# DANGER LEVEL - Quantitative Techniques for management

Usually stock should not be lower than the minimum level. But if for any reason, stock comes down below the minimum level, it is called danger level. When the stock reaches danger level, it is necessary to take urgent action on the part of the management for immediate replenishment of stock to prevent stock-out situation.

## Danger Level of Material Formula

The danger level can be calculated by applying the following formula:

Danger Level = Average consumption x Maximum Re-order period for emergency purchases

Some concerns fix danger level below the re-ordering level but above the minimum level. If action for purchase is taken as soon as the stock reaches the re-ordering level, the danger level bears no importance except that, when the stock reaches the danger level (but not yet the minimum level) a reference may be made to the purchase department to ensure that delivery is received before the actual stock reaches the minimum level.

When the danger level is fixed below the minimum, it being reaches by the actual stock, the defect in the system is identified and corrective measure becomes necessary. When the danger level is fixed above the minimum, it being reached by the actual stock, preventive measure is to be taken so that the stock may not go below the minimum level.

It is the point or level of stock which the material stock should never be allowed to reduce. It is generally a level below the minimum level. As soon as the stock of material reaches this point, urgent action is needed for replenishment of stock. This done as follows:

Re-order Quantity: The quantity which is ordered at re-order point is called re-order quantity. This is determined on the basis of minimum stock level and maximum stock level. This is normally used in notation of economic order quantity.

Numerical Solved Examples

Example : Calculate (i) Re-order Level; (ii) Minimum Level; and (iii) Maximum Level for each Component A and from the following information:

Normal Usage 50 Units per week each
Minimum Usage 25 Units per week each
Maximum Usage 75 Units per week each
Re-order Quantity A: 300 Units; B: 500 Units
Re-order Period A: 4 to 6 weeks; B: 2 to 4 weeks

Solution:

(i) Re-order Level = Maximum Usage × Maximum Re-order Period

For Component A = 75 × 6 = 450 Units
For Component B = 75 × 4 = 300 Units

(ii) Minimum Level = Re-order Level – (Normal Usage × Average Re-order Period)

For Component A = 450 – (50 × 5) = 200 Units
For Component B = 300 – (50 × 3) = 150 Units

Note: Average Re-order Period for Component A = 4+6/2 = 5

Average Re-order Period for Component B = 2+4/2 = 3

(iii) Maximum Level = (Re-order Level + Re-order Quantity – (Minimum Usage × Minimum Re-order Period)

For Component A = (450 + 300) – (25 × 4)
= 650 Units

For Component B = (300 + 500) – (25 × 2)
= 750 Units

Example : From the following particulars, calculate: (a) Re-order Level (b) Minimum Level, (c) Maximum Level, (d) Average Level:

Normal Usage 100 units per day
Minimum Usage 60 units per day
Maximum Usage 130 units per day
Economic Order Quantity 5,000 units
Re-order Period 25 to 30 days

Solution:

(a) Re-order Level = Maximum Usage × Maximum Re-order Period
= 130 × 30 = 3,900 units

(b) Minimum Level = Re-order Level – (Normal Usage × Average Re-order Period)
= 3,900 – (100 × 27.5) = 1.150 units

Note: Average Re-order Period = 25+30/2 = 27.5 days

(c) Maximum Level = (Re-order Level + Re-order Quantity or EOQ)
– (Minimum Usage × Minimum Re-order Period)
= (3,900 + 5,000) – 60 × 25)
= 7,400 Units

(d) Average Level = Minimum Level +Maximum Level/2 = 27.5
= 1150+7400/2 = 4, 275 Units

Example : A manufacturer buys costing equipment from out side suppliers Rs. 30 per unit. Total annual needs are 800 units. The following data is available:

Annual Return on Investment 10%
Rent, Insurance etc. per unit per year Re. 1
Cost of Placing an order Rs. 100
Determine Economic Order Quantity.

Solution: Where, EOQ = Economic Order Quantity
R = Annual Requirement of Inventory
Cp = Cost of placing an order
CH = Annual holding Or Carrying cost per unit per year.
Given: R = 800 units, Cp = Rs. 100, CH = Rs. 4 Example : Fair Deal Limited uses Rs. 1,00,000 materials per year. The administration cost per purchase in Rs. 100 and the carrying cost is 20% of the average inventory. The company has a purchase policy on the basis of economic order quantity but has been offered a discount of 0.5% in the case of purchase five times per year. Advise the company whether it should accept new offer or not?

Solution: Given: R (in Rs.) = 1, 00,000, Cp = Rs. 100, P = Re. 1.00,
CH = 1.00 × 20% = Re. 0.20   [Note: Here P = Re. 1, 0.5% or Re. 1 = Re. 1 = Re. 0.95, CH = 0.95 × 20% = Re. 0.199] On the basis of above analysis the offer should be accepted as it will save Rs. 1,02,000 – 1,01,980.05 = Rs. 19.95.

Example : A pharmaceutical factory consumes annually 6,000 kgms. of a chemical costing Rs. 5 per kgm. Placing each order costs Rs. 25 and the carrying cost is 6% per year per kgm. of average inventory. Find the Economic Order Quantity and the total inventory cost.

The factory works for days in a year. If the procurement time is 15 days and safety stock 200 kgms., find the re-order point and maximum and average inventories levels. If the supplier offers a discount of 5% on the cost price for a single order of annual requirement, should the factory accept it?

Solution: Given: R = 6,000 kgms.; P = Rs. 5 per kgm. Cp = Rs. 25; CH = 6% per kgm. per year of average inventory; No. of working days in a year = 300; Procurement time = 15 days; Safety Stock = 200 kgms. Re-order Point = [
R
No. of Working days
x Procurement time]+ safety stock =
=[
6,000
300
x
15
1
]+200

= 300 + 200 = 500 kgms.
Maximum Stock Level = (Re-order Point + Re-order Quantity or EOQ) – (Minimum Usage × Minimum Re-order Period)
= 500 – (20* × 15)
= 500 – 300 = 200 kgms.

* Normal Usage=
R
No. of Working days
=
6000
300
= 20 kgms

Average Stock Level = [
Minimum Stock Level Maximum Stock Level
2
]

=
200+1200
2
=
1400
2
= 700 kgms.

or

Average Stock Level=
q0
2
+ Safety Stock

=
1,000
2
+ 200 = 700 Kgms.

TIC if a single order of 6,000 kgms is placed:
Given: P = Rs. 5 – 5% of Rs. 5 i.e., 5 – .25 = Rs. 4.75

CH = 6% of Average Inventory i.e., 4.75
6
100
= Re. 285;

Cp = Rs. 25; R = 6,000 kgms; q0 = 6,000 kgms.

TIC= (RxP)+[
R
q0
x Cp]+[
6000
2
x 2.5

= 28,500 + 25 + 855 = Rs. 29,380.

The company should accept the offer of 5% discount in purchase price by placing a single order of 6,000 kgms. because the total inventory cost in this case is less by Rs. 30,300 – Rs. 29,380 = Rs. 920 as compared to total inventory cost without discount offer.

Example : A trading company expects to sell 15,000 mixers during the coming year. The cost per mixer is Rs. 200. The cost of storing a mixer for 1 year is Rs. 5 and the ordering cost is Rs. 540 per order. Find the Economic Order Quantity. Would it be profitable to the company to accept a discount offer of 30% on a single order per year? The storing cost continuing to be Rs. 5 per mixer per year. The company should accept the offer of 30% discount as it will save Rs. 30,09,000 –21,38,040 = Rs. 8,70,960.

Example : A manufacturer requires 1,000 units of a raw material, per month. The ordering cost is Rs. 15 per order. The carrying cost in addition to Rs. 2 per unit is estimated to be 15% of average inventory per unit per year. The purchase price of the raw material is Rs. 10 per unit. Find the Economic Lot Size and the total cost. The manufacturer is offered as 5% discount in purchase price for order for 2,000 units or more but less than 5,000 units. A further 2% discount is available for order of 5,000 or more units. Which of the three ways of purchase he should adopt?

Solution:

Given: R = 1,000 units per month or 12,000 units per annum; Cp = Rs. 15 per order;
P = (i) Rs. 10 per unit in case of order for less than 2,000 units.
(ii) Rs. 10 – 5% of Rs. 10 i.e., Rs. 9.50 in case of order for 2,000 or more units but less than 5,000 units.
(iii) Rs. 10 – 7% of Rs. 10 i.e., Rs. 9.30 in case of order for 5,000 or more units.
CH = (i) Rs. 2 + 15% of Rs. 2 of Average inventory i.e., Rs. 2 + 1.50 = Rs. 3.50 per unit per annum in case of order for less than 2,000 units.
(ii) Rs. 2 + 15% of Rs. 9.50 = Rs. 2 + 1.425 = Rs. 3.425 per unit per annum in case of order for 2,000 units or more but less than 5,000 units.
(iii) Rs. 2 + 15% of Rs. 9.70 = Rs. 2 + 1.395 = Rs. 3.395 per unit per annum in case of order for 5,000 or more units.

Alternative I: In case of order for less than 2,000 units:     Quantitative Techniques for management Topics