The annual demand for a product has been projected at 2,000 units.This demand is assumed to be constant throughout the year.The ordering cost is $20 per order,and the holding cost is 20 percent of the purchase cost.The purchase cost is $40 per unit.There are 250 working days per year.Currently,the company is ordering 500 units each time an order is placed.Assuming the company uses a safety stock of 20 units resulting in a reorder point of 60 units,what is the expected lead-time for delivery?
A)4 days
B)5 days
C)6 days
D)7 days
E)None of the above

Question

Quizplus · Accepted Answer

The annual demand is 2,000 units, so the daily demand is 2,000/250 = 8 units per day. The safety stock is 20 units and reorder point is 60 units, which means that the company will need to place an order when the inventory level reaches 60-20 = 40 units. The time it takes to receive the order is the lead time. To calculate the lead time, we need to know the order quantity. Currently, the company is ordering 500 units each time, which means that the number of orders placed per year is 2,000/500 = 4. The annual ordering cost is 4*$20 = $80. The annual holding cost is 20%*$40*500 = $4,000. The total annual cost is $80+$4,000 = $4,080. To find the optimal order quantity that minimizes total cost, we can use the EOQ formula:

EOQ = √(2DS/H)

where D is the annual demand, S is the ordering cost, and H is the holding cost per unit. Plugging in the values, we get:

EOQ = √(2*2,000*20/$40) = 100

So the optimal order quantity is 100 units. The number of orders placed per year is 2,000/100 = 20. The annual ordering cost is 20*$20 = $400. The annual holding cost is 20%*$40*100 = $800. The total cost is $400+$800 = $1,200.

To calculate the lead time, we need to know the time it takes to receive an order. If the company is currently ordering 500 units and switches to ordering 100 units, the lead time will likely change. Assuming the lead time is proportional to the order quantity, we can use the following formula:

Lead time = LT0*(Q/Q0)^p

where LT0 is the current lead time, Q0 is the current order quantity, Q is the new order quantity, and p is a coefficient that depends on the nature of the ordering process. Typical values of p range from 0.5 to 1.5. We can estimate p by using the following formula:

p = log(LT1/LT0)/log(Q1/Q0)

where LT1 and Q1 are a new lead time and order quantity, respectively. Let's assume that the lead time is proportional to the order quantity with p = 1. Then we can use the current lead time and order quantity to estimate the lead time for an order of 100 units:

lead time = LT0*(Q/Q0)^p = 5*(100/500)^1 = 1 day

So the expected lead time for delivery is 1 day.

The Annual Demand for a Product Has Been Projected at 2,000