Roscoe’s Maple bar sells frozen maple bars purchased from a vendor that remain a
ID: 459083 • Letter: R
Question
Roscoe’s Maple bar sells frozen maple bars purchased from a vendor that remain as fresh as they have ever been for essentially an unlimited time in the freezer. They are open 365 days of the year with average daily demand of 100 (standard deviation 25). Including cost of capital and cost of freezer space, the estimate that each bar costs about $4 per year per bar for inventory. They estimate that it costs about $50 each time they receive a shipment of bars to unload the truck, sign the paperwork, etc. What is the economic order quantity? The boss says “I would be willing to live with about one stockout per year .” Given that the lead time is 2 days (standard deviation 1 day), what should the reorder point be for an (R,Q) inventory system?
Explanation / Answer
Economic Order Quantity = 955.25
Reorder Point = 271.28
Number of order cycles per year = Annual Demand / EOQ = 36500 / 955.25 = 38.2
Service level allows one stockout per year. Therefore, service Level = (38.2 - 1)/38.2 = 97.38%.
Formula and Calculations are given below
Formula Value Daily Demand, µD µD = 100 Standard Deviation of Daily Demand, D D = 25 Working days per year, Y Y = 365 Annual Demand, D = Y*µD D = Y*µD 36500 Lead Time (days) (L) L = 2 Standard Deviation of Lead Time, L L = 1 Service level SL = 97.38% Z-value corresponding to Service Level Z = 1.94 Safety stock (ss) ss = Z(L*D2 + µD*L2 ) 71.28 Reorder Point (ROP) ROP = µD*L + ss 271.28 Ordering Cost (O) O = 50 Annual Holding Cost (H) H = 4 Lot Size / Optimal Order Qty (Q) Q = (2*D*O/H) 955.25Related Questions
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