Smith & Sons. Inc.. Milwaukee purchases a bearing for use in a its sub assemblie

Question

Smith & Sons. Inc.. Milwaukee purchases a bearing for use in a its sub assemblies at a rate of $ 50 per unit from one their time tested suppliers. As part of the price re negotiation process, the supplier agreed to offer discounted prices as given in the table below. The annual demand forecast for this product is 25000 units. Ordering costs are placed at $100 per order. Annual holding rates are 50%. The price schedule offered is us under Calculate the optimal order size so that total annual inventory cost can be minimized? What is the total annual inventory cost?

Explanation / Answer

OPTIMAL ORDER SIZE

= SQUARE ROOT OF [2(ANNUAL DEMAND) (ORDERING COST)] / HOLDING COST

= SQUARE ROOT OF [2 (25000) $100] / ($50 * 0.5)

= SQUARE ROOT OF 200000

= 447.21 OR 447 UNITS (ROUNDED)

ANNUAL INVENTORY COST

PRICE PER UNIT ($50 * 95%) = $47.5

HOLDING COST PER UNIT ($47.5 * 50%) = $23.75

NUMBER OF ORDERS (25000 / 447) = 55.92 OR 56

TOTAL INVENTORY COST

= 25000 * $47.5 + 56 * $100 + 25000 * $23.75

= $1187500 + $5600 + $593750

= $1786850

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