This paper is concerned with determining the optimal inventory policy for an infinitehorizon deterministic continuous-time continuous-state inventory model, where, in the absence of intervention, changes in inventory level are governed by a differential evolution equation. The decision maker has the option of ordering from several suppliers, each of which entails differing ordering and purchasing costs. The objective is to select the supplier and the size of the order that minimizes the discounted cost over an infinite planning horizon. The optimal policy is formulated as the solution of a quasi-variational inequality. It is shown that there are three possibilities regarding its solvability: it has a unique solution that corresponds to an (s, S) policy; it does not admit a solution corresponding to an (s, S) policy but does have a unique solution that corresponds to a generalized (s, S) policy; or, it does not admit a solution corresponding to an (s, S) policy or a generalized (s, S) policy. A necessary and sufficient condition for each possibility is obtained. Examples illustrate their occurrence.
Keywords: Optimal inventory policy, quasi-variational inequality, ($$) policy, generalized ($$) policy
@article{RO_2021__55_S1_S947_0,
author = {Benkherouf, Lakdere and Gilding, Brian H.},
title = {Optimal policies for a deterministic continuous-time inventory model with several suppliers},
journal = {RAIRO. Operations Research},
pages = {S947--S966},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020037},
mrnumber = {4223156},
zbl = {1469.90009},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020037/}
}
TY - JOUR AU - Benkherouf, Lakdere AU - Gilding, Brian H. TI - Optimal policies for a deterministic continuous-time inventory model with several suppliers JO - RAIRO. Operations Research PY - 2021 SP - S947 EP - S966 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020037/ DO - 10.1051/ro/2020037 LA - en ID - RO_2021__55_S1_S947_0 ER -
%0 Journal Article %A Benkherouf, Lakdere %A Gilding, Brian H. %T Optimal policies for a deterministic continuous-time inventory model with several suppliers %J RAIRO. Operations Research %D 2021 %P S947-S966 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2020037/ %R 10.1051/ro/2020037 %G en %F RO_2021__55_S1_S947_0
Benkherouf, Lakdere; Gilding, Brian H. Optimal policies for a deterministic continuous-time inventory model with several suppliers. RAIRO. Operations Research, Tome 55 (2021), pp. S947-S966. doi: 10.1051/ro/2020037
, and , Optimal inventory policy. Econometrica 19 (1951) 250–272. | MR | Zbl | DOI
, and , Optimal policies for inventory systems with concave ordering costs. Nav. Res. Logist. 65 (2018) 291–302. | MR | Zbl | DOI
, On the optimality of inventory policies: a quasivariational approach. J. Appl. Math. Stoch. Anal. 158193 (2008) 1–9. | MR | Zbl
and , Optimality of an policy with compound Poisson and diffusion demands: a quasi-variational inequalities approach. SIAM J. Control Optim. 48 (2009) 756–762. | MR | Zbl | DOI
, Dynamic Programming and Inventory Control. IOS Press, Amsterdam (2011). | MR | Zbl | DOI
and , Impulse Control and Quasi-Variational Inequalities. Gauthier–Villars, Paris (1984). | MR
, and , Optimality of an policy with compound Poisson and diffusion demands: a quasi-variational inequalities approach. SIAM J. Control Optim. 44 (2005) 1650–1676. | MR | Zbl | DOI
and , Impulsive control in management: prospects and applications. J. Optim. Theory App. 37 (1982) 419–442. | MR | Zbl | DOI
, and , Optimal inventory policies with two suppliers. Oper. Res. 54 (2006) 389–393. | Zbl | DOI
and , Recent trends in modeling of deteriorating inventory. Eur. J. Oper. Res. 134 (2001) 1–16. | MR | Zbl | DOI
and , Analysis of Inventory Systems. Prentice–Hall, Englewood Cliffs, NJ (1963). | Zbl
, and , Optimal ordering policy for inventory systems with quantity-dependent setup costs. Math. Oper. Res. 42 (2017) 979–1006. | MR | Zbl | DOI
, Optimality of policies in the infinite horizon dynamic inventory problem. Manage. Sci. 9 (1963) 259–267. | DOI
, and , Computing globally optimal inventory policies. Omega 40 (2012) 660–671. | DOI
, and , Optimality of policies in EOQ models with general cost structures. Int. J. Prod. Econ. 187 (2017) 216–228. | DOI
, and , Optimality of inventory policies under renewal demand and general cost structures. Prod. Oper. Manage. 27 (2018) 368–383. | DOI
, On the optimality of generalized policies. Manage. Sci. 17 (1971) 411–426. | Zbl | DOI
, The optimality of generalized policies under uniform demand densities. Manage. Sci. 18 (1972) 644–646. | MR | Zbl | DOI
, Foundations of Stochastic Inventory Theory. Stanford University Press, Stanford, CA (2002). | DOI
, A note on measurement of utility. Rev. Econ. Stud. 4 (1937) 155–161. | DOI
, The optimality of policies in the dynamic inventory problem, edited by , and . In: Mathematical Methods in the Social Sciences 1959. Stanford University Press, Stanford, CA (1960) 196–202. | MR | Zbl
, A solvable one-dimensional model of a diffusion inventory system. Math. Oper. Res. 11 (1986) 125–133. | MR | Zbl | DOI
, Explicit solution of a two-dimensional deterministic inventory problem. Math. Oper. Res. 11 (1986) 134–146. | MR | Zbl | DOI
, Inventory models with inventory-level-dependent demand: a comprehensive review and unifying theory. Eur. J. Oper. Res. 162 (2005) 792–804. | Zbl | DOI
, On the optimality of inventory policies: new conditions and a new proof. SIAM J. Appl. Math. 14 (1966) 1067–1083. | MR | Zbl | DOI
, and , Optimal control policy for a Brownian inventory system with concave ordering cost. J. Appl. Probab. 52 (2015) 909–925. | MR | Zbl | DOI
, and , Optimal policies for Brownian inventory systems with a piecewise linear ordering cost. IEEE Trans. Autom. Control 62 (2017) 3235–3248. | MR | Zbl | DOI
, A note on the optimality of policies in inventory theory. Manage. Sci. 9 (1962) 123–125. | DOI
Cité par Sources :
