Про один підхід раціонального розподілу ресурсів на виробництві

Abstract

Розглянуто задачу раціонального розподілу ресурсів, розв’язок якої зводиться до розв’язку однієї з задач геометричного проектування. Описано комбінований метод, що дозволяє розв’язок задачі раціонального розподілу наявних ресурсів звести до напрямленого перебору припустимих варіантів розподілу цих ресурсів. Як результат, визначено термін і послідовність виконання робіт, що гарантують оптимальний (у певному сенсі) розв’язок задачі в межах відведених ресурсів.

As it is known, the task of geometric design is searching for optimal allocation of certain geometric objects in specified ranges under various restrictions and some allocation quality criteria, which aim at reducing the costs for raw materials and other resources. Thus, the tasks of optimal resource allocation arise, for example, if there is complete set of the works which should be carried out and resources available for carrying out each work in the best way are limited. The aggregation of large number of theoretical and practical tasks which are associated with the optimal resources allocation to the class of geometric design tasks makes it possible to solve these tasks by the method of geometric design. The task of rational allocation of resources under the condition of limited resources and with the aim of minimizing time for project (the whole set of specified tasks) completing is considered as a task of geometric design in this research paper. Each work is presented in the form of n-parallelepiped with corresponding to the necessary for its implementation resources dimensions for the task solving. The search of some approximation to global extremum is proposed in case of NP-hard task with taking into account the characteristics of the mathematical model of the task. The proposed combined method which consists of modified method of optimization on groups of variables and the modified method of narrowing neighbourhoods allows reducing to directed search of possible variants of the resources allocation the solving the task of rational allocation of available resources. The term and work sequencing which ensure optimal (in some sense) solution of the task within the allotted resources are determined as a result. The program which implements this strategy of n-parallelepipeds allocation is elaborated. Conducted computational experiments confirm the effectiveness of this method from point of view of resource allocation which is close to optimal, at least, for small control tests. A comparison of results is conducted under exhaustion of local extremum points is occurred by the modified method of narrowing neighbourhoods or by the method of random search on the same data set.