Annual demand (D) = 2000 boxes
Ordering cost (S) = $62
Price = $76 per box
Holding cost (H) = 28% of price = 28% of $76 = $21.28
Average weekly demand (d) = D/Number of weeks per year
= 2000/52
= 38.46 boxes
a) Economic order quantity (Q*) = sqrt of (2DS / H)
= sqrt of [(2 x 2000 x 62) / 21.28)]
= 107.95 or rounded to 108 boxes
Total cost with EOQ = Holding cost + ordering cost
= [(Q/2)H] + [(D/Q) S]
= [(108/2)21.28] + [(2000/108)62]
= $1149.12 + $1148.15
= $2297.27
If with the current policy order quantity (Q) = 1000 boxes
Total cost = Ordering cost + Holding cost
= [(D/Q) S] + [(Q/2)H]
= [(2000/1000)62] + [(1000/2)21.28]
= $124 + $10640
= $10764
Extra cost = Total cost with current policy – Total cost with EOQ
= $10764 – $2297.27
= $8466.73
b) Standard deviation of weekly demand (sigmad) = 100 boxes
Lead time (L) = 2 weeks
At 99% service level value of Z = 2.33
Reorder point = d x L + (Z x sigma d x sqrt of L)
= 38.46 x 2 + (2.33 x 100 x sqrt of 2)
= 76.92 + (2.33 x 100 x 1.41)
= 76.92 + 328.53
= 405.45 boxes
a) with a periodic review system,
Review period (P) = 2 weeks
Target inventory level = d(P+L) + [Z x sigma d x sqrt of (P+L)]
= 38.46(2+2) + [2.33 x 100 x sqrt of (2+2)]
= (38.46 x 4) + (2.33 x 100 x sqrt of 4)
= 153.84 + (2.33 x 100 x 2)
= 153.84 + 466
= 619.84 boxes