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A small coffee shop consumes, on average, 5000 bags of their most popular coffee beans each month. Demand is normally distributed, with the standard deviation of the monthly demand being 180 bags. The shop pays $13 for each bag to the supplier. The cost of ordering and receiving shipments is $16 per order. Accounting estimates that the annual inventory carrying cost is 30% of its value. The supplier lead time is a constant of 2 operating days. The shop operates 240 days per year, which means it operates 20 days each month. Each order is received from the supplier in a single delivery. The coffee shop uses a continuous review (fixed-order quantity) inventory system and pays the supplier when the order is delivered (cash on delivery). There are no quantity discounts. Please keep two decimal places in your calculations.

1. What quantity should the shop order with each order?
2. How many times per year will the shop order on average?
3. How many operating days will elapse on average between two consecutive orders?
4. What is the store’s minimum total annual cost of placing orders and carrying inventory (cycle stock)?
5. The company currently carries a safety stock of 50 bags. What is the annual cost to carry the safety stock of 50 bags?

Answer :

The small coffee shop should order approximately 160 bags per order, with an average of 623 orders per year. The shop should expect an average of 0.38 operating, with a minimum total annual cost of $10,372.56.

The quantity that the shop should order with each order can be calculated using the economic order quantity (EOQ) formula:

EOQ = [tex]\sqrt{(2 \times demand \times ordering cost) / carrying cost}[/tex]

Given:

  • Demand (D) = 5000 bags per month
  • Ordering cost (S) = $16 per order
  • Carrying cost (H) = 30% of the value of the inventory
  • Cost per bag (C) = $13

First, we calculate the annual demand:

  • Annual Demand = Monthly Demand × Operating Days per Month
  • Annual Demand = 5000 bags × 20 days = 100,000 bags

Next, we can calculate the EOQ:

  • EOQ = [tex]\sqrt{(2 \times 100,000 \times 16) / (0.30 \times 100,000 \times 13)][/tex]
  • EOQ = 160.49

Therefore, the shop should order approximately 160 bags with each order.

The average number of times the shop will order per year can be calculated using the formula:

  • Order frequency = (Annual Demand / EOQ)
  • Order frequency = 100,000 / 160.49
  • Order frequency ≈ 623.04

Therefore, the shop will order on average approximately 623 times per year.

The average number of operating days that will elapse between two consecutive orders can be calculated using the formula:

Order interval = (Operating Days per Year / Order Frequency)

  • Order interval = 240 / 623.04
  • Order interval ≈ 0.38

Therefore, on average, approximately 0.38 operating days will elapse between two consecutive orders.

The minimum total annual cost of placing orders and carrying inventory (cycle stock) can be calculated using the formula:

  • Total Annual Cost = (Annual Demand / EOQ) × Ordering Cost + (EOQ / 2) × Carrying Cost
  • Total Annual Cost = (100,000 / 160.49) × 16 + (160.49 / 2) × (0.30 × 13)
  • Total Annual Cost ≈ $10,372.56

Therefore, the store's minimum total annual cost of placing orders and carrying inventory is approximately $10,372.56.

The annual cost to carry the safety stock of 50 bags can be calculated by multiplying the carrying cost per bag by the quantity of the safety stock:

Annual Cost of Safety Stock = Carrying Cost per Bag × Safety Stock Quantity

Given:

  • Carrying cost (H) = 30% of the value of the inventory
  • Cost per bag (C) = $13
  • Safety Stock Quantity = 50 bags

  • Annual Cost of Safety Stock = (0.30 × 13) × 50
  • Annual Cost of Safety Stock ≈ $195

Therefore, the annual cost to carry the safety stock of 50 bags is approximately $195.

Learn more about total annual cost: brainly.com/question/28384721

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