Economic order quantity PDF

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Economic order Quantity...

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Economic order quantity (EOQ) EOQ is the order size that minimizes the sum of ordering and holding costs related to raw materials or merchandise inventories. In other words, it is the optimal inventory size that should be ordered with the supplier to minimize the total annual inventory cost of the business. Other names used for economic order quantity are optimal order size and optimal order quantity.The economic order quantity is computed by both manufacturing companies and merchandising companies. Manufacturing companies compute it to find the optimal order size of raw materials inventory and merchandising companies compute it to find the optimal order size of ready to use merchandise inventory. The ordering and holding costs The two significant factors that are considered while determining the economic order quantity (EOQ) for any business are the ordering costs and the holding costs. A brief explanation of both the costs is given below: Ordering costs The ordering costs are the costs that are incurred every time an order for inventory is placed with the supplier. Examples of these costs include telephone charges, delivery charges, invoice verification expenses and payment processing expenses etc. The total ordering cost usually varies according to the frequency of placing orders. Mostly, it is directly proportional to the number of orders placed during the year which means If the number of orders placed during the year increases, the annual ordering cost will also increase and if, on the other hand, the number of orders placed during the year decreases, the annual ordering cost will also decrease. Holding costs The holding costs (also known as carrying costs) are the costs that are incurred to hold the inventory in a store or warehouse. Examples of costs associated with holding of inventory include occupancy of storage space, rent, shrinkage, deterioration, obsolescence, insurance and property tax etc. The total holding cost usually depends upon the size of the order placed for inventory. Mostly, the larger the order size, the higher the annual holding cost and vice versa. The total holding cost is some time expressed as a percentage of total investment in inventory.The economic order quantity is the level of quantity at which the combined ordering and holding cost is at the minimum level. Relation between the ordering and holding cost: There is an inverse relationship between ordering cost and holding cost. Keeping the annual demand constant if for example the number of orders decreases, the ordering cost will also decrease but the holding cost will rise and vice versa.

Economic order quantity formula The following formula is used to determine the economic order quantity (EOQ):

Where,

 D = Demand per year  Co = Cost per order  Ch = Cost of holding per unit of inventory Example The material DX is used uniformly throughout the year. The data about annual requirement, ordering cost and holding cost of this material is given below:  Annual requirement: 2,400 units  Ordering cost: $10 per order  Holding cost: $0.30 per unit Required: Determine the economic order quantity (EOQ) of material DX using above data. Solution

The economic order quantity for material DX is 400 units. Now, we can compute the number of orders to be placed per year, annual ordering cost, annual holding cost and combined annual ordering and holding cost as follows: Number of orders per year = Annual demand/EOQ = 2,400 units/400 units = 6 orders per year Ordering cost = Number or orders per year × Cost per order = 6 orders × $10 = $60 Holding cost = Average units × Holding cost per unit = (400/2) × 0.3 = $60 Combined ordering and holding cost at economic order quantity (EOQ): = Ordering cost + Holding cost = $60 + $60 = $120 Notice that both ordering cost and holding cost are $60 at economic order quantity. The holding cost and ordering cost at EOQ tend to be the same. Underlying assumptions of economic order quantity (EOQ) The computation of economic order quantity (EOQ) is based on the following assumptions: 1. 2. 3. 4. 5. 6. 7.

The total number of units to be consumed during the period is known with certainty. The total ordering cost remains constant throughout the period. The inventory cost remains constant throughout the period. There are no cash or quantity discounts available. The whole quantity of ordered inventory is delivered in one batch. The optimal quantity for each invariable or stock item is computed separately. The lead time does not fluctuate and the order is received on time with the total order quantity.

The assumptions described above are also known as the limitations of economic order quantity (EOQ).

Maximum Level of Stock The maximum level of stock is the level above which a business does not or cannot hold stock in its premises. The maximum level of inventory could be described as the maximum capacity of a business to stock goods (inventory or raw material) in its store, which may be due to reasons like demand limitation of goods (in production or sales), the storage capacity of business, rationed funds etc. The ‘maximum level of stock’ is usually achieved when those goods arrive which were ordered at the ‘re-order level’ of the stock. This stock is then used in the production process (in case of raw materials) or sold (in case of finished goods) and then re-ordered again at the reorder level which again fills up the stock to the ‘maximum level’. This is an on-going process. Formula: Maximum Level = Re-order level + Re-order quantity – (Minimum usage × Minimum lead time) Minimum Level of Stock The minimum level of inventory is a kind of a precautionary level of inventory which indicates that the delivery of raw materials or merchandise may take more than the normal lead time. Lead time is the expected time taken by the supplier to deliver goods at the warehouse or at the point of consumption. If the level of stock strikes the minimum level, the management of the company must make sure that they corroborate with the supplier and take other necessary measures to make the goods (inventory or raw materials) available in time so that the business operations are not disturbed or delayed. Formula: Minimum Level of Inventory = (Maximum usage × Maximum lead time) – (Average usage × Average lead time) OR, Minimum Level of inventory = Re-order level – (Average usage × Average lead time) Both the formulas are equivalent and produce the same result. .Reorder Level of Stock Reorder level of stock (also known as reorder point or ordering point) in a business is a preset level of stock or inventory at which the business places a new order with its suppliers to obtain the delivery of raw materials or finished goods inventory. Every business has to maintain a certain level of raw materials or finished goods in its store. This is done in order to sustain the continuity of production in case of raw materials and the continuity of sales in case of finished goods. For this purpose, the business must set a specific level at which it should place a new order with the suppliers of inventory.

Formula: The two formulas used to calculate the re-order level are given below: 1. When the business does not need to maintain safety stock: Maximum demand or usage (in days, weeks or months) × Maximum lead time (in days, weeks or months) 2. When the business needs to maintain a safety stock: [Maximum demand or usage (in days, weeks or months) × Maximum lead time (in days, weeks or months)] + Safety stock Lead Time The timing difference between placing an order with the supplier and arrival of the goods is known as the lead time. Safety Stock (Also known as buffer stock) In some scenarios, it may be unlikely that the reorder level could be estimated accurately. This is because the demand and the lead time of the goods could differ than the usual trends and in that case the business may run out of stock. So, a level of safety stock is set to avoid such a condition. It is also known as buffer stock. Economic Order Quantity with Discount EOQ generally minimizes the total inventory cost. However, EOQ may not be optimal when discounts are factored into the calculation. The optimal order quantity when discounts are involved is either:  

EOQ; or Any one of the minimum order quantities above EOQ that qualify for additional discount.

The optimum quantity is determined by comparing the total inventory cost of the different order quantities listed above. For example, if the EOQ is 1000 units and discounts of 2%, 5% and 8% are offered at 500 units, 1000 units and 2000 units, the order quantity that shall lead to the lowest total inventory cost will either be the EOQ (i.e. 1000 units) or 2000 units. In order to determine the optimum quantity, we need to compare the total inventory cost of order quantities of 1000 units and 2000 units. We can ignore the total inventory cost of 500 units as it is below the EOQ level. Example

BIKO is a bike retailer located in the outskirts of Paris. BIKO purchases bikes from PMX in orders of 250 bikes which is the current economic order quantity.

PMX is now offering the following bulk discounts to its customers:



2% discount on orders above 200 units



4% discount on orders above 500 units



6% discount on orders above 600 units

BIKO is wondering if the EOQ model is still the most economical and whether increasing the order size would actually be more beneficial.



Following information is relevant to forming the decision:



Annual demand is 5000 units



Ordering cost is $100 per order



Annual holding cost is comprised of the following: o 5% insurance premium for the average inventory held during the year calculated using the net purchase price o Warehousing cost of $6 per unit



Purchase price is $200 per unit before discount

Solution

We need to compare the total inventory cost of the order quantities at the various discount levels with that of the economic order quantity.Since the holding cost is partially determined on the

basis of purchase price, we need to re-calculate the EOQ by applying a discount. As the EOQ seems likely to fall within the 200 to 400 units range, we should use 2% discount in our calculation.

Order Quantity

252 units

500 units

1,000 units

5000 ÷ 500 = 10

5,000 ÷ 1,000 = 5

Number of orders (Annual demand ÷ Order Quantity)

5,000 ÷ 252 = 19.84

Ordering Cost (number of orders × $100)

10 x 100 = 19.84 x 100 = $1,984

5 x 100 = $500 $1,000

6 × 500/2 =

Warehousing Cost ($6 ×

6 × 1000/2 = $3,000

6 × 252/2 = $756 Average number of units)

≈252 units

$1,500

Insurance Cost (5% × Purchase

0.05×(200×0.98)×(25 0.05×(200×0.96)×(50

Price × Average

2/2) = $1,235

0/2) = $2,400

0.05×(200×0.94)×

(1000/2) = $4,700

Inventory)

Cost of Purchase (Purchase Price × 200×5000×(1.0-0.02) 200×5000×(1.0-0.04)

200×5000×(1.0-0.06)

Annual Demand = $980,000

= $960,000

$983,975

$964,900

× (100 - discount

= $940,000

%)

Total Inventory Cost

Based on the above analysis, the optimum order quantity is 1000 units.

$948,200

Significance of Economic Order Quantity



To the business owners, lowering costs can greatly help in generating profits. By calculating Economic Order Quantity, the business owners would be able to order the right quantities and then they would be able to reduce the ordering and the carrying costs. And that will result into more profits.



By using this, the business owners would be able to take decisions regarding materials (and orders) quickly which will result into less time and effort wasted. As a result, the processes would get improved.



By using Economic Order Quantity, the business owners can choose the right vendors and can avail better packages to save costs and to earn better profits....