Chapter 4

Ordering and Accounting for Inventory

Ordering, Receiving and issuing materials

Ordering, Receiving and issuing materials

Documents

Purchase Requisition formPurchase order formDelivery note

Goods Received NoteMaterials requisition note

Materials returned notes

Materials Transfer notes

Document Completed by Sent to Information included

Purchase Requisition form Production department Purchasing department Goods requiredManager’s authorisation

Purchase order form Purchasing Department SupplierAccounting (copy)Goods receiving department (copy)

Goods required

Delivery note Supplier Goods Receiving Department

Check of goods delivered against order form

Goods Received Note Goods receiving department Purchasing department Verification of goods received to enable payment

Materials requisition note Production department Stores Authorisation to release goodsUpdate stores record

Materials returned notes Production Department Stores Details of goods returned to storesUpdate stores record

Materials Transfer notes Production Department A Production Department B Goods transferred between departmentsUpdate stores records

Double entry

Double entry

Control Procedures

Chapter 5

Order Quantities and Reorder Levels

Types of Inventory

• Raw materials• Purchased parts and supplies• Work-in-process (partially completed)

products (WIP)• Items being transported• Tools and equipment

Independent and Dependent Demand Independent and Dependent Demand InventoryInventory

• Independent demand– items demanded by external customers (Kitchen

Tables)

• Dependent demand– items used to produce final products (table top,

legs, hardware, paint, etc.)– Demand determined once we know the type and

number of final products

Inventory and Quality Management

• Customers usually perceive quality service as availability of goods they want when they want them

• Inventory must be sufficient to provide high-quality customer service in TQM

Inventory Costs• Holding costHolding cost

cost of holding an item in inventorycost of holding an item in inventory• Ordering costOrdering cost

cost of replenishing inventorycost of replenishing inventory• Shortage costShortage cost

temporary or permanent loss of temporary or permanent loss of sales when demand cannot be sales when demand cannot be metmet

Holding & Ordering Costs

Minimise total of holding, ordering and stock-out costs

The cost of Holding InventoryA company uses components at the rate of 6,000 units per year, which are bought in at a cost of £1.20 each from the supplier. The company orders 1,000 units each time it places an order and the average inventory held is 500 units. It costs $20 each time to place an order, regardless of the quantity ordered.The total holding cost is 20% per annum of the average inventory held.The annual holding cost will be $The annual ordering cost will be $

Solution

• The annual holding cost will be $120• 500 units * $1.20 * 20 %• The annual ordering cost will be

$120• 6,000/1,000 = 6• 6 * 20 = $120

The cost of Holding Inventory

• A company has recorded the following details for Component 427 which is sold in boxes of 10 components. Component 427 is currently ordered in batches of 240 boxes at a time. The average inventory held is 120 boxes.

• Ordering cost $32 per order placed• Purchase price $20 per box of 10 components• Holding cost 10% of purchase price• Monthly demand 1,500 components

The cost of Holding Inventory

• Required:• Calculate the annual holding cost and the

annual ordering cost for Component 427.• Annual holding cost = average inventory held

x cost per box x 10% = 120 x $20 x 10% = $240• Annual ordering costs = (1800/240) *32 =

$240

Ordering Costs

• Associated with placing orders• Includes :• Administrative costs : fixed costs per Order• Delivery costs: Fixed charge per delivery

order, behave as variable costs• Increased in number of orders will have an

increase in ordering costs

Water Tank Analogy for Inventory

Supply RateInventory Level

Demand Rate

Inventory Level

Buffers Demand Rate from Supply Rate

Economic Order Quantity (EOQ) Models

• EOQ–optimal order quantity that

will minimize total inventory costs

• Basic EOQ model• Production quantity model

EOQ Cost Model

Order Quantity, Order Quantity, QQ

Annual Annual cost ($)cost ($) Total CostTotal Cost

holding Cost =holding Cost =CCccQQ

22

Slope = 0Slope = 0

Minimum Minimum total costtotal cost

Optimal orderOptimal order QQoptopt

Ordering Cost =Ordering Cost =CCooDD

QQ

Economic Order QuantityThe EOQ minimises the total of holding, ordering & stock-out costs

2C0D

ChQ=EOQ =

Where : Q= Reorder Quantity (EOQ)D = demand per annum.C0 = Cost of placing one orderCh = cost of holding one unit per yearAnnual ordering costs = C0D/QAnnual holding cost = Ch*Q/2

√

• Average Inventory held is equal to half of the EOQ=EOQ/2

• The number of orders in a year = Expected annual demand/EOQ

• Total annual holding cost=Average Inventory (EOQ/2) * holding cost per unit of Inventory

• Total annual ordering cost = Number of orders * cost of placing an order.

Economic Order Quantity

Total Annual Cost

• Total Annual Cost = PD + (Co * D/Q) + (Ch* Q/2)• There is also a formula that allows us to

calculate the Total Annual Costs (TAC) i.e. the total of purchasing costs, holding costs and ordering costs :

• Note that the formula for the TAC is not provided in your exam.

• Total Annual Cost = PD + (Co * D/Q) + (Ch* Q/2)Where:• P = Purchase cost per unit• D = Demand per annum• Co = Cost of placing one order• Ch = Cost of holding one unit for one year• Q = Reorder quantity (EOQ)

Total Annual Cost

Assumptions of Basic EOQ Model

• Demand is known with certainty Demand is known with certainty and is constant over timeand is constant over time

• No shortages are allowedNo shortages are allowed• Lead time for the receipt of Lead time for the receipt of

orders is constantorders is constant• Order quantity is received all at Order quantity is received all at

onceonce

Example• A company uses components at the rate of

500 units per month, which are bought in at a cost of $1.20 each from the supplier. It costs $20 each time to place an order, regardless of the quantity ordered.

• The total holding cost is 20% per annum of the value of inventory held.

• EOQ ? • The total annual cost ?

Example

• A company is planning to purchase 90,800 units of a particular item in the year ahead. The item is purchased in boxes each containing 10 units of the item, at a price of $200 per box. A safety inventory of 250 boxes is kept.

• The cost of holding an item in inventory for a year (including insurance, interest and space costs) is 15% of the purchase price.

Example cont…

• The cost of placing and receiving orders is to be estimated from cost data collected relating to similar orders, where costs of $5,910 were incurred on 30 orders. It should be assumed that ordering costs change in proportion to the number of orders placed. 2% should be added to the above ordering costs to allow for inflation. Assume that usage of the item will be even over the year.

• The order quantity which minimises total costs is ?• This will mean ordering the item every weeks ?

Bulk Discounts

Bulk Discount

• The steps involved in calculating the EOQ when quantity discounts are available are as follows:

• If a quantity discount is accepted this will have the following effects:

• – The annual purchase price will decrease.• – The annual holding cost will increase.• – The annual ordering cost will decrease

Bulk Discount

• To establish whether the discount should be accepted or not, the following calculations should be carried out.

• – Calculate TAC with the discount.• – Compare this with the annual costs without

the discount (at the EOQ point).

Bulk Discount

• 1) Calculate the EOQ, ignoring discounts.• (2) If the EOQ is smaller than the minimum

purchase quantity to obtain a bulk discount, calculate the total for the EOQ of the annual inventory holding costs, inventory ordering costs and inventory purchase costs.

Bulk Discount

• (3) Recalculate the annual inventory holding costs, inventory ordering costs and inventory purchase costs for a purchase order size that is only just large enough to qualify for the bulk discount.

• (4) Compare the total costs when the order quantity is the EOQ with the total costs when the order quantity is just large enough to obtain the discount. Select the minimum cost alternative.

Bulk Discount

• (5) If there is a further discount available for an even larger order size,

• repeat the same calculations for the higher discount level.

Quantity Discount Model

QQoptopt

holding cost holding cost

Ordering cost Ordering cost

Inve

ntor

y co

st (

$)In

vent

ory

cost

($)

QQ((dd1 1 ) = 100) = 100 QQ((dd2 2 ) = 200) = 200

TC TC ((dd2 2 = $6 ) = $6 )

TCTC ( (dd1 1 = $8 )= $8 )

TC TC = ($10 )= ($10 ) ORDER SIZE PRICE0 - 99 $10100 – 199 8 (d1)200+ 6 (d2)

Example• A company uses components at the rate of

500 units per month, which are bought in at a cost of $1.20 each from the supplier. It costs $20 each time to place an order, regardless of the quantity ordered.

• The supplier offers a 5% discount on the purchase price for order quantities of 2,000 items or more. The current EOQ is 1,000 units.

• The total holding cost is 20% per annum of the value of inventory held.

• Should the discount be accepted?

Gradual Replenishment

• Manufacturing their own products internally.• Involve deciding whether to produce large

batches at long intervals OR produce small batches at short intervals.

• EBQ (economic batch quantity) model.• As the items are being produced, there is a

machine setup cost. This replaces the ordering cost of the EOQ.

EBQ

• In the EOQ, inventory is replenished instantaneously whereas here, it is replenished over a period of time.

• Depending on the demand rate, part of the batch will be sold or used while the remainder is still being produced.

• For the same size of batch (Q), the average inventory held in the EOQ model (Q/2) is greater than the average in this situation

Economic Batch Quantity

2C0DCh(1-D/R)EBQ = √

The number of manufactured items to produce in a batch, to minimise total costs

Where : D = demand p.a.C0 = Cost of setting up batchCh = cost of holding one unit per yearR = Annual replenishment (annual production) rateAnnual setup costs = C0D/QAnnual holding cost = Ch*Q/2 (1-D/R)

Example EBQ

• Production is at a rate of 500 units per week.• Demand is 10,000 units per annum; evenly

spread over 50 working weeks.• Setup cost is $2,700 per batch.• Storage cost is $2.50 per unit for a year.• Calculate the economic batch quantity (EBQ)

for Item X.

Example EBQ• AB Ltd makes a component for one of the

engines that it builds. It uses, on average, 2,000 of these components, steadily throughout the year.

• The component costs $16 per unit to make and it costs an additional $320 to setup the production process each time a batch of components is made. The holding cost per unit is 10% of the unit production cost.

Example EBQ

• The company makes these components at a rate of 200 per week, and the factory is open for 50 weeks per annum.

• Required: Calculate the EBQ.

Re-order levels• Reorder level –Place replenishment order• Lead time – this is the time expected to elapse

between placing an order and receiving an order for inventory.

• Reorder quantity – when the reorder level is reached, the quantity of inventory to be ordered is known as the reorder or EOQ.

• Demand – this is the rate at which inventory is being used up. It is also known as inventory usage.

Re-order levelsThe pre-determined level of inventory at which order is placed, to avoid stock-outs.

Re-order level = usage per day * lead time in days

When lead time and demand in lead time is not constant :

Re-order level = maximum usage*maximum lead time

Maximum Inventory level = Re-order level + re-order quantity – (minimum usage*minimum lead time)

Minimum Inventory level (buffer stock) = Re-order level – (average usage *average lead time)

Average inventory = (Re-order quantity / 2) + minimum inventory

EOQ Inventory Order CycleEOQ Inventory Order CycleDemand rate

0 TimeLead time

Lead time

Order Placed

Order Placed

Order Received

Order Received

Inve

nto

ry

Lev

el

Reorder point, R

Order qty, Q

As Q increases, average inventory level increases, but number of orders placed decreases

ave = Q/2

Example reorder level.

• A company uses Component M at the rate of 1,500 per week. The time between placing an order and receiving the components is five weeks.

• The reorder quantity is 12,000 units.• Required:• Calculate the reorder level.