I need assistance to solve the following problem in Operations Analysis.2) A coffee store is experiencing sales of 280 pounds of coffee beans per year.  The supplier charges the store $2.40 per pound, and the paperwork and labor costs incurred by the store in placing an order total $45 per order.  Holding costs are based on 20% interest rate per annum.a) What is the optimal order size (write down the model name, its parameters and formula)?b) What is the time between order placements (include the formula)?  c) What is the average annual holding cost (include the formula)?d) If the lead time is 3 weeks, what is the reorder level based on inventory on hand (include the formula)?

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Asked Feb 26, 2019
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I need assistance to solve the following problem in Operations Analysis.

2) A coffee store is experiencing sales of 280 pounds of coffee beans per year.  The supplier charges the store $2.40 per pound, and the paperwork and labor costs incurred by the store in placing an order total $45 per order.  Holding costs are based on 20% interest rate per annum.

a) What is the optimal order size (write down the model name, its parameters and formula)?

b) What is the time between order placements (include the formula)?  

c) What is the average annual holding cost (include the formula)?

d) If the lead time is 3 weeks, what is the reorder level based on inventory on hand (include the formula)? 

 

 

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Expert Answer

Step 1

Step1: Calculating the value of optimal order size. We have,

Model Name: Economic order quantity (EOQ)

The formula of EOQ is as follow:

EOQ = Square Root of [2 x Demand x ordering cost per purchase order/ Holding cost per unit, per year]

Here,

Demand of coffee beans = 280 pounds

Ordering cost per purchase order = $ 45 per order

Holding cost = $ 2.40 x 20% = $ 0.48 per pound, per year

By substituting this value in the above formula. We get;

EOQ = Square Root of [2 x 280 x $ 45 / $ 0.48]

EOQ = Square Root of [52,500]

EOQ = 229.13 Pounds

Step 2

Step2: Calculating the time between order placements. We have,

Number of order = EOQ / Annual Demand

Number of order = 229.13 pounds / 280 pounds

Number of order = 0.82

Assuming 52 weeks in a year.

Time between order placement = Number of order x Number of weeks in a year

Time between order placement = 0.82 x 52

Time between order placement = 42.64 weeks

Step 3

Step3: Calculating the value of the average annual holding cost. We have,

Average annual holding cost = EOQ/2 x Hol...

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