Demand for a popular athletic shoe is nearly constant at 800

Demand for a popular athletic shoe is nearly constant at 800 pairs per week for a regional division of a national retailer. The cost per pair is $54. It costs $72 to place an order, and annual holding costs are charged at 22% of the cost per unit. The lead time is two weeks.

a. What is the EOQ?

b. What is the reorder point?

c. What is the cycle time?

d. What is the total annual cost?

Solution

a. Annual holding cost per unit = 54 * 22% = 11.88 D = 800 / wk = 41,600 / yr H = 11.88 S = 72 EOQ = sqrt ( (2DS) / H ) = sqrt( (2*41,600*72) / 11.88 ) = 710.10 = 710 c. Cycle time = Q / D = 710 / 41,600 = 0.01707 yrs = 6.23 days b. LT = 14 days CT = 6.23 days if LT > CT, reorder point = fraction (LT / CT) * Q = fraction (14 / 6.23) * 710 = fraction(2.247)*710 = 0.247*710 = 175.5 = 175 d. Total annual cost = Cost os shoes + annual holding cost + ordering cost = 41,600*54 + 710/2 * 11.88 + 41,600/710 * 72 = 2,254,835.99