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Market static model for software development based on a transport problem with quadratic cost additions
 
PIIS042473880021697-5-1
DOI10.31857/S042473880021697-5
Publication type Article
Status Published
Authors
Ilya Lesik 
Occupation: Senior Engineer
Affiliation: Joint-Stock Company «Scientific and Production Association Russian basic information technology
Address: Moscow, Russian Federation
Aleksandr Perevozchikov
Occupation: Senior Research Scholar
Affiliation: Joint-Stock Company «Scientific and Production Association Russian basic information technology
Address: Russian Federation
Journal nameEkonomika i matematicheskie metody
EditionVolume 58 Issue 3
Pages94-101
Abstract

The authors propose to formulate a market continuous static model for software development based on the transport problem with quadratic cost additions. In contrast to the existing transport problem with fixed cost surcharges, the authors propose a statement that minimizes the sum of transportation costs, which may contain non-fixed additions proportional to the squares of the volumes of appointments. Thus, a quadratic formulation of the transport problem with non-fixed additions is proposed. It is shown that transport problem with quadratic additions can be reduced to a convex programming problem, which can be solved numerically by the subgradient method, or by the conjugate gradient method for the dual problem. The authors describe the interpretation of transport problem with quadratic additions as an assignment problem with non-fixed price discounts, taking into account the difference between the wholesale and retail prices. This makes possible to apply the set task to build digital platforms in the software development market for loading assignments to performers.

Keywordstransport problem with quadratic cost additions, reduction to a convex programming problem, Polyak's method, dual problem, conjugate directions method.
Received11.03.2022
Publication date22.09.2022
Number of characters14061
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1. Balinski M.L. (1961). Fixed-cost transportation problems. Naval Res. Log. Quart, 8, 1, 41–54.
2. Debreu G. (1954). Valuation equilibrium and pareto optimum. Proceedings of the National Academy of Sciences of the USA, 40, 588–592.
3. Ding X., Wang K., Gibbons P.B., Zhang X. (2012). BWS: Balanced work stealing for time-sharing multicores. Proceedings of the 7-th ACM European Conferens on Computer Systems. EuroSys, 12, 365–378. New York.
4. Fedorov V.V. (1979). Numerical methods of maximin. Moscow: Nauka (in Russian).
5. Finkilstein Y.Y. (1976). Approximate methods and applied problems of discrete programming. Moscow: Nauka (in Russian).
6. Ford L., Fulkerson D. (1966). Flows in networks. Moscow: Mir (in Russian).
7. Khachaturov V.R., Khachaturov R.V., Khachaturov R.V. (2012). Optimization of supermodular functions (supermodular programming). Journal of Computational Mathematics and Mathematical Physics, 52,  6, 999–1000 (in Russian).
8. Korbut A.A., Finkilstein Y.Y. (1969). Discrete programming. D.B. Yudin (ed.). Moscow: Nauka (in Russian).
9. Makarov V.L., Rubinov F.M. (1973). Mathematical theory of economic dynamics and equilibrium. Moscow: Nauka (in Russian).
10. Mesoeconomics of development (2011). G.B. Kleiner (ed.). Moscow: Nauka (in Russian).
11. Perevozchikov A.G., Lesik I.A. (2014). Non-stationary model of investment in fixed assets of the enterprise. Applied Mathematics and Computer Science: Proceedings of the Faculty of Computational Mathematics and Cybernatics of Lomonosov Moscow State University. V.I. Dmitriev (ed.).  Moscow: MAKS Press, 46, 76–88 (in Russian).
12. Perevozchikov A.G., Lesik I.A. (2016). Determination of optimal production volumes and sales prices in a linear model of a multi-product monopoly. Economics and Mathematical Methods, 52, 1, 140–148 (in Russian).
13. Perevozchikov A.G., Lesik I.A. (2020). A dynamic model of investment in scientific research of an oligopoly. Economics and Mathematical Methods, 56, 2, 102–114 (in Russian).
14. Perevozchikov A.G., Lesik I.A. (2021). A dynamic model of software development based on the problem of assignment to bottlenecks. Economics and Mathematical Methods, 56, 4, 102–114 (in Russian).
15. Polyak B.T. (1983). Introduction to optimization. Moscow: Nauka (in Russian).
16. Sergienko A.M., Simonenko V.P., Simonenko A.V. (2016). Improved assignment algorithm for task schedulers in heterogeneous distributed computing systems.  System Research and Information Technologies, 2, 20–35 (in Russian).
17. Sukharev A.G., Timokhov V.V., Fedorov V.V. (1986). Course in optimization methods. Moscow: Nauka (in Russian).
18. Ustyuzhanina E.V., Dement’ev V.E., Evsyukov S.G. (2021). Transactional digital platforms: The task of ensuring efficiency. Economics and Mathematical Methods, 57, 1, 5–18 (in Russian).
19. Vasin A.A., Grigor’eva O.M., Lesik I.A. (2017). Synthesis of the transport system of a multi-node competitive market with variable demand. Applied Mathematics and Computer Science: Proceedings of the Faculty of Computational Mathematics and Cybernatics of Lomonosov Moscow State University. V.I. Dmitriev (ed.). Moscow: MAKS Press, 55, 74–90 (in Russian).
20. Vasin A.A., Grigor’eva O.M., Lesik I.A. (2018). The problem of optimizing the transport system of the energy market. In: The IX Moscow International Conference on Operations Research (ORM2018). Proceedings. A.A. Vasin, A.F. Izmailov (resp. eds.), 247–251 (in Russian).
21. Vasin A.A., Morozov V.V. (2005). Game theory and models of mathematical economics. Moscow: MAKS Press (in Russian).
22. Vasin A.A., Grigor’eva O.M., Cyganov N.I. (2017). Optimization of the transport system of the energy market. Doklady Akademii Nauk, 475,  4,  377–381 (in Russian).

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