2. SEC, a Semiconductor (fabrication) Equipment Company, has a central spare par

Question

2. SEC, a Semiconductor (fabrication) Equipment Company, has a central spare parts warehouse to support its chip fabrication plant customers located around the world. As new generations of fab equipment are introduced, the installed base of older models declines and ultimately disappears. As a consequence, SEC must at some point retire support for the older model. Once a model has been scheduled for retirement, SEC makes a "final buy" for service parts that are required to maintain support of the equipment until the retirement date. If inventory of a part runs out before retirement, then an emergency order is placed with the part vendor. Inventory remaining in the warehouse at the retirement date is scrapped for salvage materials. Consider one model that has 50 machines installed throughout the world and SEC has just announced the model will be retired in one year. Focus on part A in this machine. Part A's current cost to purchase is $10,000. The expected cost for an emergency order of part A after the final buy is $25,000. Part A's estimated salvage value is $2,000 and its total annual demand (across the 50 machines) is estimated to be Poisson with mean 3.5. Suppose there are currently 2 of these parts in inventory (a) If SEC does not order any of these parts in the final buy, what fraction of demand until retirement will be filled without the use of an emergency order? (6) (b) How many part A's should SEC order in the final buy to minimize its expected cost? (6)

Explanation / Answer

(a)

The order quantity (Q) = 0

Demand (X) can be fulfilled only when it is up to 2 units. For Poisson (=3.5), the following probability distribution values were generated using Excel.

So, P(Demand <= 2) = 0.32 and P(Demand > 2) = 1 - 0.32 = 0.68. So, a 32% of the order will be fulfilled and a 68% will remain unmnet.

(b)

Cu = Cost of underage (i.e. cost of one unit short of demand) = $25,000 - $10,000 = $15,000
Co = Cost of overage (i.e. cost of one unit excess of demand) = $10,000 - $2,000 = $8,000

Critical Ratio = Cu / (Co+Cu) = 15/(8+15) = 0.6521

At optimality, the target in-stock level should be greater than or equal to the critical ratio. This is possible only when X=4. Since we already have 2 units in the stock, the optimal order quantity (Q*) should be 2 units.

X P(X) F(X) 0 0.030197 0.030197 1 0.105691 0.135888 2 0.184959 0.320847 3 0.215785 0.536633 4 0.188812 0.725445 5 0.132169 0.857614

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