Abstract
We study here a set of quasi-variational inequalities related to inventory/production stochastic problems. We mainly focus our attention on two subjects: (i) From a theoretical point of view, we compare the advantages of global controls versus a decentralized approach via a model of an inventory serial system with Gaussian demand. (ii) We consider discretized systems, we solve the simple model of (i), and we apply a similar technique for solving a more complex system with Poissonian demand. The centralized approach naturally leads to large-scale problems; we solve them using a fast algorithm of resolution with very good performances. We conclude with some numerical results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Bensoussan and J.L. Lions,Contrôle Impulsionnel et Inéquations Quasi-variationnelles (Dunod, 1982).
S. Belbas and I. Mayergoyz, Applications of fixed-point methods to discrete variational and quasi-variational inequalities, Numer. Math. 51(1987)631–654.
A. Clark, An informal survey of multi-echelon inventory theory, Naval Rec. Log. Quart. 14 (1972).
M. Crouhy,Gestion Informatique de la Production Industrielle (Editions de l'Usine Nouvelle, 1983).
A. Clark and H. Scarf, Optimal policies for a multi-echelon inventory problem, Manag. Sci. 6(1960)475–490.
A. Clark and H. Scarf, Approximate solution to a simple multi-echelon inventory problem, in:Studies in Applied Probability and Management Science, ed. K. Arrow, S. Karlin and H. Scarf (Stanford University Press, 1962) pp. 161–184.
W. Fleming and R. Rishel,Deterministic and Stochastic Optimal Control (Springer, 1975).
R. González and E. Rofman, Deterministic control problems: An approximation procedure for the optimal cost, SIAM J. Contr. Optim. 23(1985)242–285.
S. Graves, Multistage lot sizing: An iterative approach, in:Multi-level Production/Inventory Control Systems: Theory and Practice, ed. L. Schwarz, TIMS Studies in Management Science 16 (1981) pp. 95–110.
R. González, E. Rofman and C. Sagastizábal, Global optimization of arborescent multilevel inventory systems, J. Global Optim. 6(1995)269–292.
R. González and C. Sagastizábal, Un algorithme pour la résolution rapide d'équations discrètes de Hamilton-Jacobi-Bellman, C.R. Acad. Sci., Série I, 311(1990)45–50.
R. González and M. Tidball, Fast solution of discrete Isaacs' inequalities, Rapport de Recherche 1167, INRIA (1990).
R. González and M. Tidball, Sur l'ordre de convergence des solutions discrétisées en temps et en espace de l'équation de Hamilton-Jacobi, C.R. Acad. Sci., Série I, 314(1992)479–482.
F. Kabbaj, J.L. Menaldi and E. Rofman, Variational approach of serial multi-level production/inventory systems, J. Optim. Theory Appl. 65(1990)447–483.
R. Peterson and E. Silver,Decision Systems for Inventory Management and Production Planning (Wiley, 1979).
H. Scarf,A Survey of Analytic Techniques in Inventory Theory, ed. H. Scarf, D. Gilford and M. Shelly (1963) pp. 185–225.
D. Stroock and S. Varadhan,Multidimensional Diffusion Processes (Springer, 1979).
A. Veinott, The status of mathematical inventory theory, Manag. Sci. 12(1966)745–777.
W. Zangwill, A backlogging model and a multi-echelon model of a dynamical lot size production system: A network approach, Manag. Sci. 15(1969)506–627.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sagastizábal, C.A. A vindication of centralized controls in inventory management. Ann Oper Res 58, 361–378 (1995). https://doi.org/10.1007/BF02038861
Issue Date:
DOI: https://doi.org/10.1007/BF02038861