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(b) How many service representatives should be in each training group?
（b） 每個培訓組應有多少名服務代表？
© How many training programs should CSL undertake each year?
© CSL 每年應該開展多少個培訓專案？
(d) How many trained service reps will be available when each training program begins?
（d） 每個培訓計劃開始時，將有多少訓練有素的服務代表可用？
9. A newspaper has 500,000 -subscribers who pay $ 4 $ 4 $4\$ 4 per month for the paper. It costs the company $ 200 , 000 $ 200 , 000 $200,000\$ 200,000 to bill all its customers. Assume that the company can earn interest at a rate of 20 % 20 % 20%20 \% per year on all revenues. Determine how often the newspaper should bill its customers. (Hint: Look at unpaid subscriptions as the inventoried good.)
9. 一家報紙有 500,000 名訂閱者，他們每月為報紙付費 $ 4 $ 4 $4\$ 4 。公司 $ 200 , 000 $ 200 , 000 $200,000\$ 200,000 向所有客戶收費的成本很高。假設公司可以按 20 % 20 % 20%20 \% 每年的利率從所有收入中賺取利息。確定報紙應向其客戶收費的頻率。（提示：將未付費訂閱視為庫存商品。
10. Consider a firm that knows that the price of the product it is ordering is going to increase permanently by $ X $ X $X\$ X. How
10. 考慮一家公司，該公司知道它訂購的產品的價格將永久上漲 $ X $ X $X\$ X 。如何
much of the product should be ordered before the price increase goes into effect?
大部分產品應該在漲價生效之前訂購嗎？
Here is one approach to this question: Suppose the firm orders Q Q QQ units before the price increase goes into effect.
這是這個問題的一種方法：假設公司在價格上漲生效之前訂購 Q Q QQ 了單位。
(a) What extra holding cost is incurred by ordering Q Q QQ units now?
（a） 現在訂購 Q Q QQ 單位會產生哪些額外的持有成本？
(b) How much in purchasing costs is saved by ordering Q Q QQ units now?
（b） 現在訂購 Q Q QQ 單位可以節省多少採購成本？
© What value of Q Q QQ maximizes purchasing cost savings less extra holding costs?
© Q Q QQ 什麼價值可以最大限度地提高採購成本節省減去額外的持有成本？
(d) Suppose that annual demand is 1000 units, holding cost per unit-year is $ 7.50 $ 7.50 $7.50\$ 7.50, and the price of the item is going to increase by $ 10 $ 10 $10\$ 10. How large an order should be placed before the price increase goes into effect?
（d） 假設年需求量為 1000 個單位，每單位年的持有成本為 $ 7.50 $ 7.50 $7.50\$ 7.50 ，並且該專案的價格將增加 $ 10 $ 10 $10\$ 10 。在漲價生效之前，應該下多大的訂單？
16-3 COMPUTING THE OPTIMAL ORDER QUANTITY WHEN QUANTITY DISCOUNTS ARE ALLOWED
16-3 在允許數量折扣的情況下計算最佳訂貨數量
Up to now, we have assumed that the annual purchase cost does not depend on the order size. In Section 16.2, this assumption allowed us to ignore the annual purchasing cost when we computed the order quantity that minimizes total annual cost. In real life, however, suppliers often reduce the unit purchasing price for large orders. Such price reductions are referred to as quantity discounts. If a supplier gives quantity discounts, the annual purchasing cost will depend on the order size. If holding cost is expressed as a percentage of an item’s purchasing cost, the annual holding cost will also depend on the order size. Since the annual purchasing cost now depends on the order size, we can no longer ignore purchasing cost while trading off holding cost against setup cost. Thus, the approach used in Section 16.2 to find the optimal order quantity is no longer valid, and a new approach is needed. q枚每次下單訂購曗
到目前為止，我們假設年度採購成本不取決於訂單大小。在 Section 16.2 中，這個假設允許我們在計算最小化年度總成本的訂單數量時忽略年度採購成本。然而，在現實生活中，供應商通常會降低大訂單的單價。此類降價稱為數量折扣。如果供應商提供數量折扣，則年度採購成本將取決於訂單大小。如果持有成本以商品採購成本的百分比表示，則年度持有成本也將取決於訂單規模。由於年度採購成本現在取決於訂單大小，因此我們不能再在權衡持有成本與設置成本的同時忽略採購成本。因此，Section 16.2 中用於查找最佳 order quantity 的方法不再有效，需要一種新的方法。q枚每次下單訂購曗
If we let q q qq be the quantity ordered each time an order is placed, the general quantity discount model analyzed in this section may be described as follows:
如果我們假設 q q qq 每次下訂單時訂購的數量，則本節中分析的一般數量折扣模型可以描述如下：
If q < b 1 , each item costs p 1 dollars. If b 1 ≤ q < b 2 , each item costs p 2 dollars. If b k − 2 ≤ q < b k − 1 , each item costs p k − 1 dollars. If b k − 1 ≤ q < b k = ∞ , each item costs p k dollars.  If  q < b 1 , each item costs  p 1  dollars.   If  b 1 ≤ q < b 2 , each item costs  p 2  dollars.   If  b k − 2 ≤ q < b k − 1 , each item costs  p k − 1  dollars.   If  b k − 1 ≤ q < b k = ∞ , each item costs  p k  dollars.  {:[" If "q < b_(1)", each item costs "p_(1)" dollars. "],[" If "b_(1) <= q < b_(2)", each item costs "p_(2)" dollars. "],[" If "b_(k-2) <= q < b_(k-1)", each item costs "p_(k-1)" dollars. "],[" If "b_(k-1) <= q < b_(k)=oo", each item costs "p_(k)" dollars. "]:}\begin{aligned} & \text { If } q<b_{1} \text {, each item costs } p_{1} \text { dollars. } \\ & \text { If } b_{1} \leq q<b_{2} \text {, each item costs } p_{2} \text { dollars. } \\ & \text { If } b_{k-2} \leq q<b_{k-1} \text {, each item costs } p_{k-1} \text { dollars. } \\ & \text { If } b_{k-1} \leq q<b_{k}=\infty \text {, each item costs } p_{k} \text { dollars. } \end{aligned}
Since b 1 , b 2 , … , b k − 1 b 1 , b 2 , … , b k − 1 b_(1),b_(2),dots,b_(k-1)b_{1}, b_{2}, \ldots, b_{k-1} are points where a price change (or break) occurs, we refer to b 1 , b 2 , … , b k − 1 b 1 , b 2 , … , b k − 1 b_(1),b_(2),dots,b_(k-1)b_{1}, b_{2}, \ldots, b_{k-1} as price break points. Since larger order quantities should be associated with lower prices, we have p k < p k − 1 < ⋯ < p 2 < p 1 p k < p k − 1 < ⋯ < p 2 < p 1 p_(k) < p_(k-1) < cdots < p_(2) < p_(1)p_{k}<p_{k-1}<\cdots<p_{2}<p_{1}. The following example illustrates the quantity discount model.
由於 b 1 , b 2 , … , b k − 1 b 1 , b 2 , … , b k − 1 b_(1),b_(2),dots,b_(k-1)b_{1}, b_{2}, \ldots, b_{k-1} 是價格變化（或突破）發生的點，因此我們稱 b 1 , b 2 , … , b k − 1 b 1 , b 2 , … , b k − 1 b_(1),b_(2),dots,b_(k-1)b_{1}, b_{2}, \ldots, b_{k-1} 之為價格突破點。由於較大的訂單數量應該與較低的價格相關聯，因此我們有 p k < p k − 1 < ⋯ < p 2 < p 1 p k < p k − 1 < ⋯ < p 2 < p 1 p_(k) < p_(k-1) < cdots < p_(2) < p_(1)p_{k}<p_{k-1}<\cdots<p_{2}<p_{1} .以下示例說明了數量折扣模型。
E X A M P L E Buying Diskettes A local accounting firm in Smalltown orders boxes of floppy diskettes ( 10 diskettes to a box) from a store in Megalopolis. The per-box price charged by the store depends on the number of boxes purchased (see Table 2). The accounting firm uses
E X A M P L E 購買軟盤 小鎮的一家當地會計師事務所從大都市的一家商店訂購一箱箱軟盤（每盒 10 張軟盤）。商店收取的每箱價格取決於購買的箱子數量（見表 2）。會計師事務所使用

持有成本 = Q 2 × = Q 2 × =(Q)/(2)xx=\frac{Q}{2} \times 每單位儲存成本 ( け け けけけ )
持有成本 = Q 2 × = Q 2 × =(Q)/(2)xx=\frac{Q}{2} \times 每單位儲存成本 （ け け けけけ ）
B 0 Q = 2 × b × S H B 0 Q = 2 × b × S H B0Q=sqrt((2xx b xx S)/(H))B 0 Q=\sqrt{\frac{2 \times b \times S}{H}}
Table 2  表 2
Purchase Costs for Diskettes
軟盤的購買成本
訙購成本 = $ 100 = $ 100 =$100=\$ 100

訂購 ( q ) ( q ) (q)(q) 的盒子數量
NO. OF BOXES
ORDERED ( q ) ( q ) (q)(q)
NO. OF BOXES ORDERED (q)| NO. OF BOXES | | :---: | | ORDERED $(q)$ |

每個價格 箱
PRICE PER
BOX
PRICE PER BOX| PRICE PER | | :---: | | BOX |
0 ≤ q < 100 0 ≤ q < 100 0 <= q < 1000 \leq q<100 $ 50.00 $ 50.00 $50.00\$ 50.00
100 ≤ q < 300 100 ≤ q < 300 100 <= q < 300100 \leq q<300 $ 49.00 $ 49.00 $49.00\$ 49.00
q ≥ 300 q ≥ 300 q >= 300q \geq 300 $ 48.50 $ 48.50 $48.50\$ 48.50
訙購成本 =$100 "NO. OF BOXES ORDERED (q)" "PRICE PER BOX" 0 <= q < 100 $50.00 100 <= q < 300 $49.00 q >= 300 $48.50| 訙購成本 $=\$ 100$ | NO. OF BOXES <br> ORDERED $(q)$ | PRICE PER <br> BOX | | :---: | :---: | :---: | | | $0 \leq q<100$ | $\$ 50.00$ | | | $100 \leq q<300$ | $\$ 49.00$ | | | $q \geq 300$ | $\$ 48.50$ |
10.000 diskettes per year. The cost of placing an order is assumed to be $ 100 $ 100 $100\$ 100. The only holding cost is the opportunity cost of capital, which is assumed to be 20 % 20 % 20%20 \% per year. For this example, b 1 = 100 , b 2 = 300 , p 1 = $ 50.00 , p 2 = $ 49.00 b 1 = 100 , b 2 = 300 , p 1 = $ 50.00 , p 2 = $ 49.00 b_(1)=100,b_(2)=300,p_(1)=$50.00,p_(2)=$49.00b_{1}=100, b_{2}=300, p_{1}=\$ 50.00, p_{2}=\$ 49.00, and p 3 = $ 48.50 p 3 = $ 48.50 p_(3)=$48.50p_{3}=\$ 48.50.
每年 10.000 張軟盤。假設下訂單的成本為 $ 100 $ 100 $100\$ 100 。唯一的持有成本是資本的機會成本，假設為 20 % 20 % 20%20 \% 每年。在這裡示例中， b 1 = 100 , b 2 = 300 , p 1 = $ 50.00 , p 2 = $ 49.00 b 1 = 100 , b 2 = 300 , p 1 = $ 50.00 , p 2 = $ 49.00 b_(1)=100,b_(2)=300,p_(1)=$50.00,p_(2)=$49.00b_{1}=100, b_{2}=300, p_{1}=\$ 50.00, p_{2}=\$ 49.00 ， 和 p 3 = $ 48.50 p 3 = $ 48.50 p_(3)=$48.50p_{3}=\$ 48.50 .
The example is continued later in this section.
本節稍後將繼續該示例。
Before explaining how to find the order quantity minimizing total annual costs, we need the following definitions:
在解釋如何找到最小化年度總成本的訂單數量之前，我們需要以下定義：
訂購
  1. T C l ( q ) = T C l ( q ) = TC_(l)(q)=T C_{l}(q)= total annual cost (including holding, purchasing, and ordering costs) if each order is for q q qq units at a price p i p i p_(i)p_{i}.
    T C l ( q ) = T C l ( q ) = TC_(l)(q)=T C_{l}(q)= 年度總成本（包括持有、採購和訂購成本）（如果每個訂單都是 q q qq 以 價格 p i p i p_(i)p_{i} .
    ⟵ 2 ⟵ 2 longleftarrow2\longleftarrow 2. EOO = quantity that minimizes total annual cost if, for any order quantity, the purchasing cost of the item is p i p i p_(i)p_{i}.
    ⟵ 2 ⟵ 2 longleftarrow2\longleftarrow 2 。EOO = 如果對於任何訂單數量的商品採購成本為 p i p i p_(i)p_{i} ，則使年度總成本最小化的數量。
  2. E O Q i E O Q i EOQ_(i)E O Q_{i} is admissible if b i − 1 ≤ E O Q 1 < b i b i − 1 ≤ E O Q 1 < b i b_(i-1) <= EOQ_(1) < b_(i)b_{i-1} \leq E O Q_{1}<b_{i}.
    E O Q i E O Q i EOQ_(i)E O Q_{i} 如果 . b i − 1 ≤ E O Q 1 < b i b i − 1 ≤ E O Q 1 < b i b_(i-1) <= EOQ_(1) < b_(i)b_{i-1} \leq E O Q_{1}<b_{i}
  3. T C ( q ) = T C ( q ) = TC(q)=T C(q)= actual annual cost if q q qq items are ordered each time an order is placed. (We determine T C ( q ) T C ( q ) TC(q)T C(q) by using price p i p i p_(i)p_{i} if b i − 1 ≤ q < b i b i − 1 ≤ q < b i b_(i-1) <= q < b_(i)b_{i-1} \leq q<b_{i}.)
    T C ( q ) = T C ( q ) = TC(q)=T C(q)= 實際年度成本（如果 q q qq 每次下訂單時都訂購了商品）。（我們使用 price p i p i p_(i)p_{i} 來確定 T C ( q ) T C ( q ) TC(q)T C(q) if b i − 1 ≤ q < b i b i − 1 ≤ q < b i b_(i-1) <= q < b_(i)b_{i-1} \leq q<b_{i} 。
    Our goal is to find the value of q q qq minimizing T C ( q ) T C ( q ) TC(q)T C(q). Figures 6 a and 6 b illustrate these definitions. Observe that in Figure 6a, E O Q 2 E O Q 2 EOQ_(2)E O Q_{2} is admissible because b 1 < E O Q 2 < b 2 b 1 < E O Q 2 < b 2 b_(1) < EOQ_(2) < b_(2)b_{1}<E O Q_{2}<b_{2}, but E O Q 1 E O Q 1 EOQ_(1)E O Q_{1} and E O Q 3 E O Q 3 EOQ_(3)E O Q_{3} are not admissible. In each figure, T C ( q ) T C ( q ) TC(q)T C(q) is the solid portion of the curve. The dashed portion of each curve represents unattainable costs. For instance, in Figure 6 b , T C 2 ( q ) 6 b , T C 2 ( q ) 6b,TC_(2)(q)6 \mathrm{~b}, T C_{2}(q) is dotted for q < b 1 q < b 1 q < b_(1)q<b_{1} because the price is not p 2 p 2 p_(2)p_{2} for q < b 1 q < b 1 q < b_(1)q<b_{1}. In Figure 6 b , for q < b 1 q < b 1 q < b_(1)q<b_{1}, total annual cost is given by the solid portion of T C 1 ( q ) T C 1 ( q ) TC_(1)(q)T C_{1}(q) because for q < b 1 q < b 1 q < b_(1)q<b_{1}, the price is p 1 p 1 p_(1)p_{1}, and for q ≥ b 1 q ≥ b 1 q >= b_(1)q \geq b_{1}, total annual cost is given by the solid portion of T C 2 ( q ) T C 2 ( q ) TC_(2)(q)T C_{2}(q).
    我們的目標是找到 q q qq 最小化 T C ( q ) T C ( q ) TC(q)T C(q) .圖 6 a 和 6 b 說明了這些定義。請注意，在圖 6a 中， E O Q 2 E O Q 2 EOQ_(2)E O Q_{2} 是可接受的，因為 b 1 < E O Q 2 < b 2 b 1 < E O Q 2 < b 2 b_(1) < EOQ_(2) < b_(2)b_{1}<E O Q_{2}<b_{2} ，但 E O Q 1 E O Q 1 EOQ_(1)E O Q_{1} 和 E O Q 3 E O Q 3 EOQ_(3)E O Q_{3} 是不可接受的。在每個圖中， T C ( q ) T C ( q ) TC(q)T C(q) 是曲線的實線部分。每條曲線的虛線部分代表無法實現的成本。例如，在 Figure 6 b , T C 2 ( q ) 6 b , T C 2 ( q ) 6b,TC_(2)(q)6 \mathrm{~b}, T C_{2}(q) 中是虛線的， q < b 1 q < b 1 q < b_(1)q<b_{1} 因為 price 不是 p 2 p 2 p_(2)p_{2} 。 q < b 1 q < b 1 q < b_(1)q<b_{1} 在圖 6 b 中，對於 q < b 1 q < b 1 q < b_(1)q<b_{1} ，年度總成本由 的 T C 1 ( q ) T C 1 ( q ) TC_(1)(q)T C_{1}(q) 實心部分給出，因為對於 q < b 1 q < b 1 q < b_(1)q<b_{1} ，價格為 p 1 p 1 p_(1)p_{1} ，而對於 q ≥ b 1 q ≥ b 1 q >= b_(1)q \geq b_{1} ，年度總成本由 的 T C 2 ( q ) T C 2 ( q ) TC_(2)(q)T C_{2}(q) 實心部分給出。
In general, the value of q q qq minimizing T C ( q ) T C ( q ) TC(q)T C(q) can be either a break point (see Figure 6b) or some E O Q ― i E O Q _ i EOQ__(i)E O \underline{Q}_{i} (see Figure 6a).
一般來說，最小化 T C ( q ) T C ( q ) TC(q)T C(q) 的值 q q qq 可以是斷點（參見圖 6b）或一些 E O Q ― i E O Q _ i EOQ__(i)E O \underline{Q}_{i} （參見圖 6a）。
The following observations are helpful in determining the point (break point or E O Q i E O Q i EOQ_(i)E O Q_{i} ) that minimizes T C ( q ) T C ( q ) TC(q)T C(q).
以下觀察結果有助於確定最小化 T C ( q ) T C ( q ) TC(q)T C(q) 的點（斷點或 E O Q i E O Q i EOQ_(i)E O Q_{i} ）。
  1. For any value of q q qq,
    對於 q q qq ，
T C k ( q ) < T C k − 1 ( q ) < ⋯ < T C 2 ( q ) < T C 1 ( q ) T C k ( q ) < T C k − 1 ( q ) < ⋯ < T C 2 ( q ) < T C 1 ( q ) TC_(k)(q) < TC_(k-1)(q) < cdots < TC_(2)(q) < TC_(1)(q)T C_{k}(q)<T C_{k-1}(q)<\cdots<T C_{2}(q)<T C_{1}(q)
This observation is valid because for any order quantity q , T C k ( q ) q , T C k ( q ) q,TC_(k)(q)q, T C_{k}(q) will have the lowest holding and purchasing costs, since p k p k p_(k)p_{k} is the lowest available price; T C 1 ( q ) T C 1 ( q ) TC_(1)(q)T C_{1}(q) will have the highest holding and purchasing costs, because p 1 p 1 p_(1)p_{1} is the highest available price. Thus, in Figure 6a, we find that T C 3 ( q ) < T C 2 ( q ) < T C 1 ( q ) T C 3 ( q ) < T C 2 ( q ) < T C 1 ( q ) TC_(3)(q) < TC_(2)(q) < TC_(1)(q)T C_{3}(q)<T C_{2}(q)<T C_{1}(q).
此觀察是有效的，因為對於任何訂單數量 q , T C k ( q ) q , T C k ( q ) q,TC_(k)(q)q, T C_{k}(q) ，持有和採購成本最低，因為 p k p k p_(k)p_{k} 是最低的可用價格; T C 1 ( q ) T C 1 ( q ) TC_(1)(q)T C_{1}(q) 將具有最高的持有和購買成本，因為 p 1 p 1 p_(1)p_{1} 是最高的可用價格。因此，在圖 6a 中，我們發現 T C 3 ( q ) < T C 2 ( q ) < T C 1 ( q ) T C 3 ( q ) < T C 2 ( q ) < T C 1 ( q ) TC_(3)(q) < TC_(2)(q) < TC_(1)(q)T C_{3}(q)<T C_{2}(q)<T C_{1}(q) .
P i : T P i : T P_(i):TP_{i}: T;
2. If E O Q i E O Q i EOQ_(i)E O Q_{i} is admissible, then minimum cost for b i − 1 ≤ q < b i b i − 1 ≤ q < b i b_(i-1) <= q < b_(i)b_{i-1} \leq q<b_{i} occurs for q = E O Q i q = E O Q i q=EOQ_(i)q=E O Q_{i} (see Figure 7a). If E O Q i < b i − 1 E O Q i < b i − 1 EOQ_(i) < b_(i-1)E O Q_{i}<b_{i-1}, the minimum cosif for b i − 1 ≤ q < t i b i − 1 ≤ q < t i b_(i-1) <= q < t_(i)b_{i-1} \leq q<t_{i} occurs for q = b i − 1 q = b i − 1 q=b_(i-1)q=b_{i-1} (see Figure 7b). This observation follows from the fact that T C i ( q ) T C i ( q ) TC_(i)(q)T C_{i}(q) decreases for q < E O Q i q < E O Q i q < EOQ_(i)q<E O Q_{i} and increases for q > E O Q i q > E O Q i q > EOQ_(i)q>E O Q_{i}.
2. 如果 E O Q i E O Q i EOQ_(i)E O Q_{i} 可以接受，則 b i − 1 ≤ q < b i b i − 1 ≤ q < b i b_(i-1) <= q < b_(i)b_{i-1} \leq q<b_{i} 最低成本為 q = E O Q i q = E O Q i q=EOQ_(i)q=E O Q_{i} （見圖 7a）。如果 E O Q i < b i − 1 E O Q i < b i − 1 EOQ_(i) < b_(i-1)E O Q_{i}<b_{i-1} ，則 b i − 1 ≤ q < t i b i − 1 ≤ q < t i b_(i-1) <= q < t_(i)b_{i-1} \leq q<t_{i} 最小 cosif 為 出現 q = b i − 1 q = b i − 1 q=b_(i-1)q=b_{i-1} （參見圖 7b）。這一觀察結果源於以下事實： T C i ( q ) T C i ( q ) TC_(i)(q)T C_{i}(q) 減少 for q < E O Q i q < E O Q i q < EOQ_(i)q<E O Q_{i} 和 增加 q > E O Q i q > E O Q i q > EOQ_(i)q>E O Q_{i} 。
Figure 6  圖 6
Illustrations of Definitions of T C i ( q ) T C i ( q ) TC_(i)(q)T C_{i}(q) and EOQ,
和 EOQ 的 T C i ( q ) T C i ( q ) TC_(i)(q)T C_{i}(q) 定義圖解，

3. If E O Q i E O Q i EOQ_(i)E O Q_{i} is admissible, then T C ( q ) T C ( q ) TC(q)T C(q) cannot be minimized at an order quantity for which the purchasing price per item exceeds p i p i p_(i)p_{i}. Thus, if E O Q i E O Q i EOQ_(i)E O Q_{i} is admissible, the optimal order quantity must occur for either price p i , p i + 1 , … p i , p i + 1 , … p_(i),p_(i+1),dotsp_{i}, p_{i+1}, \ldots, or p k p k p_(k)p_{k}.
3. 如果 E O Q i E O Q i EOQ_(i)E O Q_{i} 可以接受，則 T C ( q ) T C ( q ) TC(q)T C(q) 不能在每件商品的採購價格超過 p i p i p_(i)p_{i} 的訂單數量時最小化。因此，如果可接受，則 E O Q i E O Q i EOQ_(i)E O Q_{i} 最佳訂貨數量必須出現在 price p i , p i + 1 , … p i , p i + 1 , … p_(i),p_(i+1),dotsp_{i}, p_{i+1}, \ldots 或 p k p k p_(k)p_{k} 。
To see why observation 3 holds, suppose E O Q i E O Q i EOQ_(i)E O Q_{i} is admissible. Why can’t an order quantity associated with a price p j > p i p j > p i p_(j) > p_(i)p_{j}>p_{i} have a lower cost than E O Q i E O Q i EOQ_(i)E O Q_{i} ? Note that E O Q i E O Q i EOQ_(i)E O Q_{i} minimizes total annual cost if price is p i p i p_(i)p_{i} and E O Q j E O Q j EOQ_(j)E O Q_{j} does not minimize total annual cost if price is p i p i p_(i)p_{i}. Thus,
要瞭解為什麼觀察 3 成立，假設 E O Q i E O Q i EOQ_(i)E O Q_{i} 是可以接受的。為什麼與價格 p j > p i p j > p i p_(j) > p_(i)p_{j}>p_{i} 關聯的訂單數量不能具有低於 E O Q i E O Q i EOQ_(i)E O Q_{i} 的成本 ？請注意，如果price是 p i p i p_(i)p_{i} ，則最小化 E O Q i E O Q i EOQ_(i)E O Q_{i} 年度總成本， E O Q j E O Q j EOQ_(j)E O Q_{j} 如果price是 p i p i p_(i)p_{i} ，則不會最小化年度總成本。因此
T C i ( E O Q i ) < T C i ( E O Q j ) T C i E O Q i < T C i E O Q j TC_(i)(EOQ_(i)) < TC_(i)(EOQ_(j))T C_{i}\left(E O Q_{i}\right)<T C_{i}\left(E O Q_{j}\right)