Product A\'s inventory is controlled by a continuous review policy. Let us consi
ID: 409802 • Letter: P
Question
Product A's inventory is controlled by a continuous review policy. Let us consider that the replenishment lead-time is 7 days. The weekly demand is normally distributed with mean 250 and standard deviation 64.55. Let us consider the optimal order quantity is 250 units.
1) If we set Re-order point R = 282. Calculate the service level?
2) Calculate the average inventory level?
3) How many stock-out cycles are expected per year? (Assume 350 days per year) and type 1 service level
4) What should the safety stock for a service level of 98%?
5) Suppose there two categories of customers X and Y. We promise a higher level of service to the X customers (e.g., 95% of demand is satisfied from stock); for Y
customers, the service level would be lower, e.g., 85% of demand satisfied from stock. Describe in words how to manage the inventory to serve the two demand categories?
6) Modify your answer to Part A if it is known that the demand is uniformly distributed in [138.2, 361.8] that is it has the same mean and standard deviation.
Explanation / Answer
Q1) Reorder point R = dL+SS where SS is safety stock, d is average daily demand(weekly demand/7) and L is lead time.
dL+z*d*L = 282 => (250*7/7)+z*64.55*7 = 282
z = 0.1874 => Service level = 57.5 % (approx) from z-table
Q2) Average Inventory level I = Q/2+SS = (250/2)+32 = 157 units
Q3) Number of order cycles = D/Q = (250*50)/250 = 50 cycles (50 weeks assuming 350 days per year)
As service level is 57.5, stockout level is 42.5 approx.
Number of stockout cycles = 0.425*50 = 21(approx)
Q4) Safety stock at 98 % service level = z*64.55*7 where z = 2.33(at 98%)
SS = 2.33*64.55*7 = 398
Q5) Depending on the service level and the demands of the customers, the inventory needs to be stocked. The customer with higher service level should be preferred first to fulfill the demand. Stock needs to be calculated based on the demands, service levels, lead time etc. for both customers and stocked accordingly.
Q6) Uniform distribution weekly demand = (138.2+361.8)/2 = 250
Standard deviation = 250
R = 282 => dL+z*d*L = 282
(250*7/7)+z*250*7 = 282 => z = 0.04837
Service level at z = 0.04837 = 52 %(approx)
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