A produce distributor uses 773 packing crates monthly, each costing $11. The manager has assigned an annual carrying cost of 33 percent per crate. Ordering costs amount to $28 per order, and currently, the manager orders monthly. How much could the company save annually on ordering and carrying costs by implementing the EOQ model?
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To calculate how much the company could save annually by implementing the Economic Order Quantity (EOQ) model, we first need to understand the basics of the EOQ formula. The EOQ model is used to determine the optimal order quantity that minimizes the total inventory costs, which include both the ordering costs and the carrying costs.
The EOQ formula is: EOQ = √(2DS / H)
Where: D = Annual demand (in units) S = Ordering cost per order H = Annual holding cost per unit
Now, let's calculate each component using the provided information:
D (Annual demand) = Monthly demand × 12 = 773 crates/month × 12 months/year = 9,276 crates/year S (Ordering cost) = $28/order H (Annual holding cost per unit) = Purchase cost per crate × Carrying cost percentage = $11/crate × 33% = $3.63/crate/year
Now, let's calculate EOQ:
EOQ = √((2 × 9,276 × 28) / 3.63) ≈ √((259,328) / 3.63) ≈ √(71441.32) ≈ 267.29
Since the company cannot order a fraction of a crate, we'll round up to the nearest whole number. Therefore, the EOQ is 268 crates per order.
Now let's calculate the total number of orders per year with EOQ:
Number of orders per year = Annual demand / EOQ = 9,276 crates/year / 268 crates/order ≈ 34.61 orders/year
Again, we'll round up, as the company can't place a fraction of an order, so they would make 35 orders per year.
Now, let's calculate the annual carrying cost and ordering cost with EOQ:
Annual ordering costs with EOQ = Number of orders per year × Ordering cost per order = 35 orders/year × $28/order = $980/year
Annual carrying costs with EOQ = (EOQ/2) × Holding cost per unit = (268 crates / 2) × $3.63/crate/year = 134 crates × $3.63/crate/year = $486.42/year
Currently, the company orders monthly, so there are 12 orders per year. The annual ordering cost currently is:
Current annual ordering cost = Number of orders per year × Ordering cost per order = 12 orders/year × $28/order = $336/year
Currently, each crate has an annual carrying cost of $3.63. The carrying cost is based on the average inventory level, which, with monthly orders, is approximately half the monthly demand.
Current annual carrying cost = (Monthly demand / 2) × Carrying cost per crate = (773 crates / 2) × $3.63/crate/year = 386.5 crates × $3.63/crate/year = $1,402.15/year
Now let's find out how much the company saves annually on ordering and carrying costs by comparing the current costs with the costs after implementing EOQ:
Total current annual costs = Current annual ordering cost + Current annual carrying cost = $336 + $1,402.15 = $1,738.15/year
Total annual costs with EOQ = Annual ordering costs with EOQ + Annual carrying costs with EOQ = $980 + $486.42 = $1,466.42/year
Annual savings by implementing EOQ = Total current annual costs - Total annual costs with EOQ = $1,738.15 - $1,466.42 = $271.73
So, by implementing the EOQ model, the company could save approximately $271.73 annually on ordering and carrying costs.