Question

You run a coffee shop where demand is constant week to week. You use 10 bags of roasted coffee each week. Currently, you order whole roasted coffee beans from an out-of-town supplier who charges $20 per bag and a fixed cost of $100 per delivery. Storage for each bag per month is estimated at $1. Assume your coffee shop operates for 52 weeks and 12 months per year. Assume there are no lead times.
Required:
a. Under these costs, what is the optimal order size (in bags)?
b. How often (in months) do I place an order under my solution to part a?
c. What are my annual total costs (including purchasing costs) under my solution to part a?

Answer 1

Answer: See explanation

Explanation:

a. Under these costs, what is the optimal order size (in bags)?

Periods per year = 52 weeks.

Weekly demand = 10bags

Annual demand, D = 10 × 52 = 520

Set up cost, S = $100

Item cost = $20.00

Holding cost per year, H= $12.00

We'll then calculate the economic order quantity, Q which will be:

= ✓2×S×D/H

= ✓(2×100×520/12

= ✓104000/12

= ✓8667

= 93

Optimal order size = 93 bags

b. How often (in months) do I place an order under my solution to part a?

Time between orders will be:

= Period per year / Orders per year

= 12 / 5.59

= 2.15

c. What are my annual total costs (including purchasing costs) under my solution to part a?

Annual total cost will be:

= Holding cost + Order cost + Purchase cost

= $11,517.14

Note that:

Orders per year = D/Q = 520/93 = 5.59