Answered Essay: Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year.

Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year.
  Item cost $ 7.00   Standard deviation of weekly demand 20 per week
  Order cost $ 218.00   Lead time 3 weeks
  Annual holding cost (%) 27 % of item cost   Service probability 99 %
  Annual demand 23,500
  Average demand 470 per week
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 units
  Reorder point 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 cost $

Expert Answer

 

  Optimal order quantity 2328 units
  Reorder point 1491 units
  1. ?Optimal order quantity

Optimal order quantity (EOQ) = ? (( 2*D*O ) / C)

Here, D = Annual Demand = 23,500

O = Order cost = 218

C = Carrying cost = 27% of item cost

Item cost = 7

So, C = 27% of 7 = 1.89

Optimal order quantity (EOQ) = ? ((2*23,500*218) / 1.89)

= 2328 units approximately

Reorder point –

Reorder point= d L + Z s L

d = Average demand = 470 per week

L = Lead time = 3 weeks

Z=2.33 from NORMSINV in excel

s L = ? (L * Standard deviation * Standard deviation) = ?(3*20*20) = 34.64

Reorder point= (470*3) + (2.33*34.64)

= 1410+80.71

= 1491 units

b.

  Holding cost $2199.96
  Ordering cost $2200.60

Holding cost = (EOQ / 2) *Carrying cost

= (2328/2) * 1.89

= $ 2199.96

Ordering cost = (Annual Demand / EOQ) * Ordering cost

=( 23,500 / 2328) * 218

= $ 2200.60

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