Module C5

Reorder Point/Service Levels

DETERMINING A REORDER POINT, r* (Without Safety Stock)

• Suppose lead time is 8 working days

• The company operates 260 days per year

• r* = LD where L and D are in the same time units

• L = 8/260 .0308 yrs D = 6240 /year

r* = .0308(6240) 192

OR,

L = 8 days; D/day = 6240/260 = 24

r* = 8(24) = 192

DETERMINING A REORDER POINT, r* (With Safety Stock)

• Suppose lead time is 8 working days

• The company operates 260 days per year

• r* = LD + SS

• Suppose a safety stock of SS = 13 is desired

• L = 8/260 .0308 yrs D = 6240 /year

r* = .0308(6240) +13 192 +13 = 205

Actual Demand Distribution

• Suppose on a short term basis demand actually more closely follows a normal distribution with:– Weekly mean demand W

– Weekly variance 2W, Weekly St’d dev. W,

• Demand over an n-week period:– normal

– Mean nW _

– Variance = n2W, St’d Dev. = (n) W

Calculating Q*

• Over the course of a year, the standard deviation becomes small relative to the mean value -- hence a common practice is to ignore any variability and calculate Q* by the usual EOQ formula

Lead Time Demand• Lead times, however, tend to be short and hence

variability must be considered.

• A cycle service level is supplied to the modeler -- the probability of not running out of stock during the lead time period.

• Suppose lead time is L weeks – Demand during lead time is normal

– Mean demand = L = LW

– St’d dev. = L = L W

Example -- Allen Appliance

• Suppose we can assume that demand follows a normal distribution– This can be checked by a “goodness of fit” test

• From our data, over the course of a week, W, we can approximate W by (105 + … + 130)/10 = 120

W2 sW

2 = ((1052 +…+1302) - 10(120)2)/9 83.33

DEMAND DISTRIBUTION DURING 8 -DAY LEAD TIME

• Normal

• 8 days = 8/5 = 1.6 weeks, so

L = (1.6)(120) = 192

L2 (1.6)(83.33) = 133.33

_____ L 133.33 = 11.55

X

Z

SAFETY STOCK

• Suppose we wish a cycle service level of 99%– WE wish NOT to run out of stock in 99% of our

inventory cycles

0 Z.01 = 2.33

.01

L = 11.55

?192

Calculating r* and Safety Stock Costs

• Reorder point, r* = L + z.01 L =

192 + 2.33(11.55) 219

• Safety stock SS = 2.33(11.55) = 27

• Safety stock cost = ChSS = 1.40(27) = $37.80

This should be added to the TOTAL ANNUAL COST

Using the Template

EnterLead TimeInformation Select

Cycle Service LevelWorksheet

Reorder Point

Module C5 Review• In the short run, demand may seem to follow a

probability distribution (normal)

• In the long term, variability is relatively insignificant in magnitude compared to the mean value-- so calculate Q* in usual way.

• Determine a cycle service level = 1- • Determine the mean and st’d deviation for demand

during lead time

• SS = zL r* = L + SS

• Safety Stock Costs = ChSS -- add to total cost

• Use of Template