Question

A small copy center uses 6 600-sheet boxes of copy paper a week. Experience suggests that usage can be well approximated by a normal distribution with a mean of 6 boxes per week and a standard deviation of .60 boxes per week. 2 weeks are required to fill an order for letterhead stationery. Ordering cost is $6, and annual holding cost is 35 cents per box.
Use Table.

a. Determine the economic order quantity, assuming a 52-week year. (Round your answer to the nearest whole number.)

EOQ             boxes

b. If the copy center reorders when the supply on hand is 13 boxes, compute the risk of a stockout. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Risk            

c. If a fixed interval of 7 weeks is used for ordering instead of an ROP, how many boxes should be ordered if there are currently 28 boxes on hand, and an acceptable stockout risk for the order cycle is .0228? (Round "z" value to 2 decimal places and final answer to the nearest whole number.)

Q₀           

Answer 1

Average weekly demand(d) = 6 boxes

Number of weeks per year = 52

Annual demand (D) = d × number of weeks per year = 6 × 52 = 312 boxes

Standard deviation of weekly demand (d) = 0.60 boxes

Ordering cost (S) = $6

Holding cost (H) = 35 cents = $0.35

Lead time (L) = 2 weeks

a) Economic order quantity = √(2DS/H)

= √[(2 × 312 × 6)/0.35]

= √(3744/0.35)

= √10697.14285

= 103.43 or rounded to 103 boxes

b) reorder point = 13 boxes

Reorder point = d × L + (Z × d × √L)

=> 13 = 6 × 2 + (Z × 0.60 × √2)

=> 13 = 12 + (Z × 0.60 × 1.41421)

=> 13 = 12 + (0.8485 × Z)

=> 0.8485 × Z = 13-12

=> 0.8485 × Z = 1

=> Z = 1/0.8485

=> Z = 1.18

The z value of 1.18 corresponds to a service level of 0.8800

so the risk of stockout = 1-service level = 1-0.8800 = 0.1200

c) order interval(T) = 7 weeks

on hand inventory (I) = 28 boxes

Risk of stockout = 0.0228. So service level = 1-0.0228 = 0.9772

At a service level of 0.9772 value of Z = 2.00

Order quantity = d(T+L)] + [Z X d X √ (T+L)] - I

= [6(7+2)] + [2.00 X 0.60 X √ (7+2)] - 28

= (6X9) + (2.00 X 0.60 X √9) - 28

= 54 + (2.00 x 0.60 x 3 ) - 28

= 54 + 3.6 - 28

= 57.6-28

= 29.6 or rounded to 30 boxes