L. Benkherouf | Kuwait University (original) (raw)
Papers by L. Benkherouf
International Journal of Systems Science, 2013
This paper revisits the classical discrete-time stationary inventory model. A new proof, based on... more This paper revisits the classical discrete-time stationary inventory model. A new proof, based on the theory of quasivariational inequality �QVI�, of the optimality of �s, S � policy is presented. This proof reveals a number of interesting properties of the optimal cost function. Further, the proof could be used as a tutorial for applications of QVI to inventory control. Copyright q 2008 Lakdere Benkherouf. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
Computers & Mathematics with Applications, 2010
RAIRO - Operations Research, 2017
Journal of Applied Mathematics and Stochastic Analysis, 2008
This paper revisits the classical discrete-time stationary inventory model. A new proof, based on... more This paper revisits the classical discrete-time stationary inventory model. A new proof, based on the theory of quasivariational inequality (QVI), of the optimality of (s,S) policy is presented. This proof reveals a number of interesting properties of the optimal cost function. Further, the proof could be used as a tutorial for applications of QVI to inventory control.
SIAM Journal on Control and Optimization, 2005
International Journal of Systems Science: Operations & Logistics, 2020
SIAM Journal on Control and Optimization, 2009
The paper proposes a general theory for the treatment of a class of optimization problems that ar... more The paper proposes a general theory for the treatment of a class of optimization problems that arise as a consequence of a search for the optimal replenishment schedule for finite time horizon inventory models. The decision variables in these optimization problems consist of the number of replenishment periods and the lengths of the periods. When the number of replenishment periods is fixed, it is shown that the optimization problems have a unique solution under some partial differential inequalities. Furthermore, the minimal value is convex as a function of the number of replenishment periods. This leads to a simple procedure for determining the optimal control policy.
International Mathematical Forum, 2006
Communications in Statistics - Simulation and Computation, 2010
Designs for estimating axial slopes of a response surface are considered. A design is said to be ... more Designs for estimating axial slopes of a response surface are considered. A design is said to be A- (D-) rotatable if the trace (determinant) of variance–covariance matrix of the estimated slopes at a point in the factor space is a function of the distance of the point from the center of the design. It is shown that for any order d and any dimension k, a design which is rotatable in the Box and Hunter (1957) sense is automatically A- and D-rotatable. Some specific examples illustrating the validity of this general result are provided.
Journal of Optimization Theory and Applications, 2015
ABSTRACT In this paper, an inventory system with production, remanufacturing and refurbishing act... more ABSTRACT In this paper, an inventory system with production, remanufacturing and refurbishing activities is studied, over a finite planning horizon. The demand is assumed time varying. Used products are returned by customers, and after inspection, they can be classified either as “remanufacturable” or as “refurbishable” items. The remanufacturing process brings “remanufacturable” items up to quality standards that are as rigorous as those of new items. The refurbished items are sold to a secondary market at a reduced price. In order to control the system, two types of policies are considered. For these two policies, a procedure is proposed that determines the order and remanufacturing quantities and the inventory level of returned (used) items at the start of the inspection and recovery processes, which minimize the total costs.
Journal of the Royal Statistical Society: Series B (Methodological)
SUMMARY An earlier study by Benkherouf and Bather considered the question of when the results of ... more SUMMARY An earlier study by Benkherouf and Bather considered the question of when the results of oil exploration in a single area were sufficiently discouraging to render it optimal to stop drilling altogether. This stopping problem is now considerably elaborated by the ...
Communications in Statistics - Simulation and Computation, 2015
IMA Journal of Management Mathematics, 2015
Mathematics and Biosciences in Interaction, 2008
ABSTRACT A predator-prey interaction is considered, where the prey has a stage structure — i.e., ... more ABSTRACT A predator-prey interaction is considered, where the prey has a stage structure — i.e., two life stages, immature and mature. The predator consumes both the immature and mature prey, and the prey is more prone to the predator at higher prey population densities. Both local and global stability of the system equilibria are discussed. With harvesting of the mature prey, there are threshold conditions for a sustainable yield.
Journal of Applied Mathematics and Decision Sciences, 2003
Stochastic Analysis and Applications, 2000
ABSTRACT In this paper, a single product continuous time stochastic inventory model for deteriora... more ABSTRACT In this paper, a single product continuous time stochastic inventory model for deteriorating items, driven by a. conditional Poisson process, is suggested. It is assumed the process Zt modulating the jump intensities of the Poisson process is a Markov chain. By observing the history of the inventory level, a finite dimensional filter for the conditional distribution of Zt is found. Further filters are found when the conditional Poisson process is replaced by an integer–valued random measure with predictable compensator depending on a right–constant sample paths process yt
Operations Research, 1994
ABSTRACT Conventional analysis of stochastic resource allocation problems based on Gittins’ indic... more ABSTRACT Conventional analysis of stochastic resource allocation problems based on Gittins’ indices frequently yield policies which involve an unacceptable amount of switching of the resource from one option to another. This paper discusses a variety of methodologies aimed at solving this problem. They principally involve the development and analysis of stochastic resource allocation models incorporating switching costs together with a consideration of a new class of single-visit policies for which each option has a single (random) period during which it is in receipt of the key resource.
International Journal of Systems Science, 2013
This paper revisits the classical discrete-time stationary inventory model. A new proof, based on... more This paper revisits the classical discrete-time stationary inventory model. A new proof, based on the theory of quasivariational inequality �QVI�, of the optimality of �s, S � policy is presented. This proof reveals a number of interesting properties of the optimal cost function. Further, the proof could be used as a tutorial for applications of QVI to inventory control. Copyright q 2008 Lakdere Benkherouf. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
Computers & Mathematics with Applications, 2010
RAIRO - Operations Research, 2017
Journal of Applied Mathematics and Stochastic Analysis, 2008
This paper revisits the classical discrete-time stationary inventory model. A new proof, based on... more This paper revisits the classical discrete-time stationary inventory model. A new proof, based on the theory of quasivariational inequality (QVI), of the optimality of (s,S) policy is presented. This proof reveals a number of interesting properties of the optimal cost function. Further, the proof could be used as a tutorial for applications of QVI to inventory control.
SIAM Journal on Control and Optimization, 2005
International Journal of Systems Science: Operations & Logistics, 2020
SIAM Journal on Control and Optimization, 2009
The paper proposes a general theory for the treatment of a class of optimization problems that ar... more The paper proposes a general theory for the treatment of a class of optimization problems that arise as a consequence of a search for the optimal replenishment schedule for finite time horizon inventory models. The decision variables in these optimization problems consist of the number of replenishment periods and the lengths of the periods. When the number of replenishment periods is fixed, it is shown that the optimization problems have a unique solution under some partial differential inequalities. Furthermore, the minimal value is convex as a function of the number of replenishment periods. This leads to a simple procedure for determining the optimal control policy.
International Mathematical Forum, 2006
Communications in Statistics - Simulation and Computation, 2010
Designs for estimating axial slopes of a response surface are considered. A design is said to be ... more Designs for estimating axial slopes of a response surface are considered. A design is said to be A- (D-) rotatable if the trace (determinant) of variance–covariance matrix of the estimated slopes at a point in the factor space is a function of the distance of the point from the center of the design. It is shown that for any order d and any dimension k, a design which is rotatable in the Box and Hunter (1957) sense is automatically A- and D-rotatable. Some specific examples illustrating the validity of this general result are provided.
Journal of Optimization Theory and Applications, 2015
ABSTRACT In this paper, an inventory system with production, remanufacturing and refurbishing act... more ABSTRACT In this paper, an inventory system with production, remanufacturing and refurbishing activities is studied, over a finite planning horizon. The demand is assumed time varying. Used products are returned by customers, and after inspection, they can be classified either as “remanufacturable” or as “refurbishable” items. The remanufacturing process brings “remanufacturable” items up to quality standards that are as rigorous as those of new items. The refurbished items are sold to a secondary market at a reduced price. In order to control the system, two types of policies are considered. For these two policies, a procedure is proposed that determines the order and remanufacturing quantities and the inventory level of returned (used) items at the start of the inspection and recovery processes, which minimize the total costs.
Journal of the Royal Statistical Society: Series B (Methodological)
SUMMARY An earlier study by Benkherouf and Bather considered the question of when the results of ... more SUMMARY An earlier study by Benkherouf and Bather considered the question of when the results of oil exploration in a single area were sufficiently discouraging to render it optimal to stop drilling altogether. This stopping problem is now considerably elaborated by the ...
Communications in Statistics - Simulation and Computation, 2015
IMA Journal of Management Mathematics, 2015
Mathematics and Biosciences in Interaction, 2008
ABSTRACT A predator-prey interaction is considered, where the prey has a stage structure — i.e., ... more ABSTRACT A predator-prey interaction is considered, where the prey has a stage structure — i.e., two life stages, immature and mature. The predator consumes both the immature and mature prey, and the prey is more prone to the predator at higher prey population densities. Both local and global stability of the system equilibria are discussed. With harvesting of the mature prey, there are threshold conditions for a sustainable yield.
Journal of Applied Mathematics and Decision Sciences, 2003
Stochastic Analysis and Applications, 2000
ABSTRACT In this paper, a single product continuous time stochastic inventory model for deteriora... more ABSTRACT In this paper, a single product continuous time stochastic inventory model for deteriorating items, driven by a. conditional Poisson process, is suggested. It is assumed the process Zt modulating the jump intensities of the Poisson process is a Markov chain. By observing the history of the inventory level, a finite dimensional filter for the conditional distribution of Zt is found. Further filters are found when the conditional Poisson process is replaced by an integer–valued random measure with predictable compensator depending on a right–constant sample paths process yt
Operations Research, 1994
ABSTRACT Conventional analysis of stochastic resource allocation problems based on Gittins’ indic... more ABSTRACT Conventional analysis of stochastic resource allocation problems based on Gittins’ indices frequently yield policies which involve an unacceptable amount of switching of the resource from one option to another. This paper discusses a variety of methodologies aimed at solving this problem. They principally involve the development and analysis of stochastic resource allocation models incorporating switching costs together with a consideration of a new class of single-visit policies for which each option has a single (random) period during which it is in receipt of the key resource.