2. A machine shop purchases spare parts for several machines with a mean of 1200
ID: 360849 • Letter: 2
Question
2. A machine shop purchases spare parts for several machines with a mean of 1200 and standard deviation of 175 per year. The cost of each part is S24, and the cost of placing an order is (a) $24. The inventory carrying cost is S3.0 per unit per year. Assuming that shortages are backordered with a shortage cost per unit short is $6.6 based on the average shortage, determine the optimal order quantity and the reorder level Assuming that any unsatisfied demand is lost and each part is sold at a price of $35, determine the optimal order quantity and the reorder level. (b)Explanation / Answer
Optimal order quantity Q*
Q* = 2 D C0 / ch
D = Demand of units of inventory per year
C0 = Ordering cost per order
Ch = CC = Carrying or holding cost per unit per period of time (Rs/unit/year)
Q* = 2 D C0 / ch
= 2 * 1200 * 24 / 3
= 138.56
Reorder Level Cs
Cs = SC * 2Q*
Cs = Reorder Point
SC = Shortage or stock out cost
Q = optimal order quantity (per order)
Cs = SC * 2Q*
= 6.6 * 2 * 138.56
= 1828.9
When each part is sold at a price of $35, then
Optimal order quantity Q*
Q* = 2 D C0 / ch
= 2 * 1200 * 35 / 3
= 167.33
Reorder Level Cs
Cs = SC * 2Q*
= 6.6 * 2 * 167.33
= 2208.7
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