the infinite horizon periodic review problem with setup costs and capacity constraints a partial characterization of the optimal policy the one item periodic review production and inventory system has been extensively studied in literature theories have been established for various basic constructs of the system of either finite or infinite horizon except for the case where production capacity is finite and production cost contains a fixed as well as a variable component it was conjectured in earlier research papers that the modified s s policy would be optimal to the finite capacity fixed cost model in infinite horizon this paper studies the long run limiting behavior of such systems it proves that the limiting cost function exists and there exist stationary policies that are optimal in the long run the optimal policy however is not of the modified s s type in general but continues to exhibit thex y band structure whenever the inventory level drops belowx order up to capacity when the inventory level is abovey do nothing when the inventory level is betweenx andy however the ordering pattern seems to be changing from problem to problem nevertheless based on a concept called c k convexity introduced in this paper thex y band is shown to be no more than one capacity of width one calculation for the bounds on suchx andy boundaries that are tight in some cases is also provided by exploring thex y band structure a linear program model is proposed to find the optimal policy completely finally an attempt is made to compare the best modified s s policy with the optimal one and a numerical example indicates that the deviation may be more than 11 in cost performance

strong convergence theorems by hybrid methods for families of nonexpansive mappings in hilbert spaces abstract in this paper we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes nakajo and takahashi s theorems k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 simultaneously furthermore we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from nakajo and takahashi using this theorem we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a hilbert space

an inventory model with limited production capacity and uncertain demands ii the discounted cost criterion this paper considers a single item periodic review inventory model with uncertain demands we assume a finite production capacity in each period with stationary data a convex one period cost function and a continuous demand distribution we show under a few additional unrestrictive assumptions that a modified basic stock policy is optimal under the discounted cost criterion both for finite and infinite planning horizons in addition we characterize the optimal base stock levels in several ways

stability analysis and optimization of an inventory system with bounded orders this paper addresses the control of a one item inventory system subject to random order lead time and random demand the key parameter of the control policy is the objective inventory in each period the order to be placed brings the inventory position as close as possible to the objective inventory the order of each period is kept between a lower bound and an upper bound we show that the distribution of the inventory level converges to its stationary distribution provided that the lower bound is smaller than the average demand the upper bound is greater than the average demand and some regularity conditions hold the average inventory cost is shown to be a convex function of the objective inventory level a simulation based approach is proposed for the determination of the optimal objective inventory a method of bisection with derivative is then used to determine the optimal objective inventory the derivatives needed in various iterations of this method are estimated using a single sample path with respect to a given objective inventory numerical results are provided

moudafi s viscosity approximations with meir keeler contractions abstract in this paper we discuss moudafi s viscosity approximations with meir keeler contractions we first present very simple proofs of xu s theorems concerning moudafi s approximations we next prove that browder s and halpern s type convergence theorems imply moudafi s viscosity approximations using them we finally state several deduced theorems

on a hybrid method for a family of relatively nonexpansive mappings in a banach space we prove strong convergence theorems by the hybrid method given by takahashi takeuchi and kubota for a family of relatively nonexpansive mappings under weaker conditions the method of the proof is different from the original one and it shows that the type of projection used in the iterative method is independent of the properties of the mappings we also deal with the problem of finding a zero of a maximal monotone operator and obtain a strong convergence theorem using this method

bounds and asymptotics for planning critical safety stocks we develop bounds and approximations for setting base stock levels in production inventory systems with limited production capacity our approximations become exact as inventories become critical meaning either that the target service level is very high or the backorder penalty is very large our bounds apply even without this requirement we consider both single stage and multi stage systems for single stage systems we find tight bounds and asymptotically exact approximations for optimal base stock levels for multistage systems our results give partial characterizations of the optimal levels part of our analysis is a precise connection in the critical regime between a multistage system and an associated single stage system consisting solely of the bottleneck facility

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0

denumerable undiscounted semi markov decision processes with unbounded rewards this paper establishes the existence of a solution to the optimality equations in undis counted semi markov decision models with countable state space under conditions generalizing the hitherto obtained results in particular we merely require the existence of a finite set of states in which every pair of states can reach each other via some stationary policy instead of the traditional and restrictive assumption that every stationary policy has a single irreducible set of states a replacement model and an inventory model illustrate why this extension is essential our approach differs fundamentally from classical approaches we convert the optimality equations into a form suitable for the application of a fixed point theorem

stability and optimality of a multi product production and storage system under demand uncertainty this work develops a discrete event model for a multi product multi stage production and storage p s problem subject to random demand the intervention problem consists of three types of possible decisions made at the end of one stage which depend on the observed demand or lack of for each item i to proceed further with the production of the same product ii to proceed with the production of another product or iii to halt the production the intervention problem is formulated in terms of dynamic programming dp operators and each possible solution induces an homogeneous markov chain that characterizes the dynamics however solving directly the dp problem is not a viable task in situations involving a moderately large number of products with many production stages and the idea of the paper is to detach from strict optimality with monitored precision and rely on stability the notion of stochastic stability brought to bear requires a finite set of positive recurrent states and the paper derives necessary and sufficient conditions for a policy to induce such a set in the studied p s problem an approximate value iteration algorithm is proposed which applies to the broader class of control problems described by homogeneous markov chains that satisfy a structural condition pointed out in the paper this procedure iterates in a finite subset of the state space circumventing the computational burden of standard dynamic programming to benchmark the approach the proposed algorithm is applied to a simple two product p s system

viscosity approximation methods for nonexpansive mappings abstract viscosity approximation methods for nonexpansive mappings are studied consider a nonexpansive self mapping t of a closed convex subset c of a banach space x suppose that the set fix t of fixed points of t is nonempty for a contraction f on c and t 0 1 let x t c be the unique fixed point of the contraction x tf x 1 t tx consider also the iteration process x n where x 0 c is arbitrary and x n 1 n f x n 1 n tx n for n 1 where n 0 1 if x is either hilbert or uniformly smooth then it is shown that x t and under certain appropriate conditions on n x n converge strongly to a fixed point of t which solves some variational inequality

convergence theorems of common fixed points for a family of lipschitz quasi pseudocontractions abstract in an infinite dimensional hilbert space the normal mann s iteration has only weak convergence in general even for nonexpansive mappings the purpose of this paper is to modify the normal mann s iteration to have strong convergence for a family of lipschitz quasi pseudocontractions in the framework of hilbert spaces our results improve and extend the corresponding ones announced by many others

on optimal policies for production inventory systems with compound poisson demand and setup costs in this paper we consider a single item one machine production inventory system with compound poisson demand the production facility may be on or off while on the production rate is constant and while off the production rate is zero system costs consist of switching costs and inventory and backlogging costs we provide conditions when s s policies are optimal under the long run average expected cost criterion these conditions are met in particular but not necessarily when the inventory costs are convex the developed method in the proof is easy to apply to more general cases moreover the method allows us to compute optimal policies very efficiently

computational complexity of the capacitated lot size problem in this paper we study the computational complexity of the capacitated lot size problem with a particular cost structure that is likely to be used in practical settings for the single item case new properties are introduced classes of problems solvable by polynomial time algorithms are identified and efficient solution procedures are given we show that special classes are np hard and that the problem with two items and independent setups is np hard under conditions similar to those where the single item problem is easy topics for further research are discussed in the last section

viscosity approximations by the shrinking projection method in hilbert spaces we consider viscosity approximations by using the shrinking projection method established by takahashi takeuchi and kubota and the modified shrinking projection method proposed by qin cho kang and zhou for finding a common fixed point of countably many nonlinear mappings and we prove strong convergence theorems which extend some known results we also consider semigroups of nonlinear mappings and obtain strong convergence of iterative schemes which approximate a common fixed point of the semigroup under certain conditions

on catch effort methods of estimating animal abundance by making a clear distinction between catch and removal catch effort methods can be applied in broader circumstances than generally believed for instance animals can be added to a population rather than removed data on animal sightings can be treated as catch and more than one kind of data e g data on both sightings and kill can be used jointly to produce population estimates models and estimation procedures are presented which illustrate these possibilities also least squares estimation generally nonlinear can be used in conjunction with any likelihood model and we illustrate this procedure in a simulation study involving both natural and catch hazard functions properly formulated least squares estimates appear to be as accurate and precise as corresponding maximum likelihood estimates

corrected diffusion approximations for a multistage production inventory system we analyze a multistage inventory system with limited production capacity facing stochastic demands each node follows a periodic review base stock policy for echelon inventory in each period each node attempts to produce enough material to restore cumulative down stream inventory to a fixed target level we develop approximations to the key measures of interest average inventories average backorders and service levels by simultaneously letting the mean demand approach the system s bottleneck capacity and letting the base stock level for finished goods increase without bound using a method of siegmund we thus obtain diffusion limits with higher order correction terms a numerical example suggests that the correction terms can substantially improve the accuracy of the approximations

viscosity approximation methods for fixed points problems the aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed point of a given nonexpansive self mapping

optimal control of a brownian production inventory system with average cost criterion in this paper we study a stochastic production inventory system with finite production capacity and random demand the cumulative production and demand are modeled by a two dimensional brownian motion process there is a setup cost for switching on the production and a convex holding and shortage cost and our objective is to find the optimal production inventory control that minimizes the average cost both lost sales and backlog cases are studied for the lost sales model we show that within a large class of policies the optimal production strategy is either to produce according to an s s policy or never turn on the machine at all thus it is optimal for the firm to not enter the business whereas for the backlog model we prove that the optimal production policy is always of the s s type our approach first develops a lower bound for the average cost among a large class of nonanticipating policies and then shows that the value function of the desired policy reaches the lower bound the results offer insights on the structure of the optimal control policies as well as the interplays between system parameters

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

a weak to strong convergence principle for feje monotone methods in hilbert spaces we consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly exploiting an idea originally proposed by haugazeau we present a simple modification of these methods that makes them strongly convergent without additional assumptions several applications are discussed

x y band and modified s s policy this paper considers the stochastic single item periodic review inventory problem most importantly we assume a finite production capacity per period and a production cost function containing a fixed as well as a variable component with stationary data a convex expected holding and shortage cost function we show that generally the modified s s policy is not optimal to the finite horizon problems the optimal policy does however show a systematic pattern which we call the x y band structure this x y band policy is interpreted as follows whenever the inventory level drops below x order up to capacity when the inventory level is above y do nothing if the inventory level is between x and y however the ordering pattern is different from problem to problem although the x and y bounds may change from period to period we prove the existence of a pair of finite x and y values that can apply for all the periods i e bounds on individual bounds one calculation for such x and y bounds that are tight in some cases is also provided by exploring the x y band structure we can drastically reduce the computation effort for finding the optimal policies