Details
Title
Application of maximum principle to optimization of production and storage costsJournal title
Archives of Control SciencesYearbook
2021Volume
vol. 31Issue
No 4Affiliation
Popescu, Liviu : University of Craiova, Faculty of Economics and Business Administration, Department of Statistics and Economic Informatics, Al. I. Cuza st., No. 13, Craiova 200585, Romania ; Dimitrov, Ramona : University of Craiova, Faculty of Economics and Business Administration, Department of Statistics and Economic Informatics, Al. I. Cuza st., No. 13, Craiova 200585, RomaniaAuthors
Keywords
optimal control ; Pontryagin Maximum Principle ; controllability ; production and storageDivisions of PAS
Nauki TechniczneCoverage
865-881Publisher
Committee of Automatic Control and Robotics PASBibliography
[1] A. Agrachev and Y.L. Sachkov: Control theory from the geometric viewpoint. Encyclopedia of Mathematical Sciences, Control Theory and Optimization, 87, Springer, 2004.[2] K.J. Arrow: Applications of control theory of economic growth. Mathematics of Decision Sciences, 2, AMS, 1968.
[3] S. Axsater: Control theory concepts in production and inventory control. International Journal of Systems Science, 16(2), (1985), 161–169, DOI: 10.1080/00207728508926662.
[4] R. Bellmann: Adaptive control processes: a guided tour. Princeton Univ. Press: Princeton, 1972.
[5] S. Benjaafar, J.P. Gayon, and S. Tepe: Optimal control of a productioninventory system with customer impatience. Operations Research Letters, 38(4), (2010), 267–272, DOI: 10.1016/j.orl.2010.03.008.
[6] R. Brocket: Lie algebras and Lie groups in control theory. In: Mayne D.Q., Brockett R.W. (eds) Geometric Methods in System Theory. NATO Advanced Study Institutes Series (Series C – Mathematical and Physical Sciences), vol. 3. Springer, Dordrecht, 1973, 43–82, DOI: 10.1007/978-94-010-2675-8_2.
[7] M. Caputo: Foundations of Dynamic Economic Analysis: Optimal Control Theory and Applications. Cambridge Univ. Press, 2005, DOI: 10.1017/CBO9780511806827.
[8] M. Danahe, A. Chelbi, and N. Rezg: Optimal production plan for a multiproducts manufacturing system with production rate dependent failure rate. International Journal of Production Research, 50(13), (2012), 3517–3528, DOI: 10.1080/00207543.2012.671585.
[9] G. Feichtinger and R. Hartl: Optimal pricing and production in an inventory model. European Journal of Operational Research, 19 (1985), 45–56, DOI: 10.1016/0377-2217(85)90307-8.
[10] C. Gaimon: Simultaneous and dynamic price, production, inventory and capacity decisions. European Journal of Operational Research, 35 (1988), 426–441.
[11] J.P. Gayon, S. Vercraene, and S.D. Flapper: Optimal control of a production-inventory system with product returns and two disposal options. European Journal of Operational Research, 262(2), (2017), 499–508, DOI: 10.1016/j.ejor.2017.03.018.
[12] C. Hermosilla, R. Vinter, and H. Zidani: Hamilton–Jacobi–Bellman equations for optimal control processes with convex state constraints. Systems & Control Letters, 109 (2017), 30–36, DOI: 10.1016/j.sysconle.2017.09.004.
[13] V. Jurdjevic: Geometric Control Theory. Cambridge Studies in Advanced Mathematics, 52, Cambridge Univ. Press, 1997, DOI: 10.1017/CBO9780511530036.
[14] M.I. Kamien and N.L. Schwartz: Dynamic optimization: The Calculus of Variations and Optimal Control in Economics and Management, 31 Elsevier, 1991.
[15] K. Kogan and E. Khmelnitsky: An optimal control model for continuous time production and setup scheduling. International Journal of Production Research, 34(3), (1996), 715–725.
[16] Y. Qiu, J. Qiao, and P. Pardalos: Optimal production, replenishment, delivery, routing and inventory management policies for products with perishable inventory. Omega-International Journal of Management Science, 82 (2019), 193–204, DOI: 10.1016/j.omega.2018.01.006.
[17] S.M. LaValle: Planning Algorithms. Cambridge University Press, 2006.
[18] M. Li and Z. Wang: An integrated replenishment and production control policy under inventory inaccuracy and time-delay. Computers&Operations Research, 88 (2017), 137–149, DOI: 10.1016/j.cor.2017.06.014.
[19] B. Li and A. Arreola-Risa: Optimizing a production-inventory system under a cost target. Computers&Operations Research, 123 (2020), 105015, DOI: 10.1016/j.cor.2020.105015.
[20] M. Ortega and L. Lin: Control theory applications to the productioninventory problem: a review. International Journal of Production Research, 42(11), (2004), 2303–2322, DOI: 10.1080/00207540410001666260.
[21] V. Pando and J. Sicilia: A new approach to maximize the profit/cost ratio in a stock-dependent demand inventory model. Computers & Operations Research, 120 (2020), 104940, DOI: 10.1016/j.cor.2020.104940.
[22] L. Popescu: Applications of driftles control affine sytems to a problem of inventory and production. Studies in Informatics and Control, 28(1), (2019), 25–34, DOI: 10.24846/v28i1y201903.
[23] L. Popescu: Applications of optimal control to production planning. Information Technology and Control, 49(1), (2020), 89–99, DOI: 10.5755/j01.itc.49.1.23891.
[24] L. Popescu, D. Militaru, and O. Mituca: Optimal control applications in the study of production management. International Journal of Computers, Communications & Control, 15(2), (2020), 3859, DOI: 10.15837/ijccc.2020.2.3859.
[25] A. Seierstad and K. Sydsater: Optimal Control Theory with Economic Applications. North-Holland, Amsterdam, NL, 1987.
[26] S.P. Sethi: Applications of the Maximum Principle to Production and Inventory Problems. Proceedings Third International Symposium on Inventories, Budapest, Aug. 27-31, (1984), 753–756.
[27] S.P. Sethi and G.L.Thompson: Optimal Control Theory: Applications to Management Science and Economics. Springer, New York, 2000.
[28] J.D. Schwartz and D.E. Rivera: A process control approach to tactical inventory management in production-inventory systems. International Journal of Production Economics, 125(1), (2010), 111–124, DOI: 10.1016/j.ijpe.2010.01.011.
[29] D.R. Towill, G.N. Evans, and P. Cheema: Analysis and design of an adaptive minimum reasonable inventory control system. Production Planning & Control, 8(6), (1997), 545–557, DOI: 10.1080/095372897234885.
[30] T.A. Weber, Optimal control theory with applications in economics. MIT Press, 2011.