混合模型:石油生产
Blending Model: Oil Production
混合油
一家石油公司生产三种品牌的油:普通油、多级油和
最高。每个牌子的油都由四种原油中的一种或多种组成,每种原油具有不同的润滑指数。原油库存相关数据如下
+-------------+-------------------+------------------+--------------------------+
| Crude Stock | Lubrication Index | Cost (€/barrell) | Supply per day (barrels) |
+-------------+-------------------+------------------+--------------------------+
| 1 | 20 | 7,10 | 1000 |
+-------------+-------------------+------------------+--------------------------+
| 2 | 40 | 8,50 | 1100 |
+-------------+-------------------+------------------+--------------------------+
| 3 | 30 | 7,70 | 1200 |
+-------------+-------------------+------------------+--------------------------+
| 4 | 55 | 9,00 | 1100 |
+-------------+-------------------+------------------+--------------------------+
每个牌子的机油都必须满足一个润滑指标的最低标准,每个牌子的机油
因此以不同的价格出售。三个品牌机油的相关数据如下
如下。
+------------+---------------------------+---------------+--------------+
| Brand | Minimum Lubrication index | Selling price | Daily demand |
+------------+---------------------------+---------------+--------------+
| Regular | 25 | 8,50 | 2000 |
+------------+---------------------------+---------------+--------------+
| Multigrade | 35 | 9,00 | 1500 |
+------------+---------------------------+---------------+--------------+
| Supreme | 50 | 10,00 | 750 |
+------------+---------------------------+---------------+--------------+
确定一天的最佳产出计划,假设生产可以是
以微不足道的成本出售或储存。
每日需求数据可能有不同的解释。调查
以下:
(a) 每日需求代表潜在销售额。换句话说,模型应该包含需求上限(上限)。最佳利润是多少?
(b) 日常要求是严格的义务。换句话说,模型应该包含精确满足的需求约束。最佳利润是多少?
(c) 每日需求代表最低销售承诺,但所有产出都可以出售。换句话说,该模型应该允许生产超过每日承诺。最佳利润是多少?
问题
我已经能够在 Excel 中构建以下模型并通过 OpenSolver 解决它,但我只能整合普通油的混合物。
我正在尝试通过 Kenneth R. Baker 的 Optimization Modeling with Spreadsheets 这本书来工作,但我坚持这个练习。虽然我可以从另一个混合问题转移逻辑,但我不确定如何一次构建多个混合的模型。
我将问题建模为不同原油库存成本的最小化问题。使用润滑指数数据,我将 R-Lub 指数的约束构建为线性约束。到目前为止,普通油的答案似乎是正确的。但是使用这种方法我不知道如何包括第二种多级油。
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Decision Variables | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | C1 | C2 | C3 | C4 | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Inputs | 1000 | 0 | 1000 | 0 | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Objective Function | | | | | | Total | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Cost | 7,10 € | 8,50 € | 7,70 € | 9,00 € | | 14.800,00 € | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Constraints | | | | | | LHS | | RHS |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C1 supply | 1 | | | | | 1000 | <= | 1000 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C2 supply | | 1 | | | | 0 | <= | 1100 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C3 supply | | | 1 | | | 1000 | <= | 1200 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C4 supply | | | | 1 | | 0 | <= | 1100 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| R- Lub Index | -5 | 15 | 5 | 30 | | 0 | >= | 0 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| R- Output | 1 | 1 | 1 | 1 | | 2000 | = | 2000 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Blending Data | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| R- Lub | 20 | 40 | 30 | 55 | | 25 | >= | 25 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
这是具有 Excel 公式的模型:
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Decision Variables | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | C1 | C2 | C3 | C4 | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Inputs | 1000 | 0 | 1000 | 0 | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Objective Function | | | | | | Total | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Cost | 7,1 | 8,5 | 7,7 | 9 | | =SUMMENPRODUKT(B5:E5;B8:E8) | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Constraints | | | | | | LHS | | RHS |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C1 supply | 1 | | | | | =SUMMENPRODUKT($B:$E;B11:E11) | <= | 1000 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C2 supply | | 1 | | | | =SUMMENPRODUKT($B:$E;B12:E12) | <= | 1100 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C3 supply | | | 1 | | | =SUMMENPRODUKT($B:$E;B13:E13) | <= | 1200 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C4 supply | | | | 1 | | =SUMMENPRODUKT($B:$E;B14:E14) | <= | 1100 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| R- Lub Index | -5 | 15 | 5 | 30 | | =SUMMENPRODUKT($B:$E;B15:E15) | >= | 0 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| R- Output | 1 | 1 | 1 | 1 | | =SUMMENPRODUKT($B:$E;B16:E16) | = | 2000 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Blending Data | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| R- Lub | 20 | 40 | 30 | 55 | | =SUMMENPRODUKT($B:$E;B19:E19)/SUMME($B:$E) | >= | 25 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
在正确的方向上推动将是一个巨大的帮助。
我想我想出了一个解决方案,但我不确定这是否正确。
| Decision Variables | | | | | | | | | | | | | | | | |
|--------------------|---------|--------|--------|--------|-------------|--------|--------|--------|--------|--------|--------|--------|---|--------------------------------|----|------|
| | C1R | C1M | C1S | C2R | C2M | C2S | C3R | C3M | C3S | C4R | C4M | C4S | | | | |
| Inputs | 1000 | 0 | 0 | 800 | 0 | 300 | 0 | 1200 | 0 | 200 | 300 | 600 | | | | |
| | | | | | | | | | | | | | | | | |
| Objective Function | | | | | | | | | | | | | | Total Profit (Selling - Cost) | | |
| Cost | 7,10 € | 7,10 € | 7,10 € | 8,50 € | 8,50 € | 8,50 € | 7,70 € | 7,70 € | 7,70 € | 9,00 € | 9,00 € | 9,00 € | | 3.910,00 € | | |
| | | | | | | | | | | | | | | | | |
| Constraints | | | | | | | | | | | | | | LHS | | RHS |
| Regular | -5 | | | 15 | | | 5 | | | 30 | | | | 13000 | >= | 0 |
| Multi | | -15 | | | 5 | | | -5 | | | 20 | | | 0 | >= | 0 |
| Supreme | | | -30 | | | -10 | | | -20 | | | 5 | | 0 | >= | 0 |
| C1 Supply | 1 | 1 | 1 | | | | | | | | | | | 1000 | <= | 1000 |
| C2 Supply | | | | 1 | 1 | 1 | | | | | | | | 1100 | <= | 1100 |
| C3 Supply | | | | | | | 1 | 1 | 1 | | | | | 1200 | <= | 1200 |
| C4 Supply | | | | | | | | | | 1 | 1 | 1 | | 1100 | <= | 1100 |
| Regular Demand | 1 | | | 1 | | | 1 | | | 1 | | | | 2000 | >= | 2000 |
| Multi Demand | | 1 | | | 1 | | | 1 | | | 1 | | | 1500 | >= | 1500 |
| Supreme Demand | | | 1 | | | 1 | | | 1 | | | 1 | | 900 | >= | 750 |
| | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | |
| Selling | | | | | | | | | | | | | | | | |
| Regular | 8,50 € | x | 2000 | = | 17.000,00 € | | | | | | | | | | | |
| Multi | 9,00 € | x | 1500 | = | 13.500,00 € | | | | | | | | | | | |
| Supreme | 10,00 € | x | 900 | = | 9.000,00 € | | | | | | | | | | | |
| | | | | | 39.500,00 € | | | | | | | | | | | |
我认为您希望 objective 为利润,我将其定义为销售额总和 - 成本总和。
要包括所有混合物,请计算每种混合物的产量、润滑油指数、成本和价值。对使用的库存量、生产量和润滑油指数应用约束,并针对利润进行优化。
我整理的模型如下...
- A 到 D 列是您提供的信息。
- G2:J5 中的 10 是每个混合中使用的库存量的种子值。求解器将操纵这些。
- K 列包含生产的总产品量。根据您的调查 (a)、(b) 和 (c),这些将以不同的方式受到限制。
=SUM(G3:J3)
向下填充。
- L 列是产品的润滑油指数。正如您所指出的,它是线性混合 - 对于混合问题通常不是这样。这些值将在规划求解中受到限制。它是
{=SUMPRODUCT(G3:J3,TRANSPOSE($B:$B))/$K3}
向下填充的。请注意,这是一个 Control-Shift-Enter (CSE) 公式,因为 TRANSPOSE.
- M 列是用于创建产品的库存成本。这用于利润计算。是
{=SUMPRODUCT(G3:J3,TRANSPOSE($C:$C))}
,往下填。这也是一个CSE公式。
- N 列是所生产产品的价值。这用于利润计算。
=K3*C8
向下填充。
- 第 7 行是用于生成所有混合的总库存量。这些值将在规划求解中受到限制。它是
=SUM(G3:G5)
,向右填充。
- 利润计算为
=SUM(N3:N5)-SUM(M3:M5)
。
下面是“规划求解”对话框的快照...
它执行以下操作...
- objective是利润最大化
- 它将通过控制每次混合的存货量来实现。
- 前四个约束 (
$G through $J
) 确保不违反可用库存量。
- 接下来的三个约束条件 (
$K through $K
) 适用于情况 (a) - 生产的产品不超过需求。
- 最后三个约束条件 (
$L through $L
) 确保润滑油指数满足最低规格。
- 未显示 - 我为 GRG 非线性选择了选项并选择了 "Use Multistart" 并取消选择了 "Require Bounds on Variables"。
下面是案例 (a) 的结果...
对于情况 (b),将列 K 的约束更改为“=”而不是“<=”。下面是结果...
对于情况 (c),将列 K 的约束更改为“>=”。下面是结果...
混合油
一家石油公司生产三种品牌的油:普通油、多级油和 最高。每个牌子的油都由四种原油中的一种或多种组成,每种原油具有不同的润滑指数。原油库存相关数据如下
+-------------+-------------------+------------------+--------------------------+
| Crude Stock | Lubrication Index | Cost (€/barrell) | Supply per day (barrels) |
+-------------+-------------------+------------------+--------------------------+
| 1 | 20 | 7,10 | 1000 |
+-------------+-------------------+------------------+--------------------------+
| 2 | 40 | 8,50 | 1100 |
+-------------+-------------------+------------------+--------------------------+
| 3 | 30 | 7,70 | 1200 |
+-------------+-------------------+------------------+--------------------------+
| 4 | 55 | 9,00 | 1100 |
+-------------+-------------------+------------------+--------------------------+
每个牌子的机油都必须满足一个润滑指标的最低标准,每个牌子的机油 因此以不同的价格出售。三个品牌机油的相关数据如下 如下。
+------------+---------------------------+---------------+--------------+
| Brand | Minimum Lubrication index | Selling price | Daily demand |
+------------+---------------------------+---------------+--------------+
| Regular | 25 | 8,50 | 2000 |
+------------+---------------------------+---------------+--------------+
| Multigrade | 35 | 9,00 | 1500 |
+------------+---------------------------+---------------+--------------+
| Supreme | 50 | 10,00 | 750 |
+------------+---------------------------+---------------+--------------+
确定一天的最佳产出计划,假设生产可以是
以微不足道的成本出售或储存。
每日需求数据可能有不同的解释。调查
以下:
(a) 每日需求代表潜在销售额。换句话说,模型应该包含需求上限(上限)。最佳利润是多少?
(b) 日常要求是严格的义务。换句话说,模型应该包含精确满足的需求约束。最佳利润是多少?
(c) 每日需求代表最低销售承诺,但所有产出都可以出售。换句话说,该模型应该允许生产超过每日承诺。最佳利润是多少?
问题
我已经能够在 Excel 中构建以下模型并通过 OpenSolver 解决它,但我只能整合普通油的混合物。 我正在尝试通过 Kenneth R. Baker 的 Optimization Modeling with Spreadsheets 这本书来工作,但我坚持这个练习。虽然我可以从另一个混合问题转移逻辑,但我不确定如何一次构建多个混合的模型。 我将问题建模为不同原油库存成本的最小化问题。使用润滑指数数据,我将 R-Lub 指数的约束构建为线性约束。到目前为止,普通油的答案似乎是正确的。但是使用这种方法我不知道如何包括第二种多级油。
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Decision Variables | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | C1 | C2 | C3 | C4 | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Inputs | 1000 | 0 | 1000 | 0 | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Objective Function | | | | | | Total | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Cost | 7,10 € | 8,50 € | 7,70 € | 9,00 € | | 14.800,00 € | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Constraints | | | | | | LHS | | RHS |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C1 supply | 1 | | | | | 1000 | <= | 1000 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C2 supply | | 1 | | | | 0 | <= | 1100 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C3 supply | | | 1 | | | 1000 | <= | 1200 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| C4 supply | | | | 1 | | 0 | <= | 1100 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| R- Lub Index | -5 | 15 | 5 | 30 | | 0 | >= | 0 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| R- Output | 1 | 1 | 1 | 1 | | 2000 | = | 2000 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| Blending Data | | | | | | | | |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
| R- Lub | 20 | 40 | 30 | 55 | | 25 | >= | 25 |
+--------------------+--------+--------+--------+--------+--+-------------+----+------+
这是具有 Excel 公式的模型:
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Decision Variables | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | C1 | C2 | C3 | C4 | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Inputs | 1000 | 0 | 1000 | 0 | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Objective Function | | | | | | Total | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Cost | 7,1 | 8,5 | 7,7 | 9 | | =SUMMENPRODUKT(B5:E5;B8:E8) | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Constraints | | | | | | LHS | | RHS |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C1 supply | 1 | | | | | =SUMMENPRODUKT($B:$E;B11:E11) | <= | 1000 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C2 supply | | 1 | | | | =SUMMENPRODUKT($B:$E;B12:E12) | <= | 1100 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C3 supply | | | 1 | | | =SUMMENPRODUKT($B:$E;B13:E13) | <= | 1200 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| C4 supply | | | | 1 | | =SUMMENPRODUKT($B:$E;B14:E14) | <= | 1100 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| R- Lub Index | -5 | 15 | 5 | 30 | | =SUMMENPRODUKT($B:$E;B15:E15) | >= | 0 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| R- Output | 1 | 1 | 1 | 1 | | =SUMMENPRODUKT($B:$E;B16:E16) | = | 2000 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| Blending Data | | | | | | | | |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
| R- Lub | 20 | 40 | 30 | 55 | | =SUMMENPRODUKT($B:$E;B19:E19)/SUMME($B:$E) | >= | 25 |
+--------------------+------+-----+------+----+--+----------------------------------------------------+----+------+
在正确的方向上推动将是一个巨大的帮助。
我想我想出了一个解决方案,但我不确定这是否正确。
| Decision Variables | | | | | | | | | | | | | | | | |
|--------------------|---------|--------|--------|--------|-------------|--------|--------|--------|--------|--------|--------|--------|---|--------------------------------|----|------|
| | C1R | C1M | C1S | C2R | C2M | C2S | C3R | C3M | C3S | C4R | C4M | C4S | | | | |
| Inputs | 1000 | 0 | 0 | 800 | 0 | 300 | 0 | 1200 | 0 | 200 | 300 | 600 | | | | |
| | | | | | | | | | | | | | | | | |
| Objective Function | | | | | | | | | | | | | | Total Profit (Selling - Cost) | | |
| Cost | 7,10 € | 7,10 € | 7,10 € | 8,50 € | 8,50 € | 8,50 € | 7,70 € | 7,70 € | 7,70 € | 9,00 € | 9,00 € | 9,00 € | | 3.910,00 € | | |
| | | | | | | | | | | | | | | | | |
| Constraints | | | | | | | | | | | | | | LHS | | RHS |
| Regular | -5 | | | 15 | | | 5 | | | 30 | | | | 13000 | >= | 0 |
| Multi | | -15 | | | 5 | | | -5 | | | 20 | | | 0 | >= | 0 |
| Supreme | | | -30 | | | -10 | | | -20 | | | 5 | | 0 | >= | 0 |
| C1 Supply | 1 | 1 | 1 | | | | | | | | | | | 1000 | <= | 1000 |
| C2 Supply | | | | 1 | 1 | 1 | | | | | | | | 1100 | <= | 1100 |
| C3 Supply | | | | | | | 1 | 1 | 1 | | | | | 1200 | <= | 1200 |
| C4 Supply | | | | | | | | | | 1 | 1 | 1 | | 1100 | <= | 1100 |
| Regular Demand | 1 | | | 1 | | | 1 | | | 1 | | | | 2000 | >= | 2000 |
| Multi Demand | | 1 | | | 1 | | | 1 | | | 1 | | | 1500 | >= | 1500 |
| Supreme Demand | | | 1 | | | 1 | | | 1 | | | 1 | | 900 | >= | 750 |
| | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | |
| Selling | | | | | | | | | | | | | | | | |
| Regular | 8,50 € | x | 2000 | = | 17.000,00 € | | | | | | | | | | | |
| Multi | 9,00 € | x | 1500 | = | 13.500,00 € | | | | | | | | | | | |
| Supreme | 10,00 € | x | 900 | = | 9.000,00 € | | | | | | | | | | | |
| | | | | | 39.500,00 € | | | | | | | | | | | |
我认为您希望 objective 为利润,我将其定义为销售额总和 - 成本总和。
要包括所有混合物,请计算每种混合物的产量、润滑油指数、成本和价值。对使用的库存量、生产量和润滑油指数应用约束,并针对利润进行优化。
我整理的模型如下...
- A 到 D 列是您提供的信息。
- G2:J5 中的 10 是每个混合中使用的库存量的种子值。求解器将操纵这些。
- K 列包含生产的总产品量。根据您的调查 (a)、(b) 和 (c),这些将以不同的方式受到限制。
=SUM(G3:J3)
向下填充。 - L 列是产品的润滑油指数。正如您所指出的,它是线性混合 - 对于混合问题通常不是这样。这些值将在规划求解中受到限制。它是
{=SUMPRODUCT(G3:J3,TRANSPOSE($B:$B))/$K3}
向下填充的。请注意,这是一个 Control-Shift-Enter (CSE) 公式,因为 TRANSPOSE. - M 列是用于创建产品的库存成本。这用于利润计算。是
{=SUMPRODUCT(G3:J3,TRANSPOSE($C:$C))}
,往下填。这也是一个CSE公式。 - N 列是所生产产品的价值。这用于利润计算。
=K3*C8
向下填充。 - 第 7 行是用于生成所有混合的总库存量。这些值将在规划求解中受到限制。它是
=SUM(G3:G5)
,向右填充。 - 利润计算为
=SUM(N3:N5)-SUM(M3:M5)
。
下面是“规划求解”对话框的快照...
它执行以下操作...
- objective是利润最大化
- 它将通过控制每次混合的存货量来实现。
- 前四个约束 (
$G through $J
) 确保不违反可用库存量。 - 接下来的三个约束条件 (
$K through $K
) 适用于情况 (a) - 生产的产品不超过需求。 - 最后三个约束条件 (
$L through $L
) 确保润滑油指数满足最低规格。 - 未显示 - 我为 GRG 非线性选择了选项并选择了 "Use Multistart" 并取消选择了 "Require Bounds on Variables"。
下面是案例 (a) 的结果...
对于情况 (b),将列 K 的约束更改为“=”而不是“<=”。下面是结果...
对于情况 (c),将列 K 的约束更改为“>=”。下面是结果...