Given the following information, formulate an inventory management system. The i

Question

Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year. Item cost Order cost Annual holding cost (%) 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 weelk a. 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) Optimal order quantity Reorder point 2292 units 1088 units

Explanation / Answer

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 ( 2.05 rounded to 2 decimal places )

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= 2.05x 42.42 = 86.96 ( 87 rounded to next higher whole number )

Reorder point

= Average weekly demand x Lead time ( weeks ) + Safety stock

= 550 x 2 + 87

= 1100 + 87

= 1187

OPTIMAL ORDER QUANTITY ( EOQ ) = 2292

REORDR POINT = 1187

OPTIMAL ORDER QUANTITY ( EOQ ) = 2292

REORDR POINT = 1187

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