Question

The INDY Industrial Supply Company has finished a highly-sophisticated project where they separately determined order setup (S) costs for each of their main suppliers, based on the specific ordering process for that supplier. They have determined that the ACME Supplier, from which they order six different SKUs, the setup cost for an order (which has been highly automated) to be $32.50 per order, with an additional cost of $3.25 for each line on the order. Annual demand data and cost per unit for six SKUs is provided below; assume an annual inventory holding rate of 17%.

SKU D Cost/unit

SKU1 500 $25

SKU2 900 $20

SKU3 . 600 . $28

SKU4 450 . $23

SKU5 700 $33

SKU6 200 $19

The optimal number of orders per year from this supplier is (to two decimals): _____________

The amount of SKU3 that will be ordered each time (round to nearest integer): ______________

The EOQ for SKU3, if ordered on its own, would be (round to nearest integer): _______________. Note - use the major setup cost plus the setup cost for one line when finding the EOQ of an individual item. Also, your answer should make sense (i.e. you should think about whether you think the optimal order quantity for one SKU ordered alone should be higher or lower than the optimal order quantity for that SKU when it is combined with other SKUs on an order.)

Answer 1

Common Fixed cost (S) =		$32.50
Item (j)	Demand (Dj)	Unit cost (Cj)	Unit carrying cost (Hj = 17% x Cj)	Individual ordering cost (Sj)
SKU 1	500	$25.0	$4.25	$3.25
SKU 2	900	$20.0	$3.40	$3.25
SKU 3	600	$28.0	$4.76	$3.25
SKU 4	450	$23.0	$3.91	$3.25
SKU 5	700	$33.0	$5.61	$3.25
SKU 6	200	$19.0	$3.23	$3.25

For combined ordering,

Number of order placed, N* = [Σ_j D_j.H_j / {2.(S + Σ_j S_j)}]^1/2

Σ_j D_j.H_j = 500*4.35 + 900*3.4 + 600*4.76 + 450*3.91 + 700*5.61 + 200*3.23 = 14423.5
Σ_j S_j = 6*3.25 = 19.5

So, N* = sqrt(14423.5 / (2*(32.5+19.5))) = 11.76

The optimal number of orders per year from this supplier is (to two decimals): 11.76

The amount of SKU3 that will be ordered each time (round to nearest integer) = Q₃* = D₃ / N* = 600 / 11.76 = 51

For individual ordering,

The EOQ for SKU3 = Q₃ = (2.D₃.(S+S₃) / H₃)^1/2 = sqrt(2*600*(32.5+3.25) / 4.76) = 95