Given the following information, formulate an inventory management system. The i
ID: 362157 • Letter: G
Question
Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year.
a. Determine the order quantity and reorder point. (Use Excel's NORMSINV() function to find the correct critical value for the given -level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)
b. Determine the annual holding and order costs. (Round your answers to 2 decimal places.)
c. Assume a price break of $55 per order was offered for purchase quantities of 2,500 or more units per order. If you took advantage of this price break, how much would you save annually? (Round your answer to 2 decimal places.)
Item cost $ 8.00 Standard deviation of weekly demand 20 per week Order cost $ 287.00 Lead time 3 weeks Annual holding cost (%) 33 % of item cost Service probability 99 % Annual demand 27,400 Average demand 548 per weekExplanation / Answer
Optimal Order Quantity ( EOQ ) will be determined as:
EOQ = Square root ( 2 x Co x D / Ch )
Co = Ordering cost = $287
Ch= Annual unit holding cost = 33% of item cost $8 =$ 2.64
D = Annual demand = 27400
Therefore ,
EOQ = Square root ( 2 x 287 x 27400 / 2.64)
= 2440.78 ( 2441 rounded to nearest whole number )
Given are following data :
Standard deviation of weekly demand = 20 per week
Lead time = 3 weeks
Therefore,
Standard deviation of demand during lead time
= Standard deviation of weekly demand x Square root ( Lead time )
= 20 x Square root ( 3 )
= 20 x 1.732
= 34.64
Corresponding Z value at service probability of 99% ( 0.99) = NORMSINV ( 0.99) = 2.326
Therefore ,
Safety stock
= Z value x Standard deviation of demand during lead time
= 2.326 x 34.64
= 80.57 ( 81 rounding to nearest whole number )
Reorder point = Average demand x Lead time + Safety stock
= 548 x 3 + 81 = 1725
OPTIMAL ORDER QUANTITY = 2441
REORDER POINT = 1725
Annual Holding cost
= Annual unit inventory holding cost x average Inventory
= Ch x Optimal order quantity / 2
= $2.64 x 2441/2
= $3222.12
Annual ordering cost
= Ordering cost per order x Number of orders
= Co x Annual demand / Optimal order quantity
= $ 287 x 27400 / 2441
= $3221.54
ANNUAL HOLDING COST = $3222.12
ANNUAL ORDERING COST = $3221.54
Total annual cost at Optimal order quantity
= $3222.12 + $3221.54
= $6443.66
At Purchase quantity = 2500 :
Ordering cost per order = $287 - $55 = $232
Number of orders = annual demand/ 2500 = 27400/2500
Hence, annual ordering cost = $ 232 x 27400 / 2500 = $2542.72
Annual inventory holding cost
= Annual unit inventory holding cost ( Ch) x Average inventory ( = 2500/2)
= 2.64 x 2500 / 2
= $3300
Thus total annual cost = $2542.72 + $3300 = $5842.72
Hence , annual savings = $6443.66 - $5842.72 = $600.94
ANNUAL SAVINGS = $600.94
OPTIMAL ORDER QUANTITY = 2441
REORDER POINT = 1725
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