MATHEMATICAL MODEL AND METHOD OF ANALYSIS OF THE OPERATIONAL-CALENDAR PLANNING PROBLEM - YAKHNO, VOLODYMYR; DEMKIVSKYI, IEVGEN; DEMKIVSKA, TETIANA; KALASHNYK, VALERIJ (Herald of Khmelnytskyi National University. Technical sciences, 2025)
The main task of this study is to develop a model of a typical task of operational planning of the distribution of limited resources necessary to perform a certain list of tasks. To implement the task, an analysis of problems arising during operational - calendar planning was conducted, formal models were formulated for a wide range of problems that arise, and a research algorithm was proposed. The task is formulated in this case as follows: a plan is a schedule or an indication of what means (using which resources) and at what time the work should be performed. Each work is performed using a given number of resources (the required intensity of resource use is known) or is not performed at all. The proposed model and research method formulate the task as a problem of placement (dense packing) of dimensional parallelepipeds in a limited region of dimensional space. In addition, the paper provides estimates of the complexity of the developed algorithm. The proposed technology allows at each stage to analyze only locally optimal plans, reduce the search and simplify the choice so that individual stages of the decision-making algorithm, while remaining generally exponential, will be performed in an acceptable time for the user (in experiments - instantly) on real data. In addition, the developed planning technology uses visual models that have a graphical interpretation and allow implementing a convenient and flexible planning method. The geometric location algorithm can be applied to a wide range of tasks - equipment location, cargo, material cutting.