Posted on by Judy

Office Supply Company (OSC) has a spare parts warehouse in Alaska to support its office equipment maintenance needs. Once every six months, a major replenishment shipment is received. If the inventory of any given part runs out before the next replenishment, then emergency air shipments are used to resupply the part as needed. Orders are placed semiannually, on January 1 and July 1 of each year. OSC must determine replenishment quantities for its spare parts. Historical data show that total demand for part 1AA-66 over a six-month interval is Poisson distributed with mean 6.5. The cost of inventorying the unneeded part for six months is $5 (which includes both physical and financial holding costs and is charged based on inventory at the end of the six-month period). The unit cost under regular, semiannual shipment is $32 per part, and the cost of an emergency shipment is $50 per part. It is now January 1 and OSC has three 1AA-66 parts currently in inventory. How many parts should they order under their regular shipment for the next six months? A. 2 B. 4 C. 5 D. 8

Mean demand, ? = 6.5
Underage cost, Cu = cost of emergency shipment – cost of normal shipment = 50 – 32 = 18
Overage cost, Co = cost of inventorying the unneeded part = 5
Critical ratio = Cu/(Cu+Co) = 18/(18+5) = 0.7826
Optimal order quantity, Q is determined by Goal seek setting the value of Excel function POISSON(Q,6.5,1) to 0.7826
https://d2vlcm61l7u1fs.cloudfront.net/media%2F2d7%2F2d7c48c9-647a-44f1-84ff-e3c99648cdb7%2FphpNl7wbr.png
The closest value of POISSON function to 0.7826, is for Q = 8
Therefore, optimal order quantity = 8
ANSWER: D. 8
 
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