Question

A store sells a brand of olive oil of 400 bottles per month.

The cost of each bottle is $4.85 , and the cost of placing an order is $10.00.

Assuming the holding costs are based on a 20% annual interest rate, and stock-outs are not allowed,

a) What is the optimal lot size they should order and what is the time between orders of this product?

b) If lead time is 2 weeks to get the product to the store, what is the reorder point based on the on-hand inventory?

c) If it sells for $5.99, what is the annual profit (excluding overhead and labor costs) from this item?

Answer 1

Solution:

Part a – Optimal Lot Size

Optimal Order Size = ((2 x Annual Demand x Ordering Cost per order) / Carrying Cost per unit per annum)^1/2

Here,

Ordering Cost per Order = $10

Carrying Cost per unit per annum = Cost of Each Bottle $4.85 * Holding Cost Per Annum 20%

= $0.97

Annual Demand = Monthly demand 400 * 12 = 4800 Bottles

Optimal Order Size = ((2 x Annual Demand 4,800 x Ordering Cost per order $10) / Carrying Cost per unit per annum 0.97)^1/2

= 314.59 Units or 315 Units

Time between orders of this product = 365 days in a year / Number of Time order placed during the year

Number of time order placed in a year = Annual Demand / Optimal Order Size = 4800 / 400 = 12

Time between orders of this product = 12 months or 360/365 days in a year / Number of Time order placed during the year 12

= 1 Month or 30 days or 36.5 Days

Part b –

Re-Order Point = Weekly Usage x Maximum reorder period

Weekly Usage = Annual Demand / 52 weeks in a year

= 4800 / 52

= 92.3077

Re-Order Point = 92.3077 x 2 = 184.61 or 185 Units

Part c –

Sales Revenue (4800 * 5.99)	$28,752
Less: Material Costs (4800*4.85)	-$23,280
Less: Ordering Cost (12 Orders in a year x $10 ordering cost per order)	-$120
Less: Carrying Cost (It is an opportunity cost, not deducted in calculating the Net Income but only consider in calculating the optimal order quantity and treated as opportunity cost)
Net Income	$5,352

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