Safety stocks final

SAFETY STOCKSBy:-

SHASHANK SHEKHER SINGH- 83

VIKAS SINGH-104

KUMAR RAVI-111

ANKIT SEMWAL -125

WAZIBUR REHMAN-106

NIKUNJ SHARMA-143

SAFETY STOCKS DEFINED

Safety stock is a term that is used to describe the amount of inventory or stock that is kept on hand in order to reduce the chance of a temporary shortfall of materials from taking place.

Also known as buffer stock. This type of inventory is helpful in dealing

with sudden upswings in demand or just for making sure there are enough raw materials and supplies on hand to keep production going while waiting for the next scheduled delivery of materials from a supplier.

CONTINUED..

The amount of safety stock an organization chooses to keep on hand can dramatically affect their business.

Too much safety stock can result in high holding costs of inventory. In addition, products which are stored for too long a time can spoil, expire, or break during the warehousing process.

Too little safety stock can result in lost sales and, thus, a higher rate of customer turnover. As a result, finding the right balance between too much and too little safety stock is essential.

WHY SAFETY STOCKS ARE NEEDED?

The main goal of safety stocks is to absorb the variability of the customer demand.

Indeed, the Production Planning is based on a forecast, which is (by definition) different from the real demand.

By absorbing these variations, safety stock improves the customer service level.

By creating a safety stock, you will also prevent stock-outs from other variations : an upward trend in the demand a problem in the incoming product flow

(machinery breakdown, supplies delayed, strike, ...)

UNCERTAINTIES IN INVENTORY MANAGEMENT

In actual case of inventory model, there are always uncertainties stemming from two basic reasons:Variability in sales, hence variability in the demand for the

materials or the consumption of the material.Delay in supply of raw material.

Demand is a prediction based on past history, trend factor(s), and/or known future usage of a product. The item’s actual usage will probably be more or less than this quantity. Safety stock is needed for those occasions when actual usage exceeds forecasted demand. It is “insurance” to help ensure that you can fulfill customer requests for a product during the time necessary to replenish inventory.

The anticipated lead time is also a prediction, usually based on the lead times from the last several stock receipts. Sometimes the actual lead time will be greater than what was projected. Safety stock provides protection from stock outs when the time it takes to receive a replenishment shipment exceeds the projected lead time.

SERVICE LEVEL

Service level (denoted as Fx) is typically measured as Fx = (demand filled) over (total demand).

Service level may also be defines as demand fulfilled over a particular period of time.

Service Level may also be defined as the Ratio of ‘No of units supplied without delay’ and ‘No of units demanded’

SAFETY STOCK AND SERVICE LEVEL

Safety stock determines the chance of a stockout during lead time

The complement of this chance is called the service level

Service level is defined as the probability of not incurring a stockout during any one lead time

The higher the probability inventory will be on hand, the more likely customer demand will be met.

Service level of 90% means there is a .90 probability that demand will be met during lead time and .10 probability of a stockout.

SAFETY STOCK AND SERVICE LEVEL

Service Level 0.5 1.0

S

RISK LEVEL

Defined as the percentage of demand that will not be fulfilled during a particular period of time

Service level= 1- Risk level

SAFETY STOCK AND REORDER POINT

Without safety stock:

With safety stock:

daysintimelead

unitsindemanddaily

unitsinpointreorderwhere

L

n

R

nLR

unitsin stock safety where

SS

SSnLR

SAFETY STOCK EXAMPLE

Daily demand = 20 units Lead time = 10 days S.D. of lead time demand = 50 units Service level = 90%Determine:

1. Safety stock2. Reorder point

SAFETY STOCK SOLUTION

units264641020 SSnLR

28.1:BAppendixFrom z

Step 1 – determine z

Step 2 – determine safety stock

Step 3 – determine reorder pointunits645028.1 SS

CALCULATION OF SERVICE LEVEL can also be calculated by equating Carrying

cost per unit per annum with shortage cost per unit per annum.

i.e. Cc = Cs = Csus * Prob. Of shortage *

Number of times shortage situations can

occur in a year = Csus * (1 – Fx) * R/Q (1 – Fx) = Cc * (Q÷R) * 1 / Csus Fx = 1 - Cc * (Q÷R) * 1 / Csus

CONTD.

Another formula for service level is Fx=Ku/(Ku+Ko) being

Ku= Under stocking costKo=Overstocking cost

Ajay bakery makes ginger bread; one of its fastest selling products. From past history Ajay estimates the demand pattern to be:

Demand(no. of buns)

Probability of Demand

400 0.05

500 0.10

600 0.20

700 0.30

800 0.20

900 0.10

1000 0.05The selling price of each bread is 80 paise. The buns that are not sold on the day they are made, are sold the next day at the reduced price of 40 paise each. If the cost of each bun is 55 paise, what is optimum number of buns Ajay should make?

NUMERICAL

Here Ku the understocking cost, is the profit forgone, which is the difference between sales price per unit and unit cost: (80p – 55p)= 25p

Ko, the overstocking cost, is the loss in the sale on the next day; which is the difference between the cost per unit and the salvage value per unit:

55p – 40p= 15p

Fx=Ku/(Ku+Ko)= 0.25/0.25+0.15=0.625

Demand(no. of buns)

Probability of Demand

400 0.05

500 0.10

600 0.20

700 0.30

800 0.20

900 0.10

1000 0.05

Cumm.frequency

0.05

0.15

0.35

0.65

0.85

0.95

1.00

This is met at x=700, where the cumulative probability is 0.650 slightly exceeding the value 0.625

THE CONVENTIONAL WAYS OF CALCULATING SAFETY STOCK

There are two common conventional methods for calculating the safety stock quantity for a product:

Percentage of Lead Time Demand Days Supply It refer to two variables, “forecast demand”

and “usage.” Forecast demand is a prediction of how much of a product will be sold or otherwise used in a particular month, and usage is the quantity that was actually sold or used.

Percentage of Lead Time Demand

Demand/Day = (390/30) = 13 pieces

Projected Lead Time = 8 days

Demand During the Lead Time = (8 x 13) = 104 pieces

Safety Stock = (104 x 50%) = 52 pieces

Inventory consultant Gordon Graham long advocated that, for most items, 50% of lead time demand provides an adequate safety stock quantity. Let’s look at an example:

This method is easy to understand but it tends to maintain too much or too little safety stock for many items. For example:

Products with long but very reliable lead times and with fairly consistent demand. If we use this method for an imported product with a 12-week lead time, we’ll keep six weeks stock in reserve as safety stock. If we usually receive the shipment on time and demand doesn’t vary substantially from month to month, we’ll have too much safety stock – in other words, too much money tied up in non-productive inventory.

DAYS SUPPLY

Products with very short lead times and significant variations in demand from month to month. If a product had a one-week lead time, this method will keep a three or day supply of the item in reserve as safety stock. If usage tends to vary significantly from month to month, there probably won’t be enough safety stock available to consistently fill customer demand and the company will experience stock outs.

The days supply method allows a buyer to manually specify a number of days supply of a product to hold in reserve as safety stock. Because a buyer usually does not have the time to review the safety stock parameters for every item each month, he or she will probably set the days supply to provide more than enough safety stock. After all, in the eyes of most buyers, excess inventory is usually preferable to stock outs. As a result, the days supply method often results in the accumulation of non-producing inventory.

SAFETY STOCK CALCULATION FOR CONSTANT LEAD TIME AND NORMALLY DISTRIBUTED DDLT

The projected level of demand for a product from consumers during its lead time from the supplier to the retailer

For the desired service level, find the value of “Z” from the table “Area under Normal Curve”

Other notations are

µL be Mean demand during lead time (DDLT)

σL be standard deviation of demand during

lead time

let x be stock at which order is placed

CONTD.

((X - µL)/σL = Z

Safety stock is = Z x σL

Continuous System: Deterministic Model

• The reorder point is the inventory level at which a new order is placed.

• Order must be made while there is enough stock in place to cover demand during lead time.

• Formulation:• R = dL• where d = demand rate per time period• L = lead time

Reorder Point

Reorder Point and Safety Stock

NUMERICAL 1

ABC Ltd. is engaged in production of tires. It purchases rims from DEL Ltd. an external supplier. DEL Ltd. takes 10 days in manufacturing and delivering an order. ABC's requires 10,000 units of rims. Its ordering cost is $1,000 per order and its carrying costs are $3 per unit per year. The maximum usage per day could be 50 per day. Calculate safety stock.

SOLN.

Maximum daily usage is 50 units and average daily usage is 27.4 (10,000 annual demand ÷ 365 days).

Safety Stock = (50-27.4) × 10 = 226 units. Reorder Level = Safety Stock + Average

Daily Usage × Lead Time Reorder Level = 226 units + 27.4 units × 10

= 500 units.

NUMERICAL 2

Costas Hamburger Shop uses 20 gallons of cola per day. The lead time is normally distributed with a mean of 5 days and a standard deviation of 2 days. Determine the level of safety stock and optimal reorder point. Assume a service level of 99%.

SOLN.

ROP = Expected demand during lead time + safety stock

d = 20 gallons per day.LT= 5 days.σLT = 2 days.

For a service level of 99%, z = 2.33. Safety stock = 2.33 (20)(2) = 93.2 gallons.ROP = 20(5) + 93.2 = 193.2 gallons

NUM. 3

Presume that Litely carries a modern white kitchen ceiling lamp that is quite popular. The anticipated demand during lead-time can be approximated by a normal curve having a mean of 180 units and a standard deviation of 40 units. What safety stock should Litely carry to achieve a 95% service level?

To find the safety stock for a 95% service level it is necessary to calculate the 95th percentile on the normal curve. Using the standard Normal table from the text, we find the Z value for 0.95 is 1.65 standard units. The safety stock is then given by:

( )165 40 180 66 180 246. * Ceiling Lamps

A TV dealer finds the cost of holding a TV in stock for a week as Rs 30 and cost of unit shortage as Rs 70. For a particular model of TV, the weekly sales distribution is given in the table below. How many units should the dealer order per week?

Sales 0 1 2 3 4 5 6

Prob. 0.05 0.10 0.20 0.25 0.20 0.15 0.05

SAFETY STOCK – EXAMPLE 3 (SOLUTION)

Ordering Strategy / Week

D Pr

0 0.05

1 0.10

2 0.20

3 0.25

4 0.20

5 0.15

6 0.05

Weekly Cc = Rs. 30 , Cs = Rs. 70

SAFETY STOCK – EXAMPLE 3 (SOLUTION)


D Pr 0 1 2 3 4 5 6

0 0.05

1 0.10

2 0.20

3 0.25

4 0.20

5 0.15

6 0.05


SAFETY STOCK – EXAMPLE 3 CONTD.


D Pr 0 1 2 3 4 5 6

0 0.05 0

1 0.10 70

2 0.20 140

3 0.25 210

4 0.20 280

5 0.15 350

6 0.05 420Expected cost




D Pr 0 1 2 3 4 5 6

0 0.05 0 30 60 90 120 150 180

1 0.10 70 0 30 60 90 120 150

2 0.20 140 70 0 30 60 90 120

3 0.25 210 140 70 0 30 60 90

4 0.20 280 210 140 70 0 30 60

5 0.15 350 280 210 140 70 0 30

6 0.05 420 350 280 210 140 70 0Expected cost



D Pr 0 1 2 3 4 5 6

0 0.05 0 30 60 90 120 150 180

1 0.10 70 0 30 60 90 120 150

2 0.20 140 70 0 30 60 90 120

3 0.25 210 140 70 0 30 60 90

4 0.20 280 210 140 70 0 30 60

5 0.15 350 280 210 140 70 0 30

6 0.05 420 350 280 210 140 70 0Expected cost 97



D Pr 0 1 2 3 4 5 6

0 0.05 0 30 60 90 120 150 180

1 0.10 70 0 30 60 90 120 150

2 0.20 140 70 0 30 60 90 120

3 0.25 210 140 70 0 30 60 90

4 0.20 280 210 140 70 0 30 60

5 0.15 350 280 210 140 70 0 30

6 0.05 420 350 280 210 140 70 0Expected cost 217 152 97 62 52 62 87



D Pr 0 1 2 3 4 5 6

0 0.05 0 30 60 90 120 150 180

1 0.10 70 0 30 60 90 120 150

2 0.20 140 70 0 30 60 90 120

3 0.25 210 140 70 0 30 60 90

4 0.20 280 210 140 70 0 30 60

5 0.15 350 280 210 140 70 0 30

6 0.05 420 350 280 210 140 70 0Expected cost 217 152 97 62 52 62 87

EXAMPLE 4

Sai electrical buy electrical switches for the assembly of variety of electrical products. Sai observes that the usage pattern of these bought- out switches follow normal distribution with a mean of 1000 switches per week and a standard deviation of 200. the buying process takes one week. The inventory holding cost is Rs.5/- per unit and the cost of ordering is Rs. 200/- per order. Sai allows for only 2 stock out situation in a year. Compute the safety stock required.

Thank you

Education

Safety stocks final