Suppose Joe is considering making the malt in-house. He anticipates putting in a production process

Suppose Joe is considering making the malt in-house. He anticipates putting in a production process that can make 7,000 gallons of malt per week. The per-gallon cost if they make it in-house will remain at $1.20 per gallon. What is the largest reorder cost such that it will be cheaper for him to make the malt in-house (compare against the supplier accepting orders that are not in units of 1,000 gallons, i.e. not the situation in the previous question)? Joe needs to purchase malt for his micro-brew production. His supplier charges $35 per delivery [no matter how much is delivered] and $1.20 per gallon. Joe’s annual holding cost per unit is 35% of the dollar value of the unit Joe uses 5,000 gallons of malt per week. Assume Joe operates 52 weeks a year and zero lead time. How many gallons should Joe order from his supplier with each order? What is the cycle length? What is the reorder level? Suppose lead time from the supplier is two weeks. How does his inventory policy (i.e. order quantity and reorder level) change from your answer to the previous question?

Expert Answer

Here following information is known :

Cost of Malt per gallon = USD 1.2

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Inventory holding cost = 35% of the dollar value of the unit = 1.2 X 35 /100 = 0.42 USD per gallon

Weekly Requirement of Malt = 5000 gallons

Total number of weeks in a year = 52 weeks

Annual requirement of Malt = 5000 X 52 = 260000 gallons

Order cost in the question is not given we are assuming 35 USD given in the question as delivery charge as Ordering cost.

So ordering cost = 35 USD

Now economic order quantity is given by the formula

EOQ = Square root of (2 X Annual Quantity X Cost per order) / (Inventory Holding Cost per unit per annum)

= Square root of ( 2 X 260000 X 35)/( 0.42) = 6582.8 gallons = 6583 gallons

In the question it is given that the supplier is not accepting orders if it is not in 1000 gallons . So based upon this we are rounding off the order quantity from 6583 gallons to 7000 gallons.

Total number of orders to be placed in the year = 260000 / 7000 = 37.14 = 37 orders

Cycle length = Total number of weeks / Total number of orders = 52 / 37 = 1.4 week

So ordering should be every 1.4 week and assuming production is running 7 days a week order should be placed on every 10th day.

If the lead time from supplier is 2 weeks then re order level will be = Weekly requirement in Gallons X 2

= 5000 X 2 = 10000 gallons

If we assume that in the begining of the year Stock is 0 our first order should be = 7000 + 10000 = 17000 gallons

After this 1st order for 17000 gallons all subsequent orders should be placed for 7000 gallons.

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