# Inventory Control Models Entity needs to maintain inventory at appropriate level keeping balance in contrasting factors inventory levels e.g if large amount of inventory is ordered ordering cost is reduced but opportunity cost is much increased , money tied could be used for other profitable investments. So keeping all factors in mind entity needs appropriate models to be used for inventory management to save from irrelevant costs , help profits to boost up

Let’s study different systems showing to   manage inventory in best ways.  Prominent methods include:

## EOQ Without Discounts

Example

Acompany utilizes 5000 units per year,

Purchase price of each unit is \$2,

Cost of placing order (ordering cost) =\$10

Holding cost =10% of unit cost

Find

• EOQ
• Total Co
• Total Ch

SLOUTION =√2.10.5000/ 10%* 2

707.10

Annual Ordering Cost

D/ EOQ * Co per unit

= 5000/707.10*10

\$14.14

Annual Holding Cost

EOQ/2*Ch per unit

=707.10/2* 0.2

=\$71

## EOQ with dicounts

In case of purchase of large quantities, supplier offers discounts So its necessary to calculate EOQ considering those discounts, so can decision can be  regarding acceptance or rejection of those large orders with discounts(keeping in mind high holding costs for large quantities order)

STEPS TO FOLLOW

• Calculate EOQ in normal circumstances(without discounts)
• Calculate total COSTS without discounts on basis of EOQ calculated
• Now calculate total costs on basis of large orders quantities(with discounts)
• In case of more than one offers, calculate costs with each offer and choose the best one

###### EXAMPLE # 1         ACCA DEC 2010

WQZ Co is considering making the following changes in the area of working capital management

It has been suggested that the order size for Product KN5 should be determined using the economic order quantity model (EOQ).WQZ Co forecasts that demand for Product KN5 will be 160,000 units in the coming year and it has traditionally ordered 10% of annual demand per order. The ordering cost is expected to be \$400 per order while the holding costis expected to be \$5·12 per unit per year. A buffer inventory of 5,000 units of Product KN5 will be maintained, whether orders are made by the traditional method or using the economic ordering quantity model.

SOLUTION

Cost of the current ordering policy

Order size = 10% of 160,000 = 16,000 units per order

Number of orders per year = 160,000/16,000 = 10 orders per year

Annual ordering cost = 10 x 400 = \$4,000 per year

Holding cost ignoring buffer inventory = 5·12 x (16,000/2) = \$40,960 per year

Holding cost of buffer inventory = 5·12 x 5,000 = \$25,600 per year

Total cost of current policy = 4,000 + 40,960 + 25,600 = \$70,560 per year

###### Cost of the ordering policy using the EOQ model

Order size = (2 x 400 x 160,000/5·12)0·5 = 5,000 units per order

Number of orders per year = 160,000/5,000 = 32 orders per year

Annual ordering cost = 32 x 400 = \$12,800 per year

Holding cost ignoring buffer inventory = 5·12 x (5,000/2) = \$12,800 per year

Holding cost of buffer inventory = 5·12 x 5,000 = \$25,600 per year

Total cost of EOQ policy = 12,800 + 12,800 + 25,600 = \$51,200 per year

Change in costs of inventory management by using EOQ model

Decrease in costs = 70,560 – 51,200 = \$19,360

###### EXAMPLE #2       ACCA DEC2012

KXP Co  orders 15,000 units per month of Product Z, demand for which is constant. There is only one supplier of Product Z and the cost of Product Z purchases over the last year was \$540,000. The supplier has offered a 2% discount for orders of Product Z of 30,000 units or more. Each order costs KXP Co \$150 to place and the holding cost is 24 cents per unit per year. KXP Co has an overdraft facility charging interest of 6% per year

Calculate whether the bulk purchase discount offered by the supplier is financially acceptable and comment

SOLUTION

Cost of current inventory policy

Cost of materials = \$540,000 per year

Annual ordering cost = 12 x 150 = \$1,800 per year

Annual holding cost = 0·24 x (15,000/2) = \$1,800 per year

Total cost of current inventory policy = 540,000 + 1,800 + 1,800 = \$543,600 per year

Cost of inventory policy after bulk purchase discount

Cost of materials after bulk purchase discount = 540,000 x 0·98 = \$529,200 per year

Annual demand = 12 x 15,000 = 180,000 units per year

KXP Co will need to increase its order size to 30,000 units to gain the bulk discount

Revised number of orders = 180,000/30,000 = 6 orders per year

Revised ordering cost = 6 x 150 = \$900 per year

Revised holding cost = 0·24 x (30,000/2) = \$3,600 per year

Revised total cost of inventory policy = 529,200 + 900 + 3,600 = \$533,700 per year

Evaluation of offer of bulk purchase discount

Net benefit of taking bulk purchase discount = 543,600 – 533,700 = \$9,900 per year

The bulk purchase discount looks to be financially acceptable. However, this evaluation is based on a number of unrealistic assumptions. For example, the ordering cost and the holding cost are assumed to be constant, which is unlikely to be true in reality. Annual demand is assumed to be constant, whereas in practice seasonal and other changes in demand are likely.

## IMPORTANT FORMULAE OF MATERIALS

#### Re-Order Level:

“Minimum level set by entity at which order is made “

Maximum Usage * maximum Lead Time  (IN CASE OF WITHOUT SAFETY STOCK)

OR

Safety Stock + Lead Time Consumption

“Time lap between placement of order and delivery of order at warehouse by supplier”

Average Lead Time * Average Consumption

#### Maximum level:

ROL+ROQ-(Minimum Usage*Minimum Lead Time)       (absolute maximum inventory)

ROL+ROQ-(Average Usage*Average lead Time)  (Normal maximum inventory)

#### Average Level:

1/2(Maximum Level+ Minimum Level)

OR

Minimum Level + 1/2 ROQ

Danger Level:       Minimum Usage Rate * Minimum Lead Time

OR

Average Usage Rate * Minimum Lead Time

OR

Minimum Usage Rate * Average Lead Time

EOQ/ROQ              Square  Root of √ 2D.Co/Ch

Material T/O Ratio              Consumption / Average Stock

Average Stock      1/2(Maximum Stock+ Minimum Stock)