Lập trình tuyến tính (LP) là một thủ tục để tối ưu hóa chức năng khách quan để hạn chế bất bình đẳng và không tiêu cực hạn chế. Trong một chương trình tuyến tính, chức năng khách quan cũng như hạn chế sự bất bình đẳng tất cả các chức năng tuyến tính. LP là một thủ tục đã tìm thấy ứng dụng thực tế trong hầu như tất cả các khía cạnh của kinh doanh, từ quảng cáo kế hoạch sản xuất. Giao thông vận tải, phân phối, và các vấn đề kế hoạch sản xuất tổng hợp. | Part II. Mathematical Methods Linear Programming Linear Programming LP is a procedure for optimizing an objective function subject to inequality constraints and non-negativity restrictions. In a linear program the objective function as well as the inequality constraints are all linear functions. LP is a procedure that has found practical application in almost all facets of business from advertising to production planning. Transportation distribution and aggregate production planning problems are the most typical objects of LP analysis. The petroleum industry seems to be the most intensive user of LP. Large oil companies may spend 10 of the computer time on the processing of LP and LP-like models. The Simplex Model LP problems are generally solved via the Simplex model. The standard Solver uses a straightforward implementation of the Simplex method to solve LP problems when the Assume Linear Model Box is checked in the Solver Option dialog. If the Simplex or LP Quadratic is chosen in the Solver Parameters dialog the Premium and Quadratic Solvers use an improved implementation of the Simplex method. The Large-Scale LP Solver uses a specialized implementation of the Simplex method which fully exploits sparsity in the LP model to save time and memory. It uses automatic scaling matrix factorization etc. These same techniques often result in much faster solution times making it practical to solve LP problems with thousands of variables and constraints. Quadratic Programming Quadratic programming problems are more complex than LP problems but simpler than general NLP problems. Such problems have one feasible region with flat faces on its surface but the optimal solution may be found anywhere within the region or on its surface. Large QP problems are subject to many of the same considerations as large LP prob lems. In a straightforward or dense representation the amount of memory increases with the number of variables times the number of constraints regardless
