A national consumer electronics retailer sells an outsourced product on-line fro
ID: 424467 • Letter: A
Question
A national consumer electronics retailer sells an outsourced product on-line from a central distribution center for $250 a unit. It is estimated that the monthly market demand for this item is normally distributed, with a mean of 200 units and a standard deviation of 40 units. This item’s supplier charges the retailer a wholesale price of $90/unit and a fixed cost of $1,400 for every purchase lot delivered, regardless of the lot size. It has been observed that the delivery lead time for this product is approximately normally distributed with an average of 1 month and a standard deviation of 0.2 month. The retailer incurs a fixed order processing cost of $100 per replenishment order and has a holding cost rate of $0.30/$/year. The retailer employs a continuous review replenishment policy for this item, with an order quantity of 1,000 units and a reorder point of 250 units, based on the recommendation of the company’s comptroller, who estimates that a stockout of this item costs the firm about $9,200 per stockout incident.
(a) What is the retailer’s cycle service level resulting from the current ordering policy? Calculate the current expected annual total relevant cost (i.e. the sum of the average annual ordering, holding and stockout costs).
(b) After attending a full day seminar on 7-Sigma, the comptroller has issued an order that this product’s replenishment policy should be based on its EOQ and a 99% cycle service level. Compute the order quantity and the reorder point which would result from the comptroller’s directive and estimate the resulting annual cost savings, if any.
(c) Comment on the desirability of the recommended 99% cycle service level.
Explanation / Answer
Total ordering cost = 1400+100 =1500
EOQ = [ 2x12 x 200x1500 / 0.3 x90 ]1/2 = 516
(a) 250 = demand during lead time + z xsigma
250 = 1x200 + z x [ sigma demand2 x lead time + sigma lead time x demand2]1/2
50 = z x [ 40x40x1+0.2 x200x200]1/2 = 97.97 =98
z = 50/98 =0.51
which corresponds to the service level of 69.14%
No, of orders = 200x12 /1000 =2.4 =3
No of stockouts = (1-0.6914)x3 = 1
Total cost = 1000/2 x27 + 1500x3 + 9200 = 23200
Case II
ROP = 250+ zx 98
For 99% service level z =2.33
ROP = 250 + 2.33x98 = 479
No. of orders = 2400 / 516 = 4.61 =5
Total cost = 516/2 x27 + 5x1500 +0 = 6966+7500= 14466
(c) The 99% proposition is beneficial as total cost is significantly lower.
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