Problem 20-15 Given the following information, formulate an inventory management
ID: 2573510 • Letter: P
Question
Problem 20-15
Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year.
Determine the order quantity and reorder point. (Use Excel’s NORMSINV( ) function to find your z-value and then round that z-value to 2 decimal places. Do not round any other intermediate calculations. Round your final answers to the nearest whole number.)
Determine the annual holding and order costs. (Do not round any intermediate calculations. Round your final answers to 2 decimal places.)
Assume a price break of $50 per order was offered for purchase quantities of 2,000 units per order. If you took advantage of this price break, how much would you save annually? (Do not round any intermediate calculations (including number of setups per year). Round your final answer to 2 decimal places.)
Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year.
Explanation / Answer
a)
1.Optimal order quantity = [2 * (Annual Usage in Units * Ordering Cost) / Annual Carrying Cost per Unit]^(1/2)
= [ 2 * (24000 * 202 ) / ( 9 * 28%) p.u.p.a ] ^ (1/2)
= 1962 units
2. Reorder point = Lead time comsumption + safety stock
Lead time = 1 week
Average consumption per week = 480 units
Thus, Lead time consumption will be = 480 units
Safety stock = Standard deviation of weekly demand * Service probality
= 20 units * 90 %
= 18 units
Reorder point = 480+ 18
= 498 units
b)
Holding cost per annum :
Total no. of orders = Annual demand / EOQ
= 24000 / 1962
= 12 orders
Total ordering cost = No. of orders * ordering cost per order
= 12 * 202
= $ 2424
Total holding cost = order quantity / 2 * holding cost p.u.p.a
= 1962 / 2 * 2.52
= $ 2472
Total cost = 2424 + 2472 = $4896
Holding cost p.u.p.a = $ 9 * 28% = $2.52
c) EOQ = 2000 units
Ordering cost per order = 202 - 50 = 152
Total no. of orders = 24000/ 2000 = 12 orders
Total ordering cost will be = 12 * 152 = $ 1824
Total holding cost = 2000/2 * 2.52 = $ 2520
Total cost will be = 1824 + 2520 = $4344
Total annual saving will be = 4896 - 4344 = $ 552
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