TARU PUBLICATIONS
 Journal of Statistics and Management Systems cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0014·ISSN (Print): 0972-0510
Powered by:Powered by

The Journal of Statistics and Management Systems (JSMS) is a world leading journal publishing high quality, rigorously peer-reviewed original research on theoretical and applied statistics and management systems since 1998. The scope is intentionally broad, but papers must make a novel contribution to the field to be considered for publication. Topics include, but are not limited to, the following: • Statistics • Applied Statistics • Industrial Statistics • Statistical Inference • Interdisciplinary role of Statistics • Actuarial Sciences • Decision Sciences • Managerial Aspects • Management Sciences • Management Information Systems

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Efficient algorithm for solving some inventory control problems

*

* Corresponding author · click or hover a name for details

pp. 343–353Vol. 29Issue 4April 2026DOI: 10.47974/JSMS-1446XML
Received:
06 Feb 2024
Published Online:
20 Jan 2026
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1446
Pages:
343–353

Abstract

Some inventory control problems are considered in the paper, in particular, box constrained inventory control problems. The optimal solution is described by a characterization theorem, and an efficient convergent polynomial algorithm is proposed. 

Keywords

Subject Classifications

90B0590C25

References

[1] G. R. Bitran and A. C. Hax, “Disaggregation and resource allocation using convex knapsack problems with bounded variables”,  Management Science, vol. 27, no. 4, pp. 431-441 (1981). 
[2] P. Brucker, “An O(n) algorithm for quadratic knapsack problems”,  Operations Research Letters, vol. 3, no. 3, pp. 163-166 (1984). 
[3] J.-P. Dussault, J. A. Ferland, and B. Lemaire, “Convex quadratic programming with one constraint and bounded variables”,  Mathematical Programming, vol. 36, no. 1, pp. 90-104 (1986). 
[4] R. Helgason, J. Kennington, and H. Lall, “A polynomially bounded algorithm for a singly constrained quadratic program”,  Mathematical Programming, vol. 18, no. 3, pp. 338-343 (1980). 
[5] A. Kozma, C. Conte, and M. Diehl, “Benchmarking large-scale distributed convex quadratic programming algorithms”,  Optimization Methods and Software, vol. 30, pp. 191-214 (2015). 
[6] J. J. Moré and G. Toraldo, “Algorithms for bound constrained quadratic programming problems”,  Numerische Mathematik, vol. 55, no. 4, pp. 377-400 (1989). 
[7] P. M. Pardalos and N. Kovoor, “An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds”,  Mathematical Programming, vol. 46, no. 3, pp. 321-328 (1990). 
[8] S. M. Stefanov,  A Lagrangian Dual Method for Solving Variational Inequalities, Kluwer Series in Mathematical Programming and Operations Research, Working Paper WP-KSMPOR-99-11, 10 pp. (February 1999). 
[9] S. M. Stefanov,  On the Solution of Variational Inequality Problems by Using Cutting Plane Methods, Kluwer Series in Mathematical Programming and Operations Research, Working Paper WP-KSMPOR-99-12, 9 pp. (February 1999). 
[10] S. M. Stefanov, “On the implementation of stochastic quasigradient methods to some facility location problems”,  Yugoslav Journal of Operations Research, vol. 10, no. 2, pp. 235-256 (2000). 
[11] S. M. Stefanov,  Convex Separable Programming: Theory and Methods, Kluwer Academic Publishers, Dordrecht-Boston-London (2000). 
[12] S. M. Stefanov, “Convex separable minimization subject to bounded variables”,  Computational Optimization and Applications. An International Journal, vol. 18, no. 1, pp. 27-48 (2001). 
[13] S. M. Stefanov, “Polynomial algorithms for projecting a point onto a region defined by a linear constraint and box constraints in Rn”,  Journal of Applied Mathematics, vol. 2004, no. 5, pp. 409-431 (2004). 
[14] S. M. Stefanov, “Convex quadratic minimization subject to a linear constraint and box constraints”,  Applied Mathematics Research Express AMRX, vol. 2004, no. 1, pp. 17-42 (2004). 
[15] S. M. Stefanov, “An efficient method for minimizing a convex separable logarithmic function subject to a convex inequality constraint or linear equality contraint”,  Journal of Applied Mathematics and Decision Sciences, vol. 2006, 19 pages, Article ID 89307 (2006). 
[16] S. M. Stefanov, “Minimization of a convex linear-fractional separable function subject to a convex inequality constraint or linear equality constraint and bounds on the variables”,  Applied Mathematics Research eXpress, vol. 2006, no. 4, 24 pages, Article ID 36581 (2006). 
[17] S. M. Stefanov, “Minimization of a strictly convex separable function subject to convex separable inequality constraint and box constraints”,  Journal of Interdisciplinary Mathematics, vol. 12, no. 5, pp. 647-673 (2009). 
[18] S. M. Stefanov, “Solution of some convex separable resource allocation and production planning problems with bounds on the variables”,  Journal of Interdisciplinary Mathematics, vol. 13, no. 5, pp. 541-569 (2010). 
[19] S. M. Stefanov, “Well-posedness and primal-dual analysis of some convex separable optimization problems”,  Advances in Operations Research, vol. 2013, 10 pages, Article ID 279030 (2013). 
[20] S. M. Stefanov, “On the solution of multidimensional convex separable continuous knapsack problem with bounded variables”,  European Journal of Operational Research, vol. 247, no. 2, pp. 366-369 (2015). 
[21] S. M. Stefanov,  Separable Programming: Theory and Methods, 4th rev. enld. ed., Springer Science+Business Media, B.V., Dordrecht (2016). 
[22] S. M. Stefanov, “Strictly convex separable optimization with linear equality constraints and bounded variables”,  Journal of Statistics and Management Systems, vol. 21, no. 2, pp. 261-272 (2018). 
[23] S. M. Stefanov, “Characterization of the optimal solution of the convex generalized nonlinear transportation problem”,  Journal of Interdisciplinary Mathematics, vol. 22, no. 5, pp. 745-756 (2019). 
[24] S. M. Stefanov, “Characterization of the optimal solution of the convex separable continuous knapsack problem and related problems”,  Journal of Information and Optimization Sciences, vol. 42, no. 1, pp. 1-16 (2021). 
[25] S. M. Stefanov, “On the numerical solution of separable stochastic inventory control problems”,  Journal of Information and Optimization Sciences, vol. 42, no. 3, pp. 533-561 (2021). 
[26] S. M. Stefanov,  Separable Optimization: Theory and Methods, Springer Optimization and Its Applications, Vol. 177, Springer, Cham (2021). 
[27] S. M. Stefanov, “Separable programming: A dynamic programming approach”, In:  Separable Optimization. Springer Optimization and Its Applications, Vol. 177, Springer, Cham, pp. 85-129 (2021). 
[28] S. M. Stefanov, “Numerical solution of some systems of nonlinear algebraic equations”,  Journal of Interdisciplinary Mathematics, vol. 24, no. 6, pp. 1545-1564 (2021). 
[29] S. M. Stefanov, “Numerical solution of systems of nonlinear equations defined by convex functions”,  Journal of Interdisciplinary Mathematics, vol. 25, no. 4, pp. 951-962 (2022). 
[30] S. M. Stefanov, “On some properties of linear functionals”,  Journal of Interdisciplinary Mathematics, vol. 25, no. 8, pp. 2491-2502 (2022). 
[31] S. M. Stefanov, “On the solution of quadratic programming problems”,  Journal of Information and Optimization Sciences, vol. 44, no. 2, pp. 243-253 (2023). 
[32] S. M. Stefanov, “Continuous linear knapsack problems revisited”,  Journal of Information and Optimization Sciences, vol. 44, no. 5, pp. 909-922 (2023). 
[33] S. M. Stefanov, “Numerical solution of box constrained separable convex quadratic programming problems”,  Journal of Information and Optimization Sciences, vol. 45, no. 1, pp. 57-71 (2024). 
[34] D. G. Tian, “An exterior point polynomial-time algorithm for convex quadratic programming”,  Computational Optimization and Applications, vol. 61, pp. 51-78 (2015). 

Views: 63Downloads: 4Citations: 0