It has to be typed using software. Handwritten submission will be given zero cre
ID: 2747017 • Letter: I
Question
It has to be typed using software. Handwritten submission will be given zero credit. 1. IGC Distribution Company has three warehouses in the USA. The company would like to perform a pilot study to evaluate the inventory cost in the warehouses. The pilot study will consider the warehouse located in Houston, TX and a distribution valve. Based on the past data it is estimated that demand for the distribution valve in Houston, TX follows normal distribution with mean equal to 2000 units per week and standard deviation for demand is 350 units per week. It is also assumed that inventory holding rate will be 28% per unit per year and cost of each valve is $300. IGC pays $300 each time when an order is place for distribution valves and the lead time is five weeks. The objective customer service level is 95%. i) ii) a) b) c) d) Considering only one of the three warehouses Calculate the economic order quantity, EOQ. (2 points) Calculate safety stock, ss. (2 points) Calculate the reorder point, ROP. (2 points) IGC assumes demands at all warehouses are independent and identical. What will be the total AIL and cost of these three warehouses. (4 points) If IGC decides to serve entire US from only a single location, what would be the new EOQ, ss, and total cost at this single warehouse. (5 points) 2. A company buys item X and item Y from an office supplies wholesale store. Item X costs $10 each and item Y costs $12 each. The ordering cost is $30 for item X and $20 for item Y per order with a common cost of $80. Holding costs are based on a 30% annual interest rate. The company uses an average of 15,000 item X and 13,000 item Y annually. The standard deviation of demand for X is 200 per week and for Y is 320 units per week. Lead time for order arrival is 4 weeks for both products and the company would like to achieve 97% customer service level for both products. a. Assuming that each item is independently ordered using periodic review. Calculate ONLY TX, MaxX, and the total annual cost of item X. (4 points) b. Assuming that these items are jointly replenished, calculate the optimal inventory replenishment interval, T*, order-up-to levels, MaxX and MaxY, and the total annual cost. (6 points)
Explanation / Answer
Answer-1
a) Calculate the economic order quantity, EOQ. (2 points)
Answer: EOQ = SQRT((2*2000*300)/(300*0.28))= 119.52
b) Calculate safety stock, ss. (2 points)
Answer: at 95% z = 1.645
lead time = 5
ROP = The mean usage + z(standard deviations) = 2000 x 5 + 1.645 x 350 = 10575.75
The safety stock = ROP - the mean usage = 10575.75 - 10000 = 575.74
c) Calculate the reorder point, ROP. (2 points)
Answer: ROP = The mean usage + z(standard deviations) = 2000 x 5 + 1.645 x 350 = 10575.75
d) What will happen to ROP and ss if there is a lead time variability as well. Standard deviation of lead time is 2 weeks. (2 points)
Answer: ROP will also vary as per the lead time.
e) IGC assumes demands at all warehouses are independent and identical. What will be the total AIL and cost of these three warehouses. (2 points)
Answer: The total AIL would be the some of all the eoq's.
Answer-2
For product X
EOQ = SQRT((2*15000*30)/(10*0.3)) = 547.72
at 97% z = 1.88
lead time = 4
ROP = The mean usage + z(standard deviations) = 15000 x 4 + 1.88 x 200 = 60376
The safety stock = ROP - the mean usage = 60376 - 60000 = 376
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