Question

A retailer is considering inventory management of one of its products with the annual demand of 600 units (1 year = 50 weeks). The product is delivered directly from the manufacturer who guarantees that every order is delivered in 2 weeks. The retailer pays the manufacturer $150 per unit. Additionally, every time the manufacturer fills an order from the retailer, machine setup cost of $60 is charged on the retailer. Transportation from the manufacturer costs the retailer $40 per shipment (regardless of the number of units). Retailer pays warehouse charges of $5 per unit per year. Additionally, the retailer knows that every dollar that is not spent on items held in the warehouse will be invested in an endeavor which is expected to return around 20% per year. Calculate the overall annual holding cost per unit and the overall cost per order paid by the retailer. 2. If weekly demand is assumed to be constant, calculate the optimal quantity that the retailer should order each time. 3. Calculate the total cost of the retailer in one year. 4. How many times per year will the product be ordered? 5. What will be the time duration between two orders? Express it in weeks. 6. Calculate the reorder point assuming that the weekly demand and the lead time are constant. The retailer would like to order once per month (i.e., 12 times per year). What should be the cost of shipment for such policy to become optimal?

Answer 1

Annual demand, D = 600 units
Weekly demand, d = 600/50 = 12 units
Lead time, L = 2 weeks
Unit cost, C = $150

1.

Ordering plus setup cost, K = 60+40 = $100 per order

Unit carrying cost, h = 5 + 20%*150 = $35 per annum

2.

Optimal order size, Q = (2.D.K/h)^1/2 = SQRT(2*600*100/35) = 59 units

3.

Annual holding cost = (Q/2)*h = (59/2)*35 = $1,032.5

Annual ordering cost = (D/Q)*K = (600/59)*100 = $1,016.9

Annual cost of purchase = D.C = 600*150 = $90,000

So, the total cost per annum = 1032.5 + 1016.9 + 90000 = $92,049

4.

No. of orders per annum = D/Q = 600/59 = 10.17

5.

Time between orders = Q/D = 59/600 = 0.098 years = 0.098*50 weeks = 4.9 weeks

6.

ROP = d.L = 12*2 = 24 units.

-----------------

No. of orders per year = 12

So, the order size = D/12 = 600/12 = 50 units

For optimality, (2*600*K/35)^0.5 = 50

or, K = 72.91

So, the cost per shipment should be 72.91 - 60 = $12.91 per order