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MORARU, Vasile; ISTRATI, Daniela; ZAPOROJAN, Sergiu. Solving the days-off scheduling problem using quadratic programming with circulant matrix. In: Journal of Engineering Sciences. 2022, nr. 4, pp. 97-108. ISSN 2587-3474.
|Journal of Engineering Sciences|
|Numărul 4 / 2022 / ISSN 2587-3474 /ISSNe 2587-3482|
The purpose of this paper is the approach of a mathematical model dedicated to planning the consecutive days off of a company’s employees. Companies must find a flexible work schedule between employees, always considering the satisfaction of work tasks as well as guaranteeing consecutive days off. The analysis is based on solving a quadratic programming problem with binary variables. The proposed method uses the properties of the circulant symmetric matrix in the researched model, which allows the transformation of the considered problems into an equivalent separable non-convex optimization problem. A practical continuous convex relaxation approach is proposed. DC Algorithm is used to solve relaxed problems. A solved numerical example is presented.
scheduling problem, binary quadratic programming, circulant matrix, separable optimization, convex relaxation,
problemă de planificare, programare pătratică binară, matrice circulantă, optimizare separabilă, relaxare convexă