UNIT –III

INVENTORY PROBLEM

The primary function of inventory management is to determine:

(i) When to order?

(ii) How much to order?

When to Order?

This problem of inventory control deals with the point of time when the order for fresh inventory is
to be given. The problem of ‘when to order’ is solved by fixing the appropriate re-order level of each
type of inventory. It is determines by compromising the cost of maintaining these stocks and the
disservice to the customer if this order are not delivered in time.

Re-order Level

‘When to order’ is an important query requires a suitable answer.

Buying and issuing the inventories are the foremost tasks of all types of organizations. When the
inventories fall below a particular level as decided in advance, they are refilled with fresh
procurement. But what should be the quantity of fresh stock is always an important question which
requires a suitable answer. In short, the re-order level is the level of inventory at which the order for
additional stock should be placed.
Re-order level = Average usage × Lead time
i.e. R = Au × L

How Much to Order?

After solving the problem of ‘when to order’ the next immediate issue is ‘how much to order’.
Considering overbuying can lead to unproductive use of working capital and under-buying leads to
unwanted emergency orders and ultimately increases the workload of the purchase department, the
issue of ‘how much to order’ is of vital significance.
Hence, a balance is achieved by selecting the right quantity for each order. This quantity in short is
known as Economic Order Quantity (EOQ).
EOQ is an important technique of inventory management. The EOQ refers to the optimal order size
that will result in the lowest total of order and carrying cost for an item of inventory given its
expected usage, carrying cost and ordering cost. By calculating an economic order quantity, the firm
attempts to determine the order size that will minimize the total inventory cost.
Inventory Costs

1.Ordering Cost: The cost of placing an order and obtaining the supplies is known as ordering cost. It
includes cost related to the clerical work of preparing, calling, issuing, transportation, following and
receiving orders, physical handling of goods, inspections and machine set-up cost. This cost does not
depend or vary on the number ordered.
2.Carrying Cost: It is the cost which is incurred on account of inventory storage, handling, insurance,
etc. from the date of receipt to the date disposal. It includes store-related expenses like salaries of
staff, electricity expenses, handling, insurance, pilferage, breakage, obsolescence, depreciation,
taxes and opportunity cost of capital.

EOQ Model with Price Discount

Price discount is nothing but reduction in the price offered by a supplier for purchasing a larger
volume of an item. This could be in one step or multiple steps. Price discount decreases the unit
price as well as Ordering cost. However, inventory carrying cost tends to increase with large order
size in spite of reduction in unit cost. As a result of these, total cost may reduce or increase. Thus,
the basic decision with Quantity Discount is whether a larger quantity should be ordered to take
benefit of a unit price reduction or not.

The inventory control problem is the problem faced by a firm that must decide how much
to order in each time period to meet demand for its products. The problem can be modeled
using mathematical techniques of optimal control, dynamic programming and network
optimization.

1.From the following calculate

(i) Re-ordering Level and (ii) Minimum Level
Minimum usage 100 units per week Normal usage 200 units per week
Maximum usage 300 units per week Re-order period 4 to 6 weeks

Solution:
(i) Re-ordering Level
Re-ordering level= Maximum consumption * Lead Time [maximum]
Re-ordering level= 300 * 6
Re-ordering level= 1,800 Units per week

(ii) Minimum Level

Minimum level= Reorder level – (Average consumption x lead time [Average])
Minimum level= 1,800 – (200 x 5)
Minimum level= 1,000 Units per week

2.Calculate Ordering Level, Minimum Level and Maximum Level from the following
data:
Re-order quantity 1,500 units Re-order period 4 to 6 weeks
Maximum consumption 400 uts per week Average consumption 300 units per week
Minimum consumption 250 units per week
Solution:
(i) Ordering Level
Ordering level= Maximum consumption * Lead Time [maximum]
Ordering level= 400 * 6
Ordering level= 2,400 Units per week

(ii) Minimum Level

Minimum level= Reorder level – (Average consumption x lead time [Average])
Minimum level= 2,400 – (300 x 5)
Minimum level= 900 Units per week

(iii) Maximum Level

Maximum stock level= Reorder level – (Min consumption * Lead time [minimum])
+ EOQ
Maximum stock level= 900 – (250 * 4) + 1,500
Maximum stock level= 2,400 – (1,000) + 1,500
Maximum stock level= 2,900 Units per week

3. The following information is available in respect of component DP 5:

Maximum stock level 8,400 units
Budgeted consumption- maximum 1,500 units per month
Budgeted consumption- minimum 800 units per month
Estimated delivery period Maximum 4 months and minimum 2 months
You are required to calculate Re-order level

Ordering Level
Ordering level= Maximum consumption * Lead Time [maximum]
Ordering level= 1,500 * 4
Ordering level= 6,000 Units per week

4. From the following date for the last twelve months, compute the Average Stock
Level for a component.
Maximum usage in a month 300 units Minimum usage in a month 200 units
Average usage in a month 225 units Re-ordering quantity 750 units
Time lag procurement of material Maximum 6 months and Minimum 2 months

Solution:
Average Stock Level
Average Stock Level = Minimum Stock Level + ½ of EOQ
Minimum level= Reorder level – (Average consumption x lead time [Average])
Re-ordering level= Maximum consumption * Lead Time [maximum]

Re-ordering level= Maximum consumption * Lead Time [maximum]

Re-ordering level= 300 * 6
Re-ordering level= 1,800 Units per month

Minimum level= Reorder level – (Average consumption x lead time [Average])

Minimum level= 1,800 – (225 x 4)
Minimum level= 900 Units per month

Average Stock Level = Minimum Stock Level + ½ of EOQ

Average Stock Level = 900 + ½ (750)
Average Stock Level = 1,275 Units per month

5. Find out Minimum Stock Level, Maximum Stock Level and Ordering Level from
the following particulars:
Minimum consumption 100 units per day Maximum consumption 175 units per day
Normal consumption 125 units per day Re-order quantity 1,500 units
Minimum period for receiving goods 7 days
Maximum period for receiving goods 15 days
Normal period for receiving goods 10 days

Solution:
(i) Ordering Level
Ordering level= Maximum consumption * Lead Time [maximum]
Ordering level= 175 * 15
Ordering level= 2,625 Units per week

(ii) Minimum Level

Minimum level= Reorder level – (Average consumption x lead time [Average])
Minimum level= 2,625 – (125 x 10)
Minimum level= 1,375 Units per week
(iii) Maximum Level
Maximum stock level= Reorder level – (Min consumption * Lead time [minimum])
+ EOQ
Maximum stock level= 2,625 – (100 * 7) + 1,500
Maximum stock level= 3,425 Units per week