Economic Analysis: Theory and Practice
 

Solving the procurement optimization problem by means of inverse computation

Vol. 17, Iss. 3, MARCH 2018

Received: 30 October 2017

Received in revised form: 13 November 2017

Accepted: 12 December 2017

Available online: 27 March 2018

Subject Heading: MATHEMATICAL METHODS AND MODELS

JEL Classification: C44, С61

Pages: 586–596

https://doi.org/10.24891/ea.17.3.586

Gribanova E.B. Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russian Federation
katag@yandex.ru

ORCID id: not available

Importance The article investigates the problem of company’s procurement optimization, which consists of defining a set of goods to be ordered so as to maximally supply the demand of buyers under a limited budget.
Objectives The aims are to develop an algorithm to solve the problem of procurement optimization by defining the smallest value of objective function, adjust the obtained values by using inverse computation, compare the obtained results with classical methods.
Methods I employ classical methods for solving nonlinear programming problems, namely, the penalty method and the Lagrange multiplier technique. To solve the optimization problem, I use the inverse computation method.
Results I developed an algorithm for solving the procurement optimization problem by means of inverse computation. In the algorithm, a solution obtained through unconstrained optimization is adjusted with regard to restrictions on available budget. The offered algorithm can be used in the decision support systems for procurement planning.
Conclusions The presented algorithm is more straightforward for computer implementation as compared with classical methods. A solution to procurement optimization problem comes down to solving simultaneous equations. Computational experiments showed the same results for the three methods: inverse computation, penalty, and Lagrange multipliers.

Keywords: quadratic programming, procurement optimization, penalty method, Lagrange multiplier, inverse computation

References:

  1. Kulakova Yu.N. [Two-level approach to enterprise stockpile management]. Ekonomicheskii analiz: teoriya i praktika = Economic Analysis: Theory and Practice, 2013, no. 11, pp. 59–66. URL: https://cyberleninka.ru/article/n/dvuhurovnevyy-podhod-k-upravleniyu-zapasami-predpriyatiya (In Russ.)
  2. Chen Y.-C. A Probabilistic Approach for Traditional EOQ Model. Journal of Information and Optimization Sciences, 2003, vol. 24, iss. 2, pp. 249–253.
  3. Haksever C., Moussourakis J. A Model for Optimizing Multi-product Inventory Systems with Multiple Constraints. International Journal of Production Economics, 2005, vol. 97, iss. 1, pp. 18–30. URL: https://doi.org/10.1016/j.ijpe.2004.05.004
  4. Mitsel' A.A., Stavchuk L.G. [A three-product model to manage inventory with random demand]. Ekonomicheskii analiz: teoriya i praktika = Economic Analysis: Theory and Practice, 2017, vol. 16, iss. 3, pp. 561–572. (In Russ.) URL: https://doi.org/10.24891/ea.16.3.561
  5. Chang C.-T., Ouyang L.-Y., Teng J.-T. An EOQ Model for Deteriorating Items under Supplier Credits Linked to Ordering Quantity. Applied Mathematical Modelling, 2003, vol. 27, iss. 12, pp. 983–996. URL: https://doi.org/10.1016/S0307-904X(03)00131-8
  6. Isavnin A.G., Khamidullin M.R. [Software System for Solving Problems on Optimal Inventory Management by Means of Penalties Method Algorithms]. Vestnik IzhGTU im. M.T. Kalashnikova = Bulletin of Kalashnikov ISTU, 2012, no. 3, pp. 130–132. (In Russ.)
  7. Shekarian E., Kazemi N. Fuzzy Inventory Models: A Comprehensive Review. Applied Soft Computing, 2017, vol. 55, pp. 588–621. URL: https://doi.org/10.1016/j.asoc.2017.01.013
  8. Istomina A.A. [Mathematical models of decision support in assortment and inventory management]. Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie = Modern Technologies. System Analysis. Modeling, 2017, no. 2, pp. 126–132. (In Russ.)
  9. Teng J.-T. A Simple Method to Compute Economic Order Quantities. European Journal of Operational Research, 2009, no. 198, iss. 1, pp. 351–353. URL: https://doi.org/10.1016/j.ejor.2008.05.019
  10. Romanova L.E., Korshunova D.M. [Systematic bases the optimization of the commodity assortment]. Izvestiya Tul'skogo gosudarstvennogo universiteta. Ekonomicheskie i yuridicheskie nauki = Proceedings of TSU. Economic and Legal Sciences, 2013, no. 5, pp. 236–241. (In Russ.)
  11. Manakhov V.V. [Optimal stock modeling for non-foods retailer selling on-credit]. Statistika i ekonomika = Statistics and Economics, 2016, no. 3, pp. 78–82. (In Russ.)
  12. Farmanov R.F. [Optimization of material resources procurement in the resource-saving system of agricultural enterprises]. Voprosy strukturizatsii ekonomiki, 2008, no. 3, pp. 32–37. (In Russ.)
  13. Novikov A.I., Solodkaya T.I. [Measuring risks of the financial assets and ways to form an investment portfolio]. Fundamental'nye i prikladnye issledovaniya kooperativnogo sektora ekonomiki, 2009, no. 1, pp. 41–46. (In Russ.)
  14. Krinichanskii K.V., [Some practical tasks of the portfolio optimization model]. Zhurnal ekonomicheskoi teorii = Russian Journal of Economic Theory, 2012, no. 3, pp. 142–147. (In Russ.)
  15. Lewis R.M., Torczon V., Trosset M.W. Direct Search Methods: Then and Now. Journal of Computational and Applied Mathematics, 2000, vol. 124, iss. 1-2, pp. 191–207. URL: https://doi.org/10.1016/S0377-0427(00)00423-4
  16. Hosobe H. A Hierarchical Method for Solving Soft Nonlinear Constraints. Procedia Computer Science, 2015, vol. 62, pp. 378–384. URL: https://doi.org/10.1016/j.procs.2015.08.422
  17. Odintsov B.E. Obratnye vychisleniya v formirovanii ekonomicheskikh reshenii [Inverse computations in shaping economic decisions]. Moscow, Finansy i statistika Publ., 2004, 256 p.
  18. Odintsov B.E., Romanov A.N. [An iterative method of company management optimization using inverse calculations]. Vestnik Finansovogo universiteta = Bulletin of Financial University, 2014, no. 2, pp. 60–73. (In Russ.)
  19. Gribanova E.B. [Methods for solving inverse problems of economic analysis]. Korporativnye finansy = Journal of Corporate Finance, 2016, no. 1, pp. 119–130. (In Russ.)
  20. Gribanova E.B. [The algorithm for solving linear programming problems through inverse calculations]. Finansovaya analitika: problemy i resheniya = Financial Analytics: Science and Experience, 2017, vol. 10, iss. 9, pp. 1062–1075. (In Russ.) URL: https://doi.org/10.24891/fa.10.9.1062

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