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# 数学代写|运筹学代写Operations Research代考|KMA255 The EOQ Model and the EPQ Model

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## 数学代写|运筹学代写Operations Research代考|The EOQ Model and the EPQ Model

This section first considers the EOQ inventory model in its simplest form. We derive the EOQ formula for the optimal order quantity. We also discuss the sensitivity of this formula to changes in the data. Then, we adjust the EOQ formula to the case of quantity discount. The concept of an exchange curve is also discussed. This concept is handy for making inventory decisions when no information is available on the exact holding and ordering costs. Finally, we discuss the economic production quantity (EPQ) model, in which the stock is gradually replenished through production.

The Formula for the EOQ Inventory Model
The EOQ model is the most basic inventory model. The assumptions of the EOQ model are as follows:

• The demand is deterministic and constant over time and causes the inventory level to decrease continuously.
• The demand must be met immediately.
• There are no restrictions on the size of the replenishment order.
• The time needed to replenish the stock is negligible (that is, the lead time, the time between placing a replenishment order and receiving it, is zero).
• The complete replenishment order is delivered at the same time.
• The only relevant costs are the ordering and holding costs.

## 数学代写|运筹学代写Operations Research代考|Illustration

As an illustration, consider the following example. A distributor of Johnny Cola soft drinks supplies a large number of supermarkets. The demand for soft drinks is relatively constant and is approximately equal to 1500 crates per week. The purchase cost per crate is $€ 7.50$. The fixed ordering cost is estimated at $€ 50$. The distributor sets the annual holding cost at $20 \%$ of the average capital invested in inventory. What is the optimal order quantity?

Solution. Take a year as unit of time and apply formula (6.2) with $K=50$, $D=52 \times 1500=78000, v=7.50$, and $r=0.20$. This gives
$$Q^*=\sqrt{\frac{2 \times 50 \times 78000}{7.5 \times 0.2}}=2280.4, \text { say } 2280 \text { crates. }$$
The optimal order quantity is therefore 2280 crates. It follows from formula (6.1) that the minimum annual ordering and holding costs equal $€ 3420.53$ (excluding the annual purchase cost of $€ 585000$ that the distributor cannot influence).

## 数学代写|运筹学代写Operations Research代考|The EOQ Model and the EPQ Model

EOQ 库存模型的公式
EOQ 模型是最基本的库存模型。EOQ模型的假设如下：

• 随着时间的推移，需求是确定的和恒定的，并导致库存水平不断下降。
• 必须立即满足需求。
• 补货订单的大小没有限制。
• 补货所需的时间可以忽略不计（即，提前期，从下达补货订单到收到订单之间的时间为零）。
• 完整的补货订单同时交付。
• 唯一相关的成本是订购和持有成本。

## 数学代写|运筹学代写Operations Research代考|Illustration

$$Q^*=\sqrt{\frac{2 \times 50 \times 78000}{7.5 \times 0.2}}=2280.4, \text { say } 2280 \text { 板条箱。}$$

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