Weekly demand for diskettes at a retailer is normally distributed with a mean of

Question

Weekly demand for diskettes at a retailer is normally distributed with a mean of 1000 boxes and a standard deviation of 150. Currently, the store places orders via paper that is faxed to the supplier. Assume 50 working weeks in a year and the following data:
1. Lead time for delivery of an order is 4 weeks
2. Fixed cost per order is $100
3. Each box of diskettes costs $1
4. Holding cost is 25% of purchase cost

(a) Assuming that the retailer wants the probability of stocking out in a cycle to be no more than 5%, provide a recommendation to the store manager (who has never
been to business school) on the inventory policy (a policy regarding EOQ and ROP).

(b) Claiming that it will lower lead time to 1 week, the supplier is trying to push an electronic data interchange (EDI) system on the retailer. Provide a brief qualitative discussion on the benefits and costs of such a system. How would you make the system adoption decision?

Explanation / Answer

a. EOQ = (2*annual demand*order cost/annual carrying cost per unit)^0.5

weekly mean demand = 1,000 boxes. no. of weeks = 50. Thus annual demand = 1,000*50 = 50,000 boxes. order cost = $100 and holding cost = 25% of $1 = $0.25

Thus EOQ = (2*50,000*100/0.25)^0.5 = 40,000,000^0.5 = 6,324.56 boxes or 6,325 boxes (rounded off)

Thus the store manager should place an order of 6,325 boxes to minimize the total costs of inventory (holding cost+ordering cost).

Re-order point (ROP) = demand during lead time+safety stock.

demand during lead time = weekly demand*lead time = 1,000 boxes*4 weeks = 4,000 boxes.

safety stock = z*standard deviation of weekly demand*(number of weeks of lead time)^1/2

z at 95% service probability (1-5%) = 1.96 (from the z table). So, safety stock = 1.96*150*(4^0.5) = 1.96*150*2 = 588.

ROP = demand during lead time+safety stock = 4,000+588 = 4,588 boxes.

b. When lead time is reduced to 1 week, then ROP will also come down. demand during lead time will be = 1*1000 = 1,000 boxes. safety stock = 1.96*150*(1^0.5) = 294. Thus ROP = 1,000+294 = 1,294 boxes.

So, we can see that the safety stock as well as the ROP has reduced. Lower safety stocks will result in lower invetory holding costs. Lower lead time will also lead to increase in cash flow as inventory of diskettes will be converted into sales quickly, and money and working capital will not be tied in high safety stock and high ROP.

The system adoption decision will be made by calculating the cost savings due to lower lead time and comparing it with the costs of the EDI. If the savings are greater than the cost of the EDI, the system should be adopted.

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