reduced cost coefficient

简明释义

缩减成本系数

英英释义

例句

1.A lower reduced cost coefficient indicates a more favorable investment opportunity.

较低的减少成本系数表明更有利的投资机会。

2.During the meeting, the manager highlighted the importance of the reduced cost coefficient in project evaluation.

在会议上，经理强调了在项目评估中减少成本系数的重要性。

3.The team analyzed the reduced cost coefficient to determine the most efficient allocation of resources.

团队分析了减少成本系数以确定资源的最有效分配。

4.By calculating the reduced cost coefficient, we can identify which projects are worth pursuing.

通过计算减少成本系数，我们可以识别哪些项目值得追求。

5.The reduced cost coefficient helps in making informed decisions about budget adjustments.

在做预算调整时，减少成本系数有助于做出明智的决策。

作文

In the realm of operations research and linear programming, the concept of the reduced cost coefficient plays a crucial role in determining the optimal solution to a problem. Essentially, the reduced cost coefficient measures how much the objective function would improve if a particular variable were to enter the solution basis. This coefficient is particularly significant in the context of minimization problems. If the reduced cost coefficient for a non-basic variable is positive in a minimization problem, it indicates that increasing this variable would lead to an increase in the overall cost, thereby suggesting that this variable should not be included in the current solution. Conversely, if the coefficient is negative, it implies that including this variable could decrease the total cost, making it a candidate for entering the basis.Understanding the reduced cost coefficient is vital for decision-makers who rely on linear programming models to optimize resources. For instance, consider a manufacturing company that seeks to minimize production costs while meeting certain constraints such as labor hours and materials available. By analyzing the reduced cost coefficient of various production variables, the company can make informed decisions about which products to prioritize in their production schedule. This analysis allows them to allocate resources more efficiently, ultimately leading to higher profitability.Moreover, the reduced cost coefficient also aids in sensitivity analysis, which examines how changes in the coefficients of the objective function affect the optimal solution. By understanding how sensitive their solution is to changes in the reduced cost coefficient, managers can better prepare for fluctuations in market conditions or operational constraints. This foresight is essential in today's fast-paced business environment, where adaptability can mean the difference between success and failure.In practical applications, calculating the reduced cost coefficient involves using the tableau method in the Simplex algorithm. Each iteration of the Simplex method provides updated values for the reduced cost coefficient, allowing the optimization process to converge towards the best possible solution. As the algorithm progresses, the coefficients for non-basic variables are continuously evaluated, ensuring that the final solution is indeed optimal under the given constraints.In conclusion, the reduced cost coefficient is an indispensable tool in the field of linear programming and operations research. It not only helps in identifying which variables should be included in the solution but also provides insights into the stability and sensitivity of the optimal solution. For businesses aiming to optimize their operations, a thorough understanding of the reduced cost coefficient can lead to more strategic decision-making and enhanced overall performance. Therefore, mastering this concept is essential for anyone involved in quantitative analysis or resource management.

在运筹学和线性规划的领域中，reduced cost coefficient（减少成本系数）的概念在确定问题的最优解方面起着至关重要的作用。基本上，reduced cost coefficient测量了如果某个特定变量进入解决方案基准，目标函数将改善多少。这个系数在最小化问题的背景下尤其重要。如果在最小化问题中，一个非基变量的reduced cost coefficient是正的，这表明增加这个变量会导致总成本的增加，从而暗示该变量不应包含在当前的解决方案中。相反，如果系数是负的，这意味着包括这个变量可能会降低总成本，使其成为进入基准的候选者。理解reduced cost coefficient对依赖线性规划模型来优化资源的决策者至关重要。例如，考虑一家制造公司，旨在最小化生产成本，同时满足诸如劳动小时和可用材料等特定约束。通过分析各种生产变量的reduced cost coefficient，公司可以就优先考虑哪些产品的生产计划做出明智的决定。这种分析使他们能够更有效地分配资源，最终提高盈利能力。此外，reduced cost coefficient还帮助进行敏感性分析，该分析研究目标函数系数的变化如何影响最优解。通过了解他们的解决方案对reduced cost coefficient变化的敏感程度，管理者可以更好地为市场条件或操作约束的波动做好准备。这种前瞻性在当今快速变化的商业环境中至关重要，因为适应能力可能意味着成功与失败之间的差异。在实际应用中，计算reduced cost coefficient涉及在单纯形算法中使用表格法。单纯形法的每次迭代提供了更新的reduced cost coefficient值，使优化过程收敛到最佳可能的解决方案。随着算法的进展，非基变量的系数不断被评估，确保最终的解决方案在给定约束下确实是最优的。总之，reduced cost coefficient在线性规划和运筹学领域是一个不可或缺的工具。它不仅有助于识别哪些变量应包含在解决方案中，还提供了对最优解的稳定性和敏感性的洞察。对于旨在优化运营的企业来说，透彻理解reduced cost coefficient可以导致更具战略性的决策和整体绩效的提升。因此，掌握这一概念对任何参与定量分析或资源管理的人来说都是至关重要的。