Question

A market named Econland expects to sell 2,000 boxes of shoes in the upcoming week at a steady rate. The cost of placing an order with the manufacturer is $50. Carrying costs, based on the average number of boxes in stock are $8 per box per week. Storage costs, based on the maximum number of boxes in the warehouse, are $6 per box per week. Determine the economic order quantity that minimizes the inventory cost.

Answer 1

By given data

Weekly demand quantity is 2000 boxes of shoes

Cost placing on an order is $50.

Carrying cost of the boxes (in stock) is $8 per box per per week

Lastly storage cost of those boxes are $6 per week

Firstly let's consider that q no. of shoes per order were placed to evacuate( I don't it's meaning but sounds cool) 2000 boxes from the stock to the market and say each boxes cost p dollars (if market is self sufficient it has its own stock pile then take p=0)

Then total weekly coverage for the market would be say, T

Then

T = 2000p+50×(2000/q)+(8×q)/2+6×q.............(1)

2000p is purchase cost

50×(2000/q) ordering cost

8×q/2 is carrying cost (the average quantity in stock ,between fully replenished empty, is q/2, so this cost is 8×q/2)

4×q is storage cost

So, in equation (1) if we differentiate both side w.r.t. q and take dT/dq=0 then we'll get minimum value of T (if we double derivative it we'll see it's gonna be positive so we can say we're getting minimum value for T)

So, after derivative and putting dT/dq=0

We'll get 100000/q⁲ --10=0

imply that q=100;(as q can not be negative)

And 100 is the order quantity that would minimumalize the inventory cost

So, 100 is the optimal order quantity