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Module C5 Reorder Point/Service Levels
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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
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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
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Actual Demand Distribution Suppose on a short term basis demand actually more closely follows a normal distribution with: –Weekly mean demand W –Weekly variance 2 W, Weekly St’d dev. W, Demand over an n-week period: –normal –Mean n W _ –Variance = n 2 W, St’d Dev. = ( n) W
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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
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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 = L W –St’d 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 W 2 s W 2 = ((105 2 +…+130 2 ) - 10(120) 2 )/9 83.33
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DEMAND DISTRIBUTION DURING 8 -DAY LEAD TIME Normal 8 days = 8/5 = 1.6 weeks, so L = (1.6)(120) = 192 L 2 (1.6)(83.33) = 133.33 _____ L 133.33 = 11.55
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XZXZ 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 0Z.01 = 2.33.01 L = 11.55 ? 192
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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 = C h SS = 1.40(27) = $37.80 This should be added to the TOTAL ANNUAL COST
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Using the Template Enter Lead Time Information Select Cycle Service Level Worksheet Reorder Point
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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 = z L r* = L + SS Safety Stock Costs = C h SS -- add to total cost Use of Template
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