Given the following information, formulate an inventory management system. The i
ID: 450603 • Letter: G
Question
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 2,100 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. optimal order quantity = (2*annual demand*order cost/holding cost)^0.5
annual demand = 27,500. order cost = 230. holding cost = 34% of $9 = $3.06
Thus optimal order quantity = (2*27500*230/3.06)^0.5 = 2,033.22 or 2,033 (rounded to nearest whole number).
Re-order point = demand during lead time + z*standard deviation*(lead time)^0.5
z = normsinv(0.98) = 2.05375
Thus re-order point = 550*3 + 2.05375*30*(3)^0.5
= 1650+106.7159 = 1756.71 or 1,752 (rounded off to the nearesr whole number)
b. annual holding cost = average inventory*cost of carrying 1 unit for 1 year. average inventory = optimal quantity/2.
Thus annual holding cost = 2033/2*3.06 = $3,110.49
ordering cost = number of orders*cost per order = demand/optimal quantity*230
= 27500/2033*230 = $3,111.17
c. Total costs as calculated in "b" above = 3110.49+3111.17 = $6,221.66
Now, if ordering costs become = 230-50 = $180 per order and quantity ordered = 2,100.
ordering costs = number of orders*cost per order = demand/ quantity per order*180
= 27500/2100*180 = $2,357.14
holding cost = average inventory*cost of carrying 1 unit for 1 year. average inventory = quantity ordered /2.
= 2100/2*3.06 = $3,213.
Total cost = ordering cost+holding cost = 2357.14+3213 = $5,570.14
Annual savings = costs in case of EOQ - costs in case of order of 2100 units
= 6,221.66 - 5,570.14 = $641.52
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