Question

For Soumitra: PART II: Ashua’s Shoestore sells a large number of flat shoes. The shoes are shipped from a manufacturer in New Hampshire. Ashua, the proprietor, says, “I want to be sure that I never run out of flat shoes. I always try to keep at least two months supply in stock. When my inventory drops below that level, I order another two months of supply. I’ve been using that method for 20 years and it works.” Each pair of shoes costs $11 and sells for $20. The cost of processing an order and receiving new goods amounts to $100, and it takes three weeks to receive a shipment. Monthly demand is approximately normally distributed with mean 80 and standard deviation 20. Assume a 20 percent annual holding cost, and that a month is four weeks. REMAINING QUESTIONS: Suppose Ashua also recognizes that her order quantity of two months demand may be out-dated. What order quantity would you recommend to reduce costs? What is the average time between orders (also known as the order cycle)? After optimizing the order quantity, what would be the re-order point R be, if Ashua’s new policy in part 3 is applied? What would be the annual inventory holding cost and order cost of this most updated policy?

Answer 1

Given: Monthly Demand = d = 80

Weekly demand = 80 / 4 = 20

Annual Demand = D = 80*12 months = 720 units

Price of shoes = P = $11

Ordering Cost= S = $100

Holding cost = H = 20% = 20% * 11 = $2.2

Order quantity to reduce cost = Economic Order Quantity = EOQ = = = 255.84

Hence, the order quantity recommended to reduce the costs = 256 units

No. of orders = D / EOQ = 720 / 256 = 2.81

Average Time between orders = 12 months / No. of orders = 12 / 2.81 = 4.27 months

Standard Deviation of Monthly Demand = 20

Standard Deviation of weekly demand = Monthly demand / = 20 / = 10

Lead Time = LT = 3 weeks

For never running out of supply, let the service level be 99.99%

For 99.9%, Z value = 3.72

Hence, Reorder point ROP = Demand during Lead time + Safety Stock

Safety stock = Z * * = 64.43

ROP = Weekly Demand * LT + = 20 * 3 + 64.43 = 124.43

Hence, reorder point = 125 units.

Annual inventory holding cost and order cost = Holding cost + Order cost = = = 419.1 + 281 = $700.1

The annual inventory holding cost and order cost of this most updated policy = $700.1

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