optimal price and lot size determination for a perishable product under conditions of finite production partial backordering and lost sale the paper describes an eoq model of a perishable product for the case of price dependent demand partial backordering which depends on the length of the waiting time for the next replenishment and lost sale the model is solved analytically to obtain the optimal price and size of the replenishment in the model the customers are viewed to be impatient and a fraction of the demand is backlogged this fraction is a function of the waiting time of the customers in most of the inventory models developed so far researchers considered that inventory accumulates at the early stage of the inventory and then shortage occurs this type of inventory is called ifs inventory followed by shortage policy in the present model we consider that shortage occurs before the starting of inventory we have proved numerically that instead of taking ifs if we consider sfi shortage followed by inventory policy we would get better result i e a higher profit the model is extended to the case of non perishable product also the optimal solution of the model is illustrated with the help of a numerical example

hilbert space description on nonlinear discrete time dynamical systems it is shown that the linear recurrences of the form xn 1 xn where is analytic in xn can be brought down to a linear recurrence in hilbert space with the boson displacement operator

erratic behavior of invariant circles in standard like mappings abstract we study mappings like the standard map but with the sine replaced by another function by varying a parameter in this function it changes smoothly from the sine to a piecewise linear pwl function the function is always analytic except when it is pwl taking the function close enough to the pwl function it is found that kam tori can reappear after they disappeared when the nonlinearity is increased when plotting the boundary around the area where a kam torus with noble winding number exists in the plane of the non linearity versus the distance of the function to the pwl function self similarity is observed

bayesian single and double variable sampling plans for the weibull distribution with censoring the sampling inspection problem is one of the main research topics in quality control in this paper we employ bayesian decision theory to study single and double variable sampling plans for the weibull distribution with type ii censoring a general loss function which includes the sampling cost the time consuming cost the salvage value and the after sales cost is proposed to determine the bayes risk and the corresponding optimal sampling plan explicit expressions for the bayes risks for both single and double sampling plans are derived respectively numerical examples are given to illustrate the effectiveness of the proposed method comparisons between single and double sampling plans are made and sensitivity analysis is performed

a genetic algorithm approach for the time cost trade off in pert networks we develop a multi objective model for the time cost trade off problem in pert networks with generalized erlang distributions of activity durations using a genetic algorithm the mean duration of each activity is assumed to be a non increasing function and the direct cost of each activity is assumed to be a non decreasing function of the amount of resource allocated to it the decision variables of the model are the allocated resource quantities the problem is formulated as a multi objective optimal control problem that involves four conflicting objective functions the objective functions are the project direct cost to be minimized the mean of the project completion time min the variance of the project completion time min and the probability that the project completion time does not exceed a certain threshold max it is impossible to solve this problem optimally therefore we apply a genetic algorithm for numerical optimizations of constrained problems genocop to solve this multi objective problem using a goal attainment technique several factorial experiments are performed to identify appropriate genetic algorithm parameters that produce the best results within a given execution time in the three typical cases with different configurations finally we compare the genetic algorithm results against the results of a discrete time approximation method for solving the original optimal control problem

computing non stationary s s policies using mixed integer linear programming abstract this paper addresses the single item single stocking location non stationary stochastic lot sizing problem under the s s control policy we first present a mixed integer non linear programming minlp formulation for determining near optimal s s policy parameters to tackle larger instances we then combine the previously introduced minlp model and a binary search approach these models can be reformulated as mixed integer linear programming milp models which can be easily implemented and solved by using off the shelf optimization software computational experiments demonstrate that optimality gaps of these models are less than 0 3 of the optimal policy cost and computational times are reasonable

equivalent classes of critical circles we present numerical evidence that the fractal properties of the critical invariant circles of a typical area preserving twist map as summarized by the spectrum and the generalized dimensions d q depend only on the tails in the continued fraction expansion of the corresponding rotation numbers and d q are numerically the same for all critical invariant circles of the standard and sine maps which have the rotation numbers with the same periodic tail

variables sampling inspection scheme for resubmitted lots based on the process capability index cpk abstract this paper attempts to develop a sampling inspection scheme by variables based on process performance index for product acceptance determination which examines the situation where resampling is permitted on lots not accepted on original inspection the equations for plan parameters the required sample size and the corresponding critical value are derived based on the exact sampling distribution rather than an approximation approach hence the decisions made are more accurate and reliable moreover the efficiency of the proposed variables resubmitted sampling plan is evaluated and compared with the existing variables single sampling plan for illustrative purpose an example is presented to demonstrate the use of the derived results for making a decision on product acceptance determination

critical behavior of a kam surface i empirical results kolmogorov arnol d moser kam surfaces are studied in the context of a perturbed two dimensional twist map in particular we ask how a kam surface can disappear as the perturbation parameter is increased following greene we use cycles to numerically construct the kam curve and discover that at the critical coupling it shows structure at all length scales aspects of this structure are fitted by a scaling analysis critical indices and scaling functions are determined numerically some evidence is presented which suggests that the results are universal

frenkel kontorova model with toda interactions we have studied the frenkel kontorova fk model with toda interactions the phase diagram is found to be asymmetric due to the exponential form of the toda interaction the reflection symmetry observed in the standard fk model is broken here the singularity spectrum and the generalized dimension are calculated and their dependence on the nonlinearity parameter is discussed the critical exponents of the gap in the phonon spectrum the correlation length and the peierls nabarro barrier are found to be the same as those in the standard fk model and are independent of the nonlinearity parameter

a probabilistic approach to rank complex fuzzy numbers abstract techniques for ranking simple fuzzy numbers are abundant in the literature however we lack efficient methods for comparing complex fuzzy numbers that are induced by arithmetic operations in this paper a probabilistic approach is taken membership functions of fuzzy numbers are first converted into probability density functions the mellin transform is then introduced to compute the mean and the variance of a complex fuzzy number the fuzzy number with the higher mean is ranked higher if the means are equal the one with the smaller variance is judged higher rank two numerical examples and a fuzzy multiple attribute decision analysis are illustrated

hilbert space description of classical dynamical systems ii abstract it is shown that classical dynamical systems can be described by a hilbert space schrodinger like equation with the hamiltonian a non hermitian one expressed in terms of bose creation and annihilation operators the presented formalism includes the carleman embedding as the special case

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

the discrete frenkel kontorova model and its extensions i exact results for the ground states abstract we present a rigorous study of the classical ground states under boundary conditions of a class of one dimensional models generalizing the discrete frenkel kontorova model the extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic quasi periodic and chaotic orbits for all boundary conditions we select among all the extremum solutions of the energy of the model those which correspond to the ground states of the infinite system we prove that these ground states are either periodic commensurate or quasi periodic incommensurate but are never chaotic we also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions the topological structure of the whole set of ground states is described in details in addition to physical applications consequences for twist map homeomorphisms are mentioned part ii s aubry p y ledaeron and g andre will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map

optimization of fuzzy production inventory models in this paper we introduce two fuzzy production inventory models with fuzzy parameters for crisp production quantity or for fuzzy production quantity the fuzzy total production inventory costs of these models under the fuzzy arithmetical operations of function principle are proposed the final purpose is to find optimal solutions of these models by using graded mean integration representation method for defuzzifing fuzzy total production inventory cost and by using extension of the lagrangean method for solving inequality constrain problem furthermore we find that the optimal solutions are all crisp real numbers in addition when the fuzzy parameters fuzzy inventory cost fuzzy demand fuzzy setup cost fuzzy demand rate and fuzzy production rate are all crisp real numbers the optimal solutions of our proposed models can be specified to meet classical production inventory models

sample path derivatives for s s inventory systems for s s inventory systems we derive sample path derivatives of performance measures with respect to the two parameters s and s these derivatives yield derivative estimators which can be estimated from a single sample path or simulation of the inventory system in some cases not even requiring actual knowledge of the underlying demand distribution such derivative estimates would be useful in sensitivity analysis or in gradient based optimization techniques we consider the nondiscounted periodic review system with general independent and identically distributed i i d continuous demands full backlogging and general holding and shortage costs for the infinite horizon model consistency proofs are given for some special cases although we argue why the estimators should be correct for the more general case

using parametric classification trees for model selection with applications to financial risk management abstract we describe two parametric classification tree methods which allow formal selection of a member of a class of generalised distributions in the paper we consider generalised beta distributions for non negative random variables and the generalised skew student distribution for random variables distributed on the real line we introduce a class of symmetric generalised multivariate student distributions members of which may also be selected using the classification trees we present two versions of the parametric classification tree specific to general and general to specific we apply the classification methods to daily returns on stocks from a selection of 15 major mid cap and emerging markets the results show that the majority of return distributions follow student s t but that a non negligible minority follow a symmetric generalised student distribution we confirm a well known stylised fact about skewness it tends not to be persistent by contrast kurtosis is persistent using the symmetric generalised multivariate student distribution we present a risk management study based on efficient portfolios constructed from ukftse250 stocks and specifically concerned with the computation of value at risk the case study demonstrates that the model selection procedures based on the classification trees lead to more accurate computation of var than those based on the normal distribution or on non parametric approaches the study also shows that the normal distribution may be used for var computations for larger portfolios when the holding period is longer

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

nonanalytic twist maps and frenkel kontorova models we give a review of our recent works on a class of twist maps and frenkel kontorova fk models in which the external potential function is nonanalytic c1 and endowed with a variable degree of inflection z when z 3 recurrence of invariant curves has been observed an inverse residue criterion for the reappearance of an invariant curve complementary to the residue criterion for the disappearance of an invariant curve is introduced to make a precise determination of the reappearance point we have also studied the local and global scaling behaviors of these curves the critical exponents the singularity spectrum and the generalized dimensions are found to vary with z when 2 z 3 but remain the same for z 3 the degree of inflection thus plays a role reminiscent of that of dimensionality in phase transitions with z 2 and 3 corresponding respectively to the lower and upper critical dimensions when the same nonanalytic function is substituted for the sinusoidal external potential in the standard fk model the same conclusions are reached there exists a sequence of pinning depinning transitions and the critical exponents of the phonon gap the coherence length and the peierls nabarro barrier all show the same dependence on z

fractal boundary for the existence of invariant circles for area preserving maps observations and renormalisation explanation abstract breakup of a golden invariant circle is studied in an extended version of the standard map with two parameters the critical line in parameter space turns out to have a cantor set of cusps which can be organized in a self similar tree a theoretical explanation is conjectured in terms of a horseshoe for a renormalisation operator the results of some other researchers on similar systems are shown to fit this explanation as well

random effects weibull regression model for occupational lifetime abstract with great interest we read the recent publication of sohn et al sohn s y chang i s moon t h 2007 random effects weibull regression model for occupational lifetime european journal of operational research 179 124 131 on a weibull regression model with random effects for modelling occupational lifetime we congratulate sohn and colleagues on their comprehensive and clearly written paper nevertheless we would like to comment on two points the first regarding the moments of the underlying weibull distribution the second regarding the relations of sohn s model to the class of frailty models

the l average value and the fuzzy expectation of a fuzzy random variable abstract the concepts of fuzzy random variable and the associated fuzzy expected value have been introduced by puri and ralescu as an extension of measurable set valued functions random sets and of the aumann integral of these functions respectively on the other hand the average function has been suggested by campos and gonzalez as an appropriate function to rank fuzzy numbers in this paper we are going to analyze some useful properties concerning the average value of the expectation of a fuzzy random variable and some practical implications of these properties are also commented on

backlund transformations for nonlinear evolution equations hilbert space approach abstract a new method of determining backlund transformations for nonlinear partial differential equations of the evolution type is introduced using the hilbert space approach the problem of finding backlund transformations is brought down to the solution of an abstract equation in hilbert space

dynamic pricing of seasonal goods with spot and forward purchase demands this paper deals with the problem of jointly determining the order size and dynamic prices for a perishable inventory system over a finite time planning horizon when firms simultaneously provide customers with a prompt delivery option and a delivery schedule option customers are segmented into two types namely spot purchase customers and the forward purchase customers demands for both types of customers are assumed to be time and price dependent the decision maker of the inventory system is assumed to apply pricing policies to stimulate demand to improve revenues under the condition that customers with forward purchases may cancel their orders a mathematical model is developed to find the optimal number of price settings the optimal dynamic prices and the order quantity a solution procedure is found to determine the optimal decisions

an optimal inventory replenishment policy for a deteriorating item with time quadratic demand and time dependent partial backlogging with shortages in all cycles abstract the paper deals with an optimal inventory replenishment policy for a deteriorating item considering time quadratic demand and time dependent partial backlogging which depends on the length of the waiting time for the next replenishment over a finite time horizon and variable replenishment cycle the model is solved analytically to obtain the optimal solution of the problem it is then illustrated with the help of numerical examples

dependent chance programming a class of stochastic optimization this paper provides a theoretical framework of dependent chance programming as well as dependent chance multiobjective programming and dependent chance goal programming which are new types of stochastic optimization a stochastic simulation based genetic algorithm is also designed for solving dependent chance programming models

constraint programming for computing non stationary r s inventory policies abstract this paper proposes a constraint programming model for computing the finite horizon single item inventory problem with stochastic demands in discrete time periods with service level constraints under the non stationary version of the periodic review order up to level policy i e non stationary r s or simply r n s n it is observed that the modeling process is more natural and the required number of variables is smaller compared to the mip formulation of the same problem the computational tests show that the cp approach is more tractable than the conventional mip formulation two different domain reduction methods are proposed to improve the computational performance of solution algorithms the numerical experiments confirmed the effectiveness of these methods

an economic production lot size model with deteriorating items stock dependent demand inflation and partial backlogging in this paper we present an optimization framework to derive optimal production over a fixed planning horizon for items with a stock dependent demand rate and under inflationary conditions we consider a perishable item that follows a two parameter weibull distribution shortage is allowed and partially backlogged at a fixed rate a numerical example is taken up to illustrate the solution procedure and sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out

universal properties of the transition from quasi periodicity to chaos in dissipative systems abstract an exact renormalization group transformation is developed for dissipative systems which describes how the transition to chaos may occur in a continuous and universal manner if the frequency ratio in the quasi periodic regime is held at a fixed irrational value our approach is a natural extension of k a m theory to strong coupling most of our analysis is for analytic circle maps we have found a strong coupling fixed point where invertibility is lost which describes the universal features of the transition to chaos we find numerically that any two such critical maps with the same winding number are c 1 conjugate it follows that the low frequency peaks in an experimental spectrum are universal and we determine how their envelope scales with frequency when the winding number has a periodic continued fraction our renormalization transform has a fixed point and spectra are self similar in addition for a set of non periodic winding numbers with full measure our renormalization transformation yields an ergodic trajectory in a sub space of all critical maps physically one finds singular and universal spectra that do not scale

lot size reorder point inventory model with fuzzy demands abstract this paper discusses the lot size reorder point inventory problem with fuzzy demands different from the existing studies the shortages are backordered with shortage cost incurred the cut of the fuzzy demand is used to construct the fuzzy total inventory cost for each inventory policy q r where q is the quantity to be ordered and r is the reorder point yager s ranking method for fuzzy numbers is utilized to find the best inventory policy in terms of the fuzzy total cost five pairs of simultaneous nonlinear equations for the optimal q and r are derived for r in five different ranges of the fuzzy demand when the demand is a trapezoidal fuzzy number each pair of the simultaneous equations reduces to a set of closed form equations they are proved to be able to produce the optimal solution apparently the methodology developed in this paper can be applied to other types of inventory problems to find the best inventory policy

finding optimal s s policies is about as simple as evaluating a single policy in this paper a new algorithm for computing optimal s s policies is derived based upon a number of new properties of the infinite horizon cost function c s s as well as a new upper bound for optimal order up to levels s and a new lower bound for optimal reorder levels s the algorithm is simple and easy to understand its computational complexity is only 2 4 times that required to evaluate a specific single s s policy the algorithm applies to both periodic review and continuous review inventory systems

price determination for an eoq model for deteriorating items under perfect competition the problem of price determination for an eoq model under perfect competition is of central importance in the field of inventory control and management especially for such kind of models which study the dynamics of the market economy over time in this paper an attempt has been made to analyze and compute the price of a unit item of inventory for an eoq model for deteriorating items under the perfect competition as an important market structure along with the optimization technique the marginal revenue and marginal cost approach has been employed to determine the price of a unit item of inventory the present work is presumably believed to provide theoretical as well as applicable insight for marketing experts and inventory managers engaged in this field

design of progressively censored group sampling plans for weibull distributions an optimization problem optimization algorithms provides efficient solutions to many statistical problems essentially the design of sampling plans for lot acceptance purposes is an optimization problem with several constraints usually related to the quality levels required by the producer and the consumer an optimal acceptance sampling plan is developed in this paper for the weibull distribution with unknown scale parameter the proposed plan combines grouping of items sudden death testing in each group and progressive group removals and its decision criterion is based on the uniformly most powerful life test a mixed integer programming problem is first solved for determining the minimum number of failures required and the corresponding acceptance constant the optimal number of groups is then obtained by minimizing a balanced estimation of the expected test cost excellent approximately optimal solutions are also provided in closed forms the sampling plan is considerably flexible and allows to save experimental time and cost in general our methodology achieves solutions that are quite robust to small variations in the weibull shape parameter a numerical example about a manufacturing process of gyroscopes is included for illustration

an efficient algorithm for computing optimal s s policies this paper presents an algorithm to compute an optimal s s policy under standard assumptions stationary data well behaved one period costs discrete demand full backlogging and the average cost criterion the method is iterative starting with an arbitrary given s s policy and converging to an optimal policy in a finite number of iterations any of the available approximations can thus be used as an initial solution each iteration requires only modest computations also a lower bound on the true optimal cost can be computed and used in a termination test empirical testing suggests very fast convergence

an epq model with partial backorders considering two backordering costs abstract we propose an epq model with partial backorders considering linear and fixed backordering costs time intervals rather than ordering size and backordering level are used as decision variables to derive the closed form optimal solution our approach analyzes different optimal inventory policies and decides whether shortage period should be scheduled in addition a critical backordering rate is derived to determine the feasible optimal solution the numerical example is provided to illustrate the solution procedure

recurrence of kolmogorov arnold moser tori in nonanalytic twist maps we study a class of twist maps where the functiong 1 2 z 1 is nonanalytic c1 and endowed with a varying degree of inflectionz whenz 3 reappearance of a kam torus after its breakup has been observed we introduce an inverse residue criterion to determine the reappearance point scaling behavior at the transition points is also studied for 2 z 3 the scaling exponents are found to vary withz whereas forz 3 they are independent ofz in this sensez 3 plays a role quite similar to that of the upper critical dimension in phase transitions

an epq model with inflation in an imperfect production system in this paper a production inventory model is considered for stochastic demand with the effect of inflation generally every manufacturing system wants to produce perfect quality items however due to real life problems labor problems machine breakdown etc a certain percentage of products are of imperfect quality the imperfect items are reworked at a cost the lifetime of a defective item follows a weibull distribution due to the production of imperfect quality items a product shortage occurs the profit function is derived by using both a general distribution of demand and the uniform rectangular distribution of demand computational experiments along with graphical illustrations are presented to discuss the optimality of the probability functions

on the objective function behavior in s s inventory models the most common measure of effectiveness used in determining the optimal s s inventory policies is the total cost function per unit time es s s in stationary analysis this function is constructed through the limiting distribution of on hand inventory and it involves some renewal theoretic elements for 0 given es turns out to be convex in s so that the corresponding optimal reorder point s1 can be characterized easily however es1 is not in general unimodal on 0 this requires the use of complicated search routines in computations as there is no guarantee that a local minimum is global both for periodic and continuous review systems with constant lead times full backlogging and linear holding and shortage costs we prove in this paper that e s1 0 0 is both necessary and sufficient for a global minimum es1 is pseudoconvex on 0 if the underlying renewal function is concave the optimal stationary policy can then be computed efficiently by a one dimensional search routine the renewal function in question is that of the renewal process of periodic demands in the periodic review model and of demand sizes in the continuous review model

generalized frenkel kontorova models we have studied two generalized frenkel kontorova fk models in one of them the interatomic potential is changed from simple harmonic to toda in the other the external potential is changed from sinusoidal to nonanalytic their critical behaviors are found to be markedly different in the toda case the local critical exponents are the same as those in the standard fk model however the global singularity spectrum and the generalized dimension depend on the anharmonicity parameter in the nonanalytic fk model the critical exponents are found to vary with the degree of inflection z for 2 z 3 a sequence of pinning and depinning transitions reflecting the recurrence of kolmogorov arnol d moser tori has also been observed

optimization models and a ga based algorithm for stochastic time cost trade off problem in real life projects both the trade off between the project cost and the project completion time and the uncertainty of the environment are considerable aspects for decision makers however the research on the time cost trade off problem seldom concerns stochastic environments besides optimizing the expected value of the objective is the exclusive decision making criterion in the existing models for the stochastic time cost trade off problem in this paper two newly developed alternative stochastic time cost trade off models are proposed in which the philosophies of chance constrained programming and dependent chance programming are adopted for decision making in addition a hybrid intelligent algorithm integrating stochastic simulations and genetic algorithm is designed to search the quasi optimal schedules under different decision making criteria the goal of the paper is to reveal how to obtain the optimal balance of the project completion time and the project cost in stochastic environments

optimization of the finite production rate model with scrap rework and stochastic machine breakdown this study employs mathematical modeling along with a recursive searching algorithm to determine the optimal run time for an imperfect finite production rate model with scrap rework and stochastic machine breakdown in real life manufacturing systems generation of defective items and machine breakdown are inevitable the objective of this paper is to address these issues and to be able to derive the optimal production run time it is assumed that the proposed manufacturing system produces defective items randomly a portion of them is considered to be scrap and the other portion can be repaired through rework further the proposed system is subject to random breakdown and when it occurs the abort resume ar policy is adopted under such an inventory control policy the production of the interrupted lot will be resumed immediately when machine is fixed and restored mathematical modeling along with a recursive searching algorithm is used for deriving the replenishment policy for such a realistic production system

continuous review inventory model in mixed fuzzy and stochastic environment in this paper we consider a continuous review inventory system where fuzziness and randomness appear simultaneously into an optimization setting since demand plays an important role in such type of inventory systems we develop a model in a mixed environment by incorporating fuzzy random variable as customer demand after fuzzifying the random lead time demand we consider the annual average demand as a fuzzy random variable we provide an elegant methodology to determine the optimal order quantity and reorder point such that the total expected annual cost in the fuzzy sense has a minimum value since the expected value of a fuzzy random variable is a fuzzy quantity a method of ranking fuzzy numbers using their possibilistic mean values is adopted to achieve the optimal solution a numerical example is presented to illustrate the proposed model

two storage inventory problem with dynamic demand and interval valued lead time over finite time horizon under inflation and time value of money a finite time horizon inventory problem for a deteriorating item having two separate warehouses one is a own warehouse ow of finite dimension and other a rented warehouse rw is developed with interval valued lead time under inflation and time value of money due to different preserving facilities and storage environment inventory holding cost is considered to be different in different warehouses the demand rate of item is increasing with time at a decreasing rate shortages are allowed in each cycle and backlogged them partially shortages may or may not be allowed in the last cycle and under this circumstance there may be three different types of model here it is assumed that the replenishment cycle lengths are of equal length and the stocks of rw are transported to ow in continuous release pattern for each model different scenarios are depicted depending upon the re order point for the next lot representing the lead time by an interval number and using the interval arithmetic the single objective function for profit is changed to corresponding multi objective functions these functions are maximized and solved by fast and elitist multi objective genetic algorithm femga the models are illustrated numerically and the results are presented in tabular form

inventory models with general backorder costs abstract under the prevalent assumption of linear inventory holding and backorder costs important results have been established in many basic inventory models however the assumption is often too restrictive for many applications in this paper we study stochastic inventory models under more general backorder costs namely the penalty costs for each unit of backorder consisting of fixed and proportional components under this backorder cost structure we derive a necessary and sufficient condition for the quasiconvexity of the one step loss function this condition is satisfied by a wide spectrum of demand distributions but it is not distribution free consequently existing results based on quasiconvex loss functions are applicable in many but not all models with the above cost structure

a fully polynomial time approximation scheme for single item stochastic inventory control with discrete demand the single item stochastic inventory control problem is to find an inventory replenishment policy in the presence of independent discrete stochastic demands under periodic review and finite time horizon in this paper we prove that this problem is intractable and design for it a fully polynomial time approximation scheme

inventory without backorder with fuzzy total cost and fuzzy storing cost defuzzified by centroid and signed distance abstract in the total cost of inventory without backorders we fuzzify the total demand r and the cost of storing one unit per day a to the triangular fuzzy numbers r and a in a plan period respectively for any order quantity q 0 we get the fuzzy total cost h q r a in terms of r and a then we defuzzify by the centroid and the signed distance methods we can find the minimun total cost and the optimal order quantity by defuzzifying the total cost through the centroid method we can do the same thing by the signed distance method then we compare the results obtained by these two methods

economic lot sampling inspection from defect counts with minimum conditional value at risk abstract expected cost functions are often minimized to determine optimal inspection schemes for lot acceptance purposes however minimum mean cost sampling plans usually have high probabilities of suffering great losses a risk management perspective based on minimizing the conditional value at risk cvar is proposed in order to avoid unacceptably large costs in essence the cvar associated with an inspection scheme is the expected cost of a given proportion of the most costly cases optimal defects per unit acceptance sampling plans with controlled producer and consumer risks for screening lots of incoming materials and outgoing products are determined by minimizing the cvar for a given risk aversion degree the decision criterion is based on the uniformly most powerful test the poisson distribution is used to model the number of nonconformities per sampled unit and the natural prior uncertainty on the defect rate is described by a truncated gamma distribution a computational algorithm is suggested to solve the underlying integer nonlinear programming problem practitioners can assume a restricted range for the defect rate and prior knowledge on may be updated using past performance of the inspection plan the developed methodology is applied to the manufacturing of paper for illustrative purposes

uncertain programming a unifying optimization theory in various uncertain environments by uncertain programming we mean the optimization theory in generally uncertain random fuzzy fuzzy random grey etc environments three broad classes of uncertain programming are expected value models and chance constrained programming as well as dependent chance programming in order to solve general uncertain programming models a simulation based genetic algorithm is also documented finally some applications and further research problems appearing in this area are posed

on possibilistic mean value and variance of fuzzy numbers dubois and prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions in this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval valued possibilistic mean and investigate its relationship to the interval valued probabilistic mean we also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions which are consistent with the extension principle we also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

multi item imperfect production lot size model with hybrid number cost parameters in this study we have developed a multi item finite production lot size model with reworking of imperfect quality items when production stops defected items are assumed to rework at a constant rate the cost parameters in this model are taken here as hybrid numbers i e some of the costs are fuzzy numbers as well as random variables then the model is converted into a multi objective geometric programming gp problem a numerical example is given to support the problem a sensitivity analysis has given to study the nature of the objective functions

singularity spectrum of a critical kam torus the authors numerically determine the f alpha spectrum of scaling indices for critical kam tori in the area preserving standard map similarities and differences between the corresponding orbits of circle maps are discussed

linearization transformations for non linear dynamical systems hilbert space approach abstract a new method for the linearization of non linear dynamical systems with both a finite and an infinite number of degrees of freedom is introduced using the hilbert space approach the problem of finding the linearization transformations is reduced to the solution of abstract linear equations in hilbert space

bayesian variable sampling plans for the exponential distribution with type i censoring in this article a model of single variable sampling plan with type i censoring is studied under the assumption that the variable is exponentially distributed and the loss function is a polynomial an explicit expression of the bayes risk is derived then a simple and finite algorithm to determine an optimal sampling plan for minimizing the bayes risk is suggested furthermore a discretization method is proposed so that one can easily obtain an approximately optimal sampling plan

a renormalization approach to invariant circles in area preserving maps abstract kadanoff and shenker introduced a renormalisation approach to invariant circles in area preserving maps this paper makes more precise the connection between invariant circles and the renormalisation operator restricting attention to noble rotation numbers the stability of a simple fixed point of the renormalisation is analysed corresponding to a linear twist map it is found to be essentially attracting so that noble circles persist under perturbation giving a new view on kam theory shenker and kadanoff found evidence for another fixed point corresponding to a map with a non smooth noble circle further evidence is given in this paper it has essentially only one unstable direction and its stable manifold is believed to give the boundary of the set of twist maps with a noble circle finally noble circles are shown to be locally most robust in an important sense

an eoq model with delay in payments and stock dependent demand in the presence of imperfect production abstract in real life situation supplier generally offers a delay period to the retailer to buy more in this connection a mathematical model is considered to investigate the retailer s optimal replenishment policy under permissible delay in payment with stock dependent demand within the eoq economic order quantity framework most of the eoq models are considered with infinite replenishment rate in this article the model is considered with finite replenishment rate under progressive payment scheme with the production of defective items within the cycle time the mathematical models have been derived for obtaining the optimal cycle time so that the annual total relevant cost is minimized numerical examples along with graphical representation and sensitivity analysis are provided to illustrate the model

multi objective fuzzy inventory model with three constraints a geometric programming approach a multi item multi objective inventory model with shortages and demand dependent unit cost has been formulated along with storage space number of orders and production cost restrictions in most of the real world situations the cost parameters the objective functions and constraints of the decision makers are imprecise in nature hence the cost parameters the objective functions and constraints are imposed here in fuzzy environment this model has been solved by geometric programming method the results for the model without shortages are obtained as a particular case the sensitivity analysis has been discussed for the change of the cost parameters the models are illustrated with numerical examples

optimal bayesian sampling acceptance plan with random censoring abstract the sampling acceptance scheme with censoring is one of the important life inspection problems in this article a general model of sampling acceptance plan for the exponential distribution with exponentially distributed random censoring is presented and investigated using bayesian decision theory we consider a loss function which includes the sampling cost time consuming cost and decision loss to determine the optimal sampling acceptance plan under mild assumptions the optimal bayes rule can be proved to be of a monotonic form moreover we obtain optimal bayes rules and explicit expressions of the bayes risk for two special decision loss functions finally a numerical example is given to demonstrate the model

optimum attributes component test plans for k out of n f weibull systems using prior information abstract assuming that the proportion defective in a production process p is variable and the component lifetimes are weibull distributed integer nonlinear programming problems are formulated and solved in order to determine the optimum component inspection scheme by attributes for k out of n f system reliability demonstration using available prior knowledge a limited beta prior model is adopted to reflect the random fluctuations on p the required quantity of components to test and the permissible number of component failures up to a specified censoring time are found by solving a minimisation problem with nonlinear constraints which are related to the tolerable average producer and consumer risks first order taylor polynomials of the operating characteristic function are used to derive a quite accurate approximate solution lower and upper bounds are also deduced optimal solutions are usually robust to small variations in the weibull parameters and prior information existing technical knowledge and experience are shown to be of great practical value in designing optimal sampling plans for lot acceptance purposes the proposed approach generalises the classical viewpoint to those cases in which appreciable prior information on the fraction of defective systems exists and also allows the analyst to determine the acceptability of a k out of n f system before assembly and to limit the range of p moreover the practitioners may attain substantial savings in sample size and improved assessments of the true producer and consumer risks a 4 out of 5 f system of independent water pumps for cooling a reactor is considered to illustrate the suggested component test plans

an inventory model for imperfect items under inflationary conditions with considering inspection errors this paper represents a discounted cash flow approach for an inventory model for imperfect items under inflationary conditions with considering inspection errors the previous imperfect quality inventory studies however have mostly had the emphasis on developing cost minimizing models that do not consider imperfect inspection processes and related defect sales return issues despite their practical significance in this paper we assume that some produced items might not be perfect and the first stage inspector of product quality control might make some inspection errors during the separation of defective and perfect items thus this study proposes a profit maximizing inventory model with incorporating both imperfect production quality and two way imperfect inspection i e type one inspection error of falsely screening out a proportion of no defects and disposing of them like defects and type two inspection error of falsely not screening out a proportion of defects thereby passing them on to customers resulting in defect sales returns in addition this model includes one more stage of inspection that is after the rework process and there is no inspection error in this stage the purpose of this model is to determine the important factors of an inventory system to optimize the present value of the total profit in the finite time horizon finally a numerical example is provided to solve the presented inventory model using our proposed innovative approach which is further clarified through a sensitivity analysis

bayesian approach to single variable sampling plans summary in this paper we develop a model of sampling plans for variables with a polynomial loss function in which the decision function is either one sided or two sided based on a bayesian approach we suggest a simple finite algorithm for the determination of the optimal single sampling plan furthermore for the case of a symmetric two sided decision function we propose an approximate method for determining its optimal single sampling plan

price sensitive demand for perishable items an eoq model abstract this paper develops a finite time horizon deterministic eoq economic order quantity model where the rate of demand decreases quadratically with selling price prices at different periods are considered as decision variables the objective is to find the optimal ordering quantity and optimal sales prices that maximizes the vendor s total profit the results are discussed with numerical examples sensitivity analysis of the optimal solution with respect to the key parameters of the system is carried out

supply chain coordination based on a buyback contract under fuzzy random variable demand abstract the demand of production is random in the supply chain furthermore it is difficult to measure the demand in the real world hence the interval is more likely to be used to present the demand the interval can be viewed as a random variable this paper introduces this random variable as the demand of production into the model of supply chain we represent uncertain and fuzzy demand by a fuzzy random variable in a supply chain system based on a two level buyback contract for a newsvendor model with a single cycle for the sake of computational convenience the crisp possibilistic mean which has been widely used in supply chain is employed to defuzzify the fuzzy random demand in this paper the expected profit is defuzzified using a crisp possibilistic mean value the optimal order quantities in decentralized and centralized systems are analyzed and the conditions for supply chain coordination are obtained a realistic example is presented to illustrate the effectiveness of supply chain coordination and the impact of mixed imprecise and uncertain demand on the retailer order quantities and the expected profits for all sides

fuzzy goal programming an additive model abstract an additive model to solve fuzzy goal programming fgp is formulated the method uses arithmetic addition to aggregate the fuzzy goals to construct the relevant decision function cardinal and ordinal weights for nonequivalent fuzzy goals are also incorporated in the method the solution procedure is illustrated with a numerical example

scaling exponents at the transition by breaking of analyticity for incommensurate structures abstract a wide class of solid state models support incommensurate structures they are mostly given by either an analytic function in which case they are free to slide or a discontinuous function in which case there is a non zero minimum force required for depinning and a non zero minimum phonon frequency i propose that the boundary between these two types of state is given at least in part by the stable manifold of a fixed point of a renormalisation operator this permits one to perdict scaling laws for the depinning force phonon gap elasticity effective mass and other quantities

fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand this article considers the mixture inventory model involving variable lead time with backorders and lost sales we first fuzzify the random lead time demand to be a fuzzy random variable and obtain the total cost in the fuzzy sense then we further fuzzify the total demand to be the triangular fuzzy number and derive the fuzzy total cost by the centroid method of defuzzification we derive the estimate of total cost in the fuzzy sense also we find the optimal solution for order quantity and lead time in the fuzzy sense such that the total cost has a minimum value a numerical example is provided to illustrate the results of proposed model

a note on optimal replenishment policy for imperfect quality emq model with rework and backlogging a recent article on optimal replenishment policy of imperfect emq model by chiu s w chiu optimal replenishment policy for imperfect quality emq model with rework and backlogging applied stochastic models in business and industry 23 2007 165 178 used mathematical modeling and differential calculus to derive the optimal ordering policy that minimizes overall costs this paper presents a straightforward algebraic approach to replace the use of calculus on the cost function for determining the optimal replenishment solutions as well as the long run average production inventory costs for such an imperfect emq model the algebraic method presented in this paper may enable students or practitioners with little or no knowledge of calculus to learn or to manage with ease the real life manufacturing systems

time cost trade off analysis of project networks in fuzzy environments abstract this paper proposes a novel approach for time cost trade off analysis of a project network in fuzzy environments different from the results of previous studies in this paper the membership function of the fuzzy minimum total crash cost is constructed based on zadeh s extension principle and fuzzy solutions are provided a pair of two level mathematical programs parameterized by possibility level is formulated to calculate the lower and upper bounds of the fuzzy minimum total crash cost at by enumerating different values of the membership function of the fuzzy minimum total crash cost is constructed and the corresponding optimal activity time for each activity is also obtained at the same time an example of time cost trade off problem with several fuzzy parameters is solved successfully to demonstrate the validity of the proposed approach since the minimum total crash cost is expressed by a membership function rather than by a crisp value the fuzziness of parameters is conserved completely and more information is provided for time cost trade off analysis in project management the proposed approach also can be applied to time cost trade off problems with other characteristics

optimal selling price and lotsize with time varying deterioration and partial backlogging the article deals with an eoq economic order quantity model over an infinite time horizon for perishable items where demand is price dependent and partial backorder is permitted the rate of deterioration is taken to be time proportional and it is assumed that shortage occurs at starting of the inventory cycle based on the partial backlogging and lost sale cases the author develops the criterion for the optimal solution for the replenishment schedule and proves the optimal ordering policy is unique moreover the article suggests to new functions regarding price dependent demand and time varying deterioration rate finally numerical examples are illustrated to test the model in various issues

universal scaling of critical quasiperiodic orbits in a class of twist maps recently we have shown that the fractal properties of the critical invariant circles of the standard map as summarized by the spectrum and the generalized dimensions d q depend only on the tails in the continued fraction expansion of the corresponding rotation numbers in buric n mudrinic m and todorovic k 1997 30 l161 in the present paper this result is extended on the whole class of sufficiently smooth area preserving twist maps of cylinders we present numerical evidence that the and d q are the same for all critical invariant circles of any such map which have the rotation numbers with the same tail

sunoptimal policies with bounds for parameter adaptive decision processes a parameter adaptive decision process is a sequential decision process where some parameter or parameter set impacting the rewards and or transitions of the process is not known with certainty signals from the performance of the system can be processed by the decision maker as time progresses yielding information regarding which parameter set is operative active learning is an essential feature of these processes and the decision maker must choose actions that simultaneously guide the system in a preferred direction as well as yield information that can be used to better prescribe future actions if the operative parameter set is known with certainty the parameter adaptive problem reduces to a conventional stochastic dynamic program which is presumed solvable previous authors have shown how to use these solutions to generate suboptimal policies with performance bounds for the parameter adaptive problem here it is shown that some desirable characteristics of those bounds are shared by a larger cla