The company is using a lot size of 700 units per order.Calculate the safety stock required for a cycle service level of 97.5%.In addition, what is the cost difference between the current policy and using the EOQ lot size? (safety stock/cost)
The expected annual demand is 123,670 units.The standard deviation for a week is 345 units.The ordering cost is $200 and the carrying cost is $3.00 per unit per year.In addition, the lead time is 3 weeks and there are 52 weeks per year.

Question

Quizplus · Accepted Answer

Using the formula for safety stock, SS = z*σ*sqrt(LT), where z = 2.24 for a cycle service level of 97.5%, σ = 345 units, and LT = 3 weeks, we get SS = 1171 units.

To calculate the cost difference between the current policy and using the EOQ lot size, we need to calculate the annual cost for each option.

Current policy:
Number of orders per year = Annual demand / lot size = 123670 / 700 = 177
Ordering cost = 177 * $200 = $35,400
Average inventory = lot size / 2 = 350 units
Carrying cost = 350 * $3.00 = $1,050
Total annual cost = ordering cost + carrying cost = $36,450

EOQ lot size:
EOQ = sqrt(2SDC/O) = sqrt((2*345*123670)/200) = 8306 units
Number of orders per year = Annual demand / lot size = 123670 / 8306 = 15
Ordering cost = 15 * $200 = $3,000
Average inventory = EOQ / 2 = 4153 units
Carrying cost = 4153 * $3.00 = $12,459
Total annual cost = ordering cost + carrying cost = $15,459

The cost difference is $36,450 - $15,459 = $20,991. Therefore, it is not cost-effective to use the EOQ lot size and the best choice is to stick with the current policy.

The Company Is Using a Lot Size of 700 Units