For this question, I want you to do some “theoretical” modeling like we did to f

Question

For this question, I want you to do some “theoretical” modeling like we did to find the EOQ. The situation is basically the same as the one we used for the EOQ in that it costs $K to place an order and holding cost is $h/unit/time based on average inventory level. Further, orders are delivered instantaneously. The difference here is that there is an additional cost because the warehouse uses “fixed storage.” This strategy dedicates space in the warehouse to each part and that location neither changes nor is it ever used to store another type of part. Hence, the location must be large enough to handle the maximum number of parts that will ever be there. The cost associated with storage is assessed at a rate of $w/unit/time.

a) Write the total cost model that includes the ordering cost, the holding cost based on average inventory, and the warehouse cost based on maximum inventory.

b) Take the first derivative of this to find Q*, the cost optimal order quantity. You will discover it looks a lot like the EOQ but with $w included in a way that will resonate with your common sense.

Explanation / Answer

Answer-a Let the eoq = Q

and the total demand is D,   therefore total number of orders = D/Q

also average inventory = Q/2 where Q is the maximum inventory ordered and kept in a warehouse.

Here $k is ordering cost and $h is holding cost. $w is warehouse cost

Therefore

Total cost = T = D/Q x $k + Q/2 x $h + Q x $w

taking derivative on both sides:

dT/dQ = -Dk/Q2 + h/2 + w = 0

Q = SQRT [( 2Dk)/(2w+h)]

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