Inayatullah Syed, Touheed Nasir, Imtiaz Muhammad
Department of Mathematical Sciences, University of Karachi, Karachi, Pakistan.
Department of Mathematical Sciences, Institute of Business Administration, Karachi, Pakistan.
PLoS One. 2015 Mar 13;10(3):e0116156. doi: 10.1371/journal.pone.0116156. eCollection 2015.
This paper proposes a streamlined form of simplex method which provides some great benefits over traditional simplex method. For instance, it does not need any kind of artificial variables or artificial constraints; it could start with any feasible or infeasible basis of an LP. This method follows the same pivoting sequence as of simplex phase 1 without showing any explicit description of artificial variables which also makes it space efficient. Later in this paper, a dual version of the new method has also been presented which provides a way to easily implement the phase 1 of traditional dual simplex method. For a problem having an initial basis which is both primal and dual infeasible, our methods provide full freedom to the user, that whether to start with primal artificial free version or dual artificial free version without making any reformulation to the LP structure. Last but not the least, it provides a teaching aid for the teachers who want to teach feasibility achievement as a separate topic before teaching optimality achievement.
本文提出了一种简化形式的单纯形法，与传统单纯形法相比具有一些显著优势。例如，它不需要任何类型的人工变量或人工约束；可以从线性规划（LP）的任何可行或不可行基开始。该方法遵循与单纯形法第1阶段相同的转轴序列，无需明确显示人工变量，这也使其具有空间效率。本文后面还给出了新方法的对偶形式，为轻松实现传统对偶单纯形法的第1阶段提供了一种途径。对于初始基既不可行又对偶不可行的问题，我们的方法为用户提供了完全的自由，即可以从原始人工自由版本或对偶人工自由版本开始，而无需对LP结构进行任何重新表述。最后但同样重要的是，它为那些希望在教授最优性实现之前将可行性实现作为一个单独主题进行教学的教师提供了一种教学辅助工具。
