Question

Demand for fasteners at W.W. Grainger is 20,000 boxes per month. Holding cost at Grainger is 20 percent per year. Each order incurs a fixed cost of $400. The supplier offers an all unit discount pricing scheme with a price of $5 per box for orders under 30,000 and a price of $4.90 for all orders of 30,000 or more. How many boxes should Grainger order per replenishment

Answer 1

Solution :

Given :

The annual demand, D = $200000 \times 12$

                                      = 240,000

The ordering cost, S = $ 400

Holding cost, H = 20 percent per year

The EOQ for each year,

$EOQ=\sqrt{\frac{2DS}{H}}$

Under 30000, the cost = 5, Holding cost = 5 x 0.2 = 0

$EOQ=\sqrt{\frac{2\times 240000 \times 400}{1}}$

           = 13856.41

            = 13856 (approx.)

It is feasible as it is not with in range of 30000 or more.

So calculating total cost at order quantity, Q = 13856 and 30000

Therefore total cost = purchase cost + annual ordering cost + annual holding cost.

   $=(CD)+\frac{Q}{2}H+\frac{D}{Q}S$

Q = 13856

Total cost = $(5\times 240000)+(\frac{240000}{13856})\times 400+(\frac{12856}{2})\times 1$

                 = 1213856

Q = 30000

Total cost = $(4.9\times 240000)+(\frac{240000}{30000})\times 400+(\frac{30000}{2})\times 0.98= 1193900$

Total cost is less than Q = 30000

Order quantity = 30000 boxes