Extreme value (maximum or minimum) of the objective function under -3- condition. Specifically, linear programming can solve the problems of production process optimization, logistics transportation and resource allocation. Integer linear programming can solve the investment decision-making problems of enterprises and traveling salesman problems. The research object of dynamic programming is multi-stage decision-making problem, which is mainly used to solve the shortest path problem, multi-stage resource allocation problem, production and storage control problem and equipment renewal problem. According to the characteristics of his research problems, it is mainly used for the overall production, storage and labor coordination to make reasonable statistical planning, which is the greatest benefit. For example, a manufacturing enterprise uses the scientific theory of linear programming to allocate production costs and labor force, and finally the enterprise saves 10% of production costs in manufacturing costs. In addition, it can also be used for production operation planning and scheduling, as well as reasonable blanking, batching and boring.
(2) Decision theory. The so-called decision-making is based on objective possibility, with the help of certain theories, methods and tools, to analyze problems, put forward feasible plans, and study the method of choosing the best plan from a variety of alternative action plans. Decision-making problems usually fall into three categories: deterministic decision-making, risky decision-making and decision-making under uncertainty. In the economic field, the problem solved by decision theory is that enterprise managers make investment, production plans and material transportation plans. Marketing problems of new products, changes in new stock issuance, etc. Modern financial and accounting analysis will also use decision analysis.
(3) transportation problems. The transportation problem has incomparable convenience in studying some problems. When we encounter some bulk materials such as coal, iron, wood, etc. How to make a reasonable transportation plan to transport these materials to various consumption places with the minimum total freight. In addition to these, there are some passenger transport problems, such as air transport, which involve the arrangement of personnel service time of flights and planes. To this end, the International Association for Operational Research has also set up an aviation group to study operational research issues in air transportation. Water transport also includes ship loading plan, port configuration and operation arrangement after the ship arrives in Hong Kong. It is widely used in railways, such as the classic and famous transportation problem, the longest (short) route problem, the arrow flow problem (minimum cost commodity flow problem, multi-commodity flow problem), and the traveling salesman problem. These problems can easily find a wide range of application examples in the field of transportation.
(4) Graph theory. Linear programming is a branch of operational research, with mature theory and convenient and effective methods. However, it can still solve some problems of large-scale systems, with the characteristics of intuitive problem description, simple model calculation and implementation, and can easily decompose or transform some complex problems into possible sub-problems. Network is mainly used to solve the problems of shortest path, minimum connection, minimum cost flow and optimal allocation in production organization and planning management in the economic field. In addition, transportation and distribution in logistics.
-4- Problems, factory and warehouse location problems, etc. You can also use the knowledge of network analysis to help decision makers make optimal arrangements. In a word, network technology is an important tool, especially when planning and arranging large and complex projects.