Question

In: Operations Management

QUESTION 1 A local electrical company orders a special type of widget from an Asian supplier...

QUESTION 1

A local electrical company orders a special type of widget from an Asian supplier at a cost of $8.00 per widget. The company has a daily demand of 100 widgets with a standard deviation of 25 widgets. Annual holding cost is $2.50 per widget and cost to place an order of $15. It takes 7 days to receive an order and the company operates 250 days for the year. The manager has set a 96% service level.

  1. Determine the Economic Order Quantity (EOQ).                                                        
  2. What is the standard deviation of demand during the lead time?                                 
  3. Determine the safety stock?                                                                           
  4. What is the reorder point?      
  5. What is the total annual cost at this order quantity?

Solutions

Expert Solution

Average daily demand (d) = 100 units

Number of days per year = 250

Annual demand (D) = d × number of days per year = 100 × 250 = 25000 units

Ordering cost (S) = $15

Holding cost (H) = $2.50

Standard deviation of daily demand (d) = 25 units

Lead time (L) = 7 days

At 96% service level value of Z = 1.75

a) Economic order quantity (EOQ) = √(2DS/H)

= √[(2 × 25000 × 15)/2.50]

= √(750000/2.50)

= √300000

= 547.72 or rounded to 548 units

b) Standard deviation of demand during lead time = d × √L = 25 × √7 = 25 × 2.65 = 66.25 or rounded to 66 units

C) Safety stock = Z × Standard deviation of demand during lead time = 1.75 × 66 = 115.5 or rounded to 116 units

d) Reorder point = d × L + safety stock = 100×7+116 = 700 + 116 = 816 units

e) Annual ordering cost = (D/EOQ)S = (25000/548)15 = $684.31

Annual holding cost = (EOQ/2)H = (548/2)2.50 = $685

Total Annual cost = Annual ordering cost + Annual holding cost = $684.31 + $685 = $1369.31

keosha answered 5 days ago
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