An algorithm to search a solution to the production scheduling problem

N. P. Savenkova^a, A. Yu. Mokin^ab, A. A. Dryazhenkov^ab, L. A. Artemyeva<sup>ab

a</sup> Lomonosov Moscow State University, 1 Bld. 52 Leninskie Gory, 119991 Moscow, Russia
^b Moscow Centre of Fundamental and Applied Mathematics, 1 Leninskie Gory, 119991 Moscow, Russia

Abstract: A mathematical model of raw materials processing is proposed. The production consists of units processing raw materials, storage tanks, and mixing units. The processing units are assumed to operate in one of two known modes. Switching from one mode to another can be carried out no more than once. The problem of finding the optimal capacity of production at each of units, as well as the time of switching units from one operating mode to another is formulated in a form of discrete optimization problem. The solution of this problem should ensure an achievement of the specified production plan. A method for its solution is proposed, including a transition to a convex statement, as well as an algorithm for discretizing the obtained control. Tab. 2, illustr. 4, bibliogr. 13.

Keywords: task scheduling, material balance, optimal control, discrete optimization, quadratic programming.

UDC: 519.8

Received: 22.03.2024
Revised: 27.04.2024
Accepted: 22.06.2024

DOI: 10.33048/daio.2024.31.798

 English version: Journal of Applied and Industrial Mathematics, 2024, 18:4, 840–850