Question

You are assigned to manage the inventory of notebooks in one of the Walmart branches. The monthly demand is 2500 notebooks with a purchasing cost of $1 per item, and a holding cost of $0.15 per unit per month. It costs you $400 to place the order.

(a) (5 points) What is the optimal order quantity?

(b) (5 points) How often should you place an order?

(c) (10 points) Suppose you can only order at the beginning of every month, so you round your optimal order cycle to the nearest integer. How often do you order now? By how much does your operational cost increase?

Answer 1

A.

Optimal order quantity = (2*annual demand*ordering cost / holding cost per unit per year)^.5

Optimal order quantity = (2*12*2500*400/(.15*12))^.5

Optimal order quantity = 3651.48 units or 3651 units of notebooks

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B.

Monthly demand = 2500 units

So,

Frequency of ordering = 3651/2500 = 1.46 month

So, at each 1.46 month duration, the order will be placed.

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C.

The nearest integer is 1 month of 1.46 month order frequency. Now, at each month in the beginning, the order will be place.

Operation cost at optimal order quantity = (12*2500/3651)*400 + (3651/2)*.15*12

Operation cost at optimal order quantity = $6572.67

Operation cost at each month order quantity = (12*2500/2500)*400 + (2500/2)*.15*12

Operation cost at each month order quantity = $7050

So,

Increase in operations cost = 7050 - 6572.67

Increase in operations cost = $477.33

So, operations cost increases by $477.33 when order is placed at the beginning of each month.