INVENTORY MODELING

1
INVENTORY MODELING

• Service Levels

2
DETERMINING A REORDER POINT, r (With Safety
Stock)

• Suppose lead time is 8 working days
• The company operates 260 days per year
• Suppose a safety stock of SS 13 is desired
• L 8/260 ? .0308 yrs D 6240 /year
• r .0308(6240) 13 ? 192 13 205

Reorder Point r LD SS Where L and D are in
same time units
3
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 Std dev. ?W
• Demand over an n-week period
• normal
• Mean n?W
• Variance n?2W, Std Dev. (?n) ?W

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4
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

5
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 and estimates for µW
  and sW have been attained.
• Demand during lead time is normal
• Mean demand ?L L?W
• Std dev. ?L ?L ?W

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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 ? sW2 ((1052 1302) - 10(120)2)/9 ? 83.33
• Then sW ? ?83.33 9.129

7
DEMAND DISTRIBUTION DURING 8 -DAY LEAD TIME

• Normal distribution for lead time demand
• L 8 days 8/5 1.6 weeks, so
• ?L (1.6)(120) 192
• ?L ? ?1.6 (9.129) 11.55

8
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

?L 11.55
R 219 SS 219 192 27
?
192
0
Z.01 2.33
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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

10
Using the Template
11
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 std deviation for demand
  during lead time
• SS z??L r ?L SS
• Safety Stock Costs ChSS - add to total cost
• Use of Template