Given the following information, formulate an inventory management system. The i
ID: 422258 • Letter: G
Question
Given the following information, formulate an inventory management system. The item is weeks a year. demanded 50 ltem cost Order cost Annual holding cost (96) S 9.00 $258.00 Standard deviation of weekly demand Lead time 30 per week 2 weeks 98% 30% of item cost Service probability Annual demand Average demand 27,500 550 per week a. Determine the order quantity and reorder point (Use Excel's NORMSINVC) 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.) Optimal order quantity Reorder point units units b. Determine the annual holding and order costs. (Do not round any intermediate calculations. Round your final answers to 2 decimal places.) Holding cost Ordering costExplanation / Answer
Answer to question a :
Following data are provided :
Annual demand = D = 27500
Order cost = Co = $258
Annual unit holding cost = Ch = 30% of item cost = $ 0.3 x 9 = $2.7
Optimal order quantity ( EOQ )
= square root ( 2 x Co x D/ Ch )
= square root ( 2 x 258 x 27500 / 2.7)
= 2292.49 ( 2292 rounded to nearest whole number )
Z value for service probability of 98% = NORMSINV ( 0.98 ) = 2.0537
Standard deviation of weekly demand = 30
Lead time = 2 weeks
Therefore, standard deviation of demand of demand during lead time
= Standard deviation of weekly demand x Square root ( Lead time )
= 30 x Square root ( 2 )
= 30 x 1.414
= 42.42
Therefore,
Safety stock = Z value x Standard deviation of demand during lead time= 2.0537x 42.42 = 87.11 ( 88 rounded to next higher whole number )
Reorder point
= Average weekly demand x Lead time ( weeks ) + Safety stock
= 500 x 2 + 88
= 1000 + 88
= 1088
OPTIMAL ORDER QUANTITY ( EOQ ) = 2292
REORDR POINT = 1088
Answer to question b :
Annual holding cost
= annual unit holding cost x average inventory
= Ch x EOQ/ 2
= $2.7 x 2292/2
= $ 3094.20
Annual ordering cost
= Ordering cost x Annual demand / EOQ
= $258 x 27500 / 2292
= $3095.54
HOLDING COST = $3094.20
ORDERING COST = $3095.54
Total ordering and holding cost = $3095.54 + $3094.20 = $6189.74
Answer to question c :
Revised order quantity = 2300
Number of orders in a year = 27500 / 2300 = 11.956
Total saving in annual purchase price
= Price break of $55 / order x 11.956 orders
= $657.58
Annual ordering cost
= Ordering cost x Number of orders
= Co x Annual demand / order quantity
= $258 X 27500 / 2300
= $3084.78
Annual inventory holding cost
= Annual unit inventory holding cost x average inventory
= $2.7 x 2300/2
= $3105
Total inventory holding cost plus ordering cost = $3105 + $3084.78 = $6189.78
As , it can be seen that total inventory holding plus ordering cost ( $6189.78 ) after the price break is almost same as total inventory holding and ordering cost ($6189.74 ) before the price break.There is a savings of $6189.78 - $6189.74 = $0.04
However there is a savings of $657.58 a in purchase price after the price break.
Therefore annual savings
= Savings in purchase price + Savings in inventory holding plus ordering cost
= $657.58 + $0.04
= $657.62
ANNUAL SAVINGS = $657.62
OPTIMAL ORDER QUANTITY ( EOQ ) = 2292
REORDR POINT = 1088
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