FMA Additional Notes

7/26/2019 FMA Additional Notes

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Gradual replenishment of inventory

The situations we have looked at so far have involved inventory levels being replenishedimmediately when organisations buy inventory from suppliers. Similar problems are faced byorganisations who replenish inventory levels gradually by manufacturing their own productsinternally.

• The decisions faced by organisations that manufacture and store their own productsinvolve deciding whether to produce large batches at long intervals OR produce smallbatches at short intervals.

• An amended EOQ model is used to help organisations to decide which course of actionto take.

• The amended EOQ model is known as the EQ !economic batch "uantity# model.

• As the items are being produced$ there is a machine setup cost. This replaces theordering cost of the EOQ.

• %n the EOQ$ inventory is replenished instantaneously whereas here$ it is replenishedover a period of time.

• &epending on the demand rate$ part of the batch will be sold or used while theremainder is still being produced.

• 'or the same si(e of batch !Q#$ the average inventory held in the EOQ model !Q)*# isgreater than the average in this situation !see diagram on the ne+t page#.

• The EQ model can be shown graphically as follows.

%nventory

!units#



• The ma+imum inventory level will never be as great as the batch si(e$ because some ofthe batch will be used up while the remainder is being produced.

The EBQ

The EQ model is primarily concerned with determining the number of items that should beproduced in a batch !compared to the si(e of an order with the EOQ#.

The formula for the EQ is as follows,

-here,

Q atch si(e& &emand per annum/h /ost of holding one unit for one year /o /ost of setting up a batch ready to be producedR Annual replenishment rate

0arge or small batches1



• 2roducing large batches at long intervals will lead to low machine setup costs !as fewer machine setups will be needed# and high holding costs !high average inventory levels asmore inventory held#.

• 2roducing small batches at short intervals will lead to high machine setup costs !as moremachine setups will be needed# and low holding costs !low average inventory levels asless inventory held#.

%llustration 3 4radual replenishment of inventory

The following is relevant for %tem 5,

• 2roduction is at a rate of 677 units per week.

• &emand is 37$777 units per annum8 evenly spread over 67 working weeks.

• Setup cost is 9*$:77 per batch.

• Storage cost is 9*.67 per unit for a year.

Re"uired,

/alculate the economic batch "uantity !EQ# for %tem 5.

Solution

Annual production rate$ R 677 + 67 *6$777 units

Annual demand rate 37$777 units

/ost per setup$ /o 9*$:77

/ost of holding one item in inventory per year$ /h 9*.67

Test your understanding



A 0td makes a component for one of the engines that it builds. %t uses$ on average$ *$777 of

these components$ steadily throughout the year. The component costs 93; per unit to make and

it costs an additional 9<*7 to setup the production process each time a batch of components is

made. The holding cost per unit is 37= of the unit production cost. The company makes these

components at a rate of *77 per week$ and the factory is open for 67 weeks per annum.

Re"uired,

/alculate the EQ.

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FMA Additional Notes