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INVENTORY MODELING

INVENTORY MODELING. Service Levels. 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.

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INVENTORY MODELING

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  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 St’d dev. = W • Demand over an n-week period: • normal • Mean nW • Variance = n2W, St’d Dev. = (n) W _

  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 Lweeks and estimates for μW and σW have been attained. • Demand during lead time is normal • Mean demand = L = LW • St’d dev. = L = L W _

  6. 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 σW = 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 .01 192 + 2.33(11.55) X Z 219 • 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

  9. 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 Reorder Point Round r* to 219 Enter SS = 219 – 192 = 27 Into SS of appropriate worksheet Enter Lead Time Information Select Cycle Service Level Worksheet

  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 st’d deviation for demand during lead time • SS = zL r* = L + SS • Safety Stock Costs = ChSS - add to total cost • Use of Template

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