentary
Whilst this seems acceptable for inventory of finished goods, it may cause problems for raw materials. There may be an item which has a very small cost but which is vital for the manufacture of the finished product. Such an item would have to be included in with the Class A items because of its inherent importance, rather than its cost.
4.3
Just-in-time (JIT)
In a JIT system production and purchasing are linked closely to sales demand on a week-to-week basis. The aim is to create a continuous flow of raw materials inventory into work in progress, which becomes finished goods to go immediately to the customer. This means that negligible inventory needs to be held.
Conditions necessary include the following:
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Flexibility of both suppliers and internal workforce to expand and contract output at short notice.¾
Raw material inventory must be of guaranteed quality – indeed, quality must be maintained at every stage.¾
The workforce must be willing to increase or decrease its working hours from one period to another. This could be done by having a core workforce with a group of part-time or freelance workers.¾
The design of the factory must be such that JIT deliveries to all areas are possible.¾
Total reliance on suppliers for quality and delivery, and therefore very tight contractswith penalty clauses.
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Significant investment by suppliers, and therefore long-term contracts.4.4
Perpetual inventory methods
Where a firm keeps perpetual inventory records, there will frequently be a replenishment point that triggers an order. Such a system relies upon the accuracy of the records, not on physical counts.
It is possible to use point of sale (POS) terminals that automatically update inventory records as each successive sale is made.
One advantage of such a system is the data it provides to management to determine which product lines are moving rapidly. Sales managers may also use the data to make tactical decisions on special prices to sell slow-moving items.
4.5
Material requirements planning (MRP)
A system that uses the production schedule to decide what is needed and when. This is then linked in with suppliers’ discounts, lead times, etc to devise an optimal inventory holding and ordering policy.
Key points
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They formula for the Economic order Quantity is provided in the exam – the key is to identify the relevant data.³
Do not confuse the Economic Order Quantity (EOQ) with the Re –Order Level (ROL). EOQ tells us how large each order should be, ROL tells uswhen we should place on order for inventory
³
Just-In-Time (JIT) is the other main inventory system to be familiar withEXAMPLE SOLUTIONS
Solution 2 — Floor space
D =Solution 3 — Quantity discount
EOQ = Total cost at order quantity = 300 units
Solution 4 — Re-order level
Average demand in the lead time = 60 units Average annual demand = 60 × 50 = 3,000 units
The optimum ROL is therefore 70 units.
Solution 5 — Service level
ROL SD = 40
300 45%
5%
