Arduino is one of the largest selling items in Adafruit, which deals in circuit
ID: 354997 • Letter: A
Question
Arduino is one of the largest selling items in Adafruit, which deals in circuit boards. The circuit board sells for $150 per unit and costs $100 to purchase. Based on the previous sales data, the average monthly demand is 1,000 boards with a standard deviation of 200 boards and it appears to follow a normal distribution. Adafruit uses 10% annual interest rate to estimate inventory holding costs and the fixed cost per replenishment is $200. Assume that the replenishment lead time is a month, unfulfilled demands are backordered, and backorder cost is $10/unit/year. Compute the optimal replenishment quantity and reorder point.
Explanation / Answer
monthly demand, D = 1000 units
Standard deviation sd = 200
cost of iem, C = $100 per unit
inventory holding cost ,I = 10% per year =10%/12 per month
ordering cost, S = $200 per order
replenishment lead time, LT = 1 month
backorder cost = $10 per unit per year
optimal replinshment quantity, Q = sqrt(2DS/IC) = sqrt(2*1000*200/((0.10/12)*100)) =692.8 = 693 units
reorder Point ,ROP = D*LT+ z*sd *sqrt{LT}
z is value of z for instock probability during lead time, P
assume that, for given question of in stock probability during lead time is 90%
z = 1.29
ROP = 1000*1 + 1.29*200*1 = 1000+258 = 1258 units
The value will change with required probability for in stock
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