a note on type ii convolutional codes the result of a search for the world s second type ii doubly even and self dual convolutional code is reported a rate r 4 8 16 state time invariant convolutional code with free distance d sub free 8 was found to be type ii the initial part of its weight spectrum is better than that of the golay convolutional code gcc generator matrices and path weight enumerators for some other type ii convolutional codes are given by the wrap around technique tail biting versions of 32 18 8 type ii block codes are constructed

an approach to parameter estimation and stochastic control in water resources with an application to reservoir operation this paper presents an algorithm for the estimation of parameters in state space models that represent hydrologic processes in which the state variables are observed with error the algorithm is based on the maximization of the conditional expectation of the likelihood function of the state equation the estimation algorithm is numerically stable and guarantees local convergence under mild conditions it is also shown that the estimation algorithm can be coupled with an optimal control method to yield a combined control estimation technique that can be easily implemented an application of the theory and methods developed herein is given for flood routing via reservoir operation

on intersection of two mixing sets with applications to joint chance constrained programs we study the polyhedral structure of a generalization of a mixing set described by the intersection of two mixing sets with two shared continuous variables where one continuous variable has a positive coefficient in one mixing set and a negative coefficient in the other our developments are motivated from a key substructure of linear joint chance constrained programs ccps with random right hand sides from a finite probability space the ccps of interest immediately admit a mixed integer programming reformulation nevertheless such standard reformulations are difficult to solve at large scale due to the weakness of their linear programming relaxations in this paper we initiate a systemic polyhedral study of such joint ccps by explicitly analyzing the system obtained from simultaneously considering two linear constraints inside the chance constraint we carry out our study on this particular intersection of two mixing sets under a nonnegativity assumption on data mixing inequalities are immediately applicable to our set yet they are not sufficient therefore we propose a new class of valid inequalities in addition to the mixing inequalities and establish conditions under which these inequalities are facet defining moreover under certain additional assumptions we prove that these new valid inequalities along with the classical mixing inequalities are sufficient in terms of providing the closed convex hull description of our set we also show that linear optimization over our set is polynomial time and we independently give a high order polynomial time separation algorithm for the new inequalities we complement our theoretical results with a computational study on the strength of the proposed inequalities our preliminary computational experiments with a fast heuristic separation approach demonstrate that our proposed inequalities are practically effective as well

distributionally robust stochastic dual dynamic programming we consider a multistage stochastic linear program that lends itself to solution by stochastic dual dynamic programming sddp in this context we consider a distributionally robust variant of the

sampling based decomposition methods for multistage stochastic programs based on extended polyhedral risk measures we define a risk averse nonanticipative feasible policy for multistage stochastic programs and propose a methodology to implement it the approach is based on dynamic programming equations written for a risk averse formulation of the problem this formulation relies on a new class of multiperiod risk functionals called extended polyhedral risk measures dual representations of such risk functionals are given and used to derive conditions of coherence in the one period case conditions for convexity and consistency with second order stochastic dominance are also provided the risk averse dynamic programming equations are specialized considering convex combinations of one period extended polyhedral risk measures such as spectral risk measures to implement the proposed policy the approximation of the risk averse recourse functions for stochastic linear programs is discussed in this context we detail a stochastic dual dynamic programming algorithm which converges to the optimal value of the risk averse p

a finite branch and bound algorithm for two stage stochastic integer programs this paper addresses a general class of two stage stochastic programs with integer recourse and discrete distributions we exploit the structure of the value function of the second stage integer problem to develop a novel global optimization algorithm the proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination computational experiments on standard test problems indicate superior performance of the proposed algorithm in comparison to those in the existing literature

a cross decomposition scheme with integrated primal dual multi cuts for two stage stochastic programming investment planning problems we describe a cross decomposition algorithm that combines benders and scenario based lagrangean decomposition for two stage stochastic programming investment planning problems with complete recourse where the first stage variables are mixed integer and the second stage variables are continuous the algorithm is a novel cross decomposition scheme and fully integrates primal and dual information in terms of primal dual multi cuts added to the benders and the lagrangean master problems for each scenario the potential benefits of the cross decomposition scheme are demonstrated with numerical experiments on a number of instances of a facility location problem under disruptions in the original formulation where the underlying lp relaxation is weak the cross decomposition method outperforms multi cut benders decomposition if the formulation is improved with the addition of tightening constraints the performance of both decomposition methods improves but cross decomposition clearly remains the best method for large scale problems

decomposition algorithms for two stage chance constrained programs we study a class of chance constrained two stage stochastic optimization problems where second stage feasible recourse decisions incur additional cost in addition we propose a new model where recovery decisions are made for the infeasible scenarios to obtain feasible solutions to a relaxed second stage problem we develop decomposition algorithms with specialized optimality and feasibility cuts to solve this class of problems computational results on a chance constrained resource planing problem indicate that our algorithms are highly effective in solving these problems compared to a mixed integer programming reformulation and a naive decomposition method

a new possibilistic programming approach for solving fuzzy multiobjective assignment problem in this paper we propose a new possibilistic programming approach to solve a fuzzy multiobjective assignment problem in which the objective function coefficients are characterized by triangular possibility distributions the proposed solution approach simultaneously minimizes the best scenario the likeliest scenario and the worst scenario for the imprecise objective functions using level sets the level sets are used to define the confidence level of the fuzzy judgments of the decision maker additionally we provide a systematic framework in which the decision maker controls the search direction by updating both the membership values and aspiration levels until a set of satisfactory solutions is obtained numerical examples with dataset from realistic situations are provided to demonstrate the effectiveness of the proposed approach

a caveat concerning independence estimating equations with multivariate binary data clustered binary data occur commonly in both the biomedical and health sciences in this paper we consider logistic regression models for multivariate binary responses where the association between the responses is largely regarded as a nuisance characteristic of the data in particular we consider the estimator based on independence estimating equations iee which assumes that the responses are independent this estimator has been shown to be nearly efficient when compared with maximum likelihood ml and generalized estimating equations gee in a variety of settings the purpose of this paper is to highlight a circumstance where assuming independence can lead to quite substantial losses of efficiency in particular when the covariate design includes within cluster covariates assuming independence can lead to a considerable loss of efficiency in estimating the regression parameters associated with those covariates

two stage stochastic optimization problems with stochastic ordering constraints on the recourse abstract we consider two stage risk averse stochastic optimization problems with a stochastic ordering constraint on the recourse function two new characterizations of the increasing convex order relation are provided they are based on conditional expectations and on integrated quantile functions a counterpart of the lorenz function we propose two decomposition methods to solve the problems and prove their convergence our methods exploit the decomposition structure of the risk neutral two stage problems and construct successive approximations of the stochastic ordering constraints numerical results confirm the efficiency of the methods

stochastic decomposition an algorithm for two stage linear programs with recourse we present a cutting plane algorithm for two stage stochastic linear programs with recourse motivated by benders decomposition our method uses randomly generated observations of random variables to construct statistical estimates of supports of the objective function in general the resulting piecewise linear approximations do not agree with the objective function in finite time however certain subsequences of the estimated supports are shown to accumulate at supports of the objective function with probability one from this we establish the convergence of the algorithm under relatively mild assumptions

constrained state formulation for the stochastic control of multireservoir systems a new formulation is presented for the analysis of multireservoir systems based on the development of first and second moment expressions for the stochastic storage state variables these expressions give explicit consideration to the maximum and minimum storage bounds in the reservoir system a feature not incorporated in some existing formulations based on traditional control theory using this analysis expected values of the storage states variances of storage release policies reliability levels and failure probabilities useful information in the context of reservoir operations and design can be obtained from a nonlinear programming solution the approach does not involve any discretization of the system variables the results for the means and standard deviations of the storage states for a multireservoir system compare favorably with those obtained from simulation

accelerating the regularized decomposition method for two stage stochastic linear problems practical improvements of the regularized decomposition algorithm for two stage stochastic problems are presented they are associated with the primal simplex method for solving subproblems a penalty formulation of the subproblems is used which facilitates crash and warm starts and allows more freedom when creating the model the computational results are highly encouraging

an inexact probabilistic possibilistic optimization framework for flood management in a hybrid uncertain environment flooding is one of the leading causes of loss due to natural catastrophes and at least one third of all losses due to natural forces can be attributed to flooding flood management systems involve a variety of complexities such as multiple uncertainties dynamic variations and policy implications this paper presents an inexact probabilistic possibilistic programming with fuzzy random coefficients ipp frc model for flood management in a hybrid uncertain environment ipp frc is capable not only of tackling multiple uncertainties in the form of intervals with fuzzy random boundaries but of addressing the dynamic complexity through capacity expansion planning within a multi region multi flood level and multi option context the possibility and necessity measures used in ipp frc are suitable for risk seeking and risk averse decision making respectively a case study is used to demonstrate the applicability of the proposed methodology for facilitating flood management the results indicate that the inexact degrees of possibility and necessity would decrease with increased probabilities of occurrence implying a potential tradeoff between fulfillment of objectives and associated risks a number of decision alternatives can be obtained under different policy scenarios they are helpful for decision makers to formulate the appropriate flood management policy according to practical situations the performance of ipp frc is analyzed and compared with a possibility based fractile model

stochastic network interdiction using limited assets an interdictor attempts to destroy parts of a capacitated network through which an adversary will subsequently maximize flow we formulate and solve a stochastic version of the interdictor s problem minimize the expected maximum flow through the network when interdiction successes are binary random variables extensions are made to handle uncertain arc capacities and other realistic variations these two stage stochastic integer programs have applications to interdicting illegal drugs and to reducing the effectiveness of a military force moving materiel troops information etc through a network in wartime two equivalent model formulations allow jensen s inequality to be used to compute both lower and upper bounds on the objective and these bounds are improved within a sequential approximation algorithm successful computational results are reported on networks with over 100 nodes 80 interdictable arcs and 180 total arcs

nonlinear q design for convex stochastic control in this note we describe a version of the q design method that can be used to design nonlinear dynamic controllers for a discrete time linear time varying plant with convex cost and constraint functions and arbitrary disturbance distribution choosing a basis for the nonlinear q parameter yields a convex stochastic optimization problem which can be solved by standard methods such as sampling in principle for a large enough basis and enough sampling this method can solve the controller design problem to any degree of accuracy in any case it can be used to find a suboptimal controller using convex optimization methods we illustrate the method with a numerical example comparing a nonlinear controller found using our method with the optimal linear controller the certainty equivalent model predictive controller and a lower bound on achievable performance obtained by ignoring the causality constraint

a comparison of two bias corrected covariance estimators for generalized estimating equations summarymancl and derouen 2001 biometrics57 126 134 and kauermann and carroll 2001 jasa96 1387 1398 proposed alternative bias corrected covariance estimators for generalized estimating equations parameter estimates of regression models for marginal means the finite sample properties of these estimators are compared to those of the uncorrected sandwich estimator that underestimates variances in small samples although the formula of mancl and derouen generally overestimates variances it often leads to coverage of 95 confidence intervals near the nominal level even in some situations with as few as 10 clusters an explanation for these seemingly contradictory results is that the tendency to undercoverage resulting from the substantial variability of sandwich estimators counteracts the impact of overcorrecting the bias however these positive results do not generally hold for small cluster sizes e g 10 their estimator often results in overcoverage and the bias corrected covariance estimator of kauermann and carroll may be preferred the methods are illustrated using data from a nested cross sectional cluster intervention trial on reducing underage drinking

optimal allocation of surgery blocks to operating rooms under uncertainty the allocation of surgeries to operating rooms ors is a challenging combinatorial optimization problem there is also significant uncertainty in the duration of surgical procedures which further complicates assignment decisions in this paper we present stochastic optimization models for the assignment of surgeries to ors on a given day of surgery the objective includes a fixed cost of opening ors and a variable cost of overtime relative to a fixed length of day we describe two types of models the first is a two stage stochastic linear program with binary decisions in the first stage and simple recourse in the second stage the second is its robust counterpart in which the objective is to minimize the maximum cost associated with an uncertainty set for surgery durations we describe the mathematical models bounds on the optimal solution and solution methodologies including an easy to implement heuristic numerical experiments based on real data from a large health care provider are used to contrast the results for the two models and illustrate the potential for impact in practice based on our numerical experimentation we find that a fast and easy to implement heuristic works fairly well on average across many instances we also find that the robust method performs approximately as well as the heuristic is much faster than solving the stochastic recourse model and has the benefit of limiting the worst case outcome of the recourse problem

a new method for the real time operation of reservoir systems this paper introduces a new method for the real time operation of reservoir systems the system is represented by a set of stochastic differential equations describing the reservoir and river dynamics in state space form the formulated reservoir operation problem calls for finding policies which maximize the expected benefits of one system s objective while satisfying the remaining objectives at prespecified reliability levels the solution is obtained by a new method named extended linear quadratic gaussian elqg controller elqg draws on and extends stochastic control theory results and it is well suited for the optimization of constrained dynamical systems it is a trajectory iteration algorithm theoretically expected to exhibit reliability and computational efficiency the new method is tested and evaluated in a real world case study

applying oracles of on demand accuracy in two stage stochastic programming a computational study abstract traditionally two variants of the l shaped method based on benders decomposition principle are used to solve two stage stochastic programming problems the aggregate and the disaggregate version in this study we report our experiments with a special convex programming method applied to the aggregate master problem the convex programming method is of the type that uses an oracle with on demand accuracy we use a special form which when applied to two stage stochastic programming problems is shown to integrate the advantages of the traditional variants while avoiding their disadvantages on a set of 105 test problems we compare and analyze parallel implementations of regularized and unregularized versions of the algorithms the results indicate that solution times are significantly shortened by applying the concept of on demand accuracy

decomposition algorithms with parametric gomory cuts for two stage stochastic integer programs we consider a class of two stage stochastic integer programs with binary variables in the rst stage and general integer variables in the second stage we develop decomposition algorithms akin to the l shaped or benders methods by utilizing gomory cuts to obtain iteratively tighter approximations of the second stage integer programs we show that the proposed methodology is exible in that it allows several modes of implementation all of which lead to nitely convergent algorithms we illustrate our algorithms using examples from the literature we report computational results using the stochastic server location problem instances which suggest that our decomposition based approach scales better with increases in the number of scenarios than a state of the art solver which was used to solve the deterministic equivalent formulation

a linear decision based approximation approach to stochastic programming stochastic optimization especially multistage models is well known to be computationally excruciating moreover such models require exact specifications of the probability distributions of the underlying uncertainties which are often unavailable in this paper we propose tractable methods of addressing a general class of multistage stochastic optimization problems which assume only limited information of the distributions of the underlying uncertainties such as known mean support and covariance one basic idea of our methods is to approximate the recourse decisions via decision rules we first examine linear decision rules in detail and show that even for problems with complete recourse linear decision rules can be inadequate and even lead to infeasible instances hence we propose several new decision rules that improve upon linear decision rules while keeping the approximate models computationally tractable specifically our approximate models are in the forms of the so called second order cone soc programs which could be solved efficiently both in theory and in practice we also present computational evidence indicating that our approach is a viable alternative and possibly advantageous to existing stochastic optimization solution techniques in solving a two stage stochastic optimization problem with complete recourse

design of affine controllers via convex optimization we consider a discrete time time varying linear dynamical system perturbed by process noise with linear noise corrupted measurements over a finite horizon we address the problem of designing a general affine causal controller in which the control input is an affine function of all previous measurements in order to minimize a convex objective in either a stochastic or worst case setting this controller design problem is not convex in its natural form but can be transformed to an equivalent convex optimization problem by a nonlinear change of variables which allows us to efficiently solve the problem our method is related to the classical design procedure for time invariant infinite horizon linear controller design and the more recent purified output control method we illustrate the method with applications to supply chain optimization and dynamic portfolio optimization and show the method can be combined with model predictive control techniques when perfect state information is available

irrigation control in the presence of salinity extended linear quadratic approach an intraseasonal irrigation scheduling problem is dealt with via extended linear quadratic elq control the elq control is well suited for constrained multidimensional problems and provides openloop feedback control rules over the control horizon a conceptual model is developed to describe the dynamics of water allocation and salt movement in the root zone of a crop moisture stress and osmotic stress are combined to obtain the integrated inhibitory effect of salinity on transpiration for the intraseasonal model to be effective against perennial salt accumulation in the root zone it should be able to yield control laws which will lead to favorable root zone conditions at the end of an irrigation season thus avoiding any significant leaching prior to the next growing season this long term aspect of salinity control is handled via probabilistic state constraints which impose desired salinity and moisture levels with desired confidence level the elq control is employed in a case study of expected net benefit maximization over an irrigation season of corn in fort morgan colorado the results in general correspond well with expected irrigation schedules under different conditions and provide valuable information on both short and long term aspects of irrigation control under saline conditions the elq control being an analytic iterative solution scheme with theoretically guaranteed fast convergence has a distinct computational advantage over state of the art procedures

stochastic power generation unit commitment in electricity markets a novel formulation and a comparison of solution methods we propose a stochastic unit commitment model for a power generation company that takes part in an electricity spot market the relevant feature of this model is its detailed representation of the spot market during a whole week including seven day ahead market sessions and the corresponding adjustment market sessions the adjustment market sessions can be seen as an hour ahead market mechanism this representation takes into account the influence that the company s decisions exert on the market clearing price by means of a residual demand curve for each market session we introduce uncertainty in the form of several possible spot market outcomes for each day which leads to a weekly scenario tree the model also represents in detail the operation of the company s generation units the model leads to large scale mixed linear integer problems that are hard to solve with commercial optimizers this suggests the use of alternative solution methods we test four solution approaches with a realistic numerical example in the context of the spanish electricity spot market the first is a direct solution with a commercial optimizer which illustrates the mentioned limitations the second is a standard lagrangean relaxation algorithm the third and fourth methods are two original variants of benders decomposition for multistage stochastic integer programs the first benders decomposition algorithm builds approximations for the recourse function relaxing the integrality constraints of the subproblems the second variant strengthens these cuts by performing one iteration of the lagrangean of each subproblem we analyze the advantages of these four methods and compare the results

adaptive multicut aggregation for two stage stochastic linear programs with recourse outer linearization methods for two stage stochastic linear programs with recourse such as the l shaped algorithm generally apply a single optimality cut on the nonlinear objective at each major iteration while the multicut version of the algorithm allows for several cuts to be placed at once in general the l shaped algorithm tends to have more major iterations than the multicut algorithm however the trade offs in terms of computational time are problem dependent this paper investigates the computational trade offs of adjusting the level of optimality cut aggregation from single cut to pure multicut specifically an adaptive multicut algorithm that dynamically adjusts the aggregation level of the optimality cuts in the master program is presented and tested on standard large scale instances from the literature computational results reveal that a cut aggregation level that is between the single cut and the multicut can result in substantial computational savings over the single cut method

a cutting plane method from analytic centers for stochastic programming the stochastic linear programming problem with recourse has a dual block angular structure it can thus be handled by benders decomposition or by kelley s method of cutting planes equivalently the dual problem has a primal block angular structure and can be handled by dantzig wolfe decomposition the two approaches are in fact identical by duality here we shall investigate the use of the method of cutting planes from analytic centers applied to similar formulations the only significant difference form the aforementioned methods is that new cutting planes or columns by duality will be generated not from the optimum of the linear programming relaxation but from the analytic center of the set of localization

real time forecasting and daily operation of a multireservoir system during floods by linear quadratic gaussian control the problem of short term daily operation of a multireservoir system during floods is examined the problem is how to use all available real time information to solve the tactical problem of regulating reservoirs to minimize the expected value of flood damage during a relatively short operating horizon and to do so consistently with the long term operating strategy a state space mathematical model is presented for short term forecasting of river flows and description of the dynamics of a multireservoir system the model includes reduced order state space unit hydrographs to forecast storm runoff from effective rainfall and state space representations of linear flood routing the optimization problem is solved in the framework of discrete time linear quadratic gaussian lqg control lqg control is a computationally efficient and flexible method of solving the large dimensional optimization problems associated with the solution of the tactical problem of short term operation of reservoirs for application of the lqg control methodology the system must be represented in state space form with quadratic cost functions subject to linear equality constraints given by the state transition equations the scheme was found to be suitable for operation under moderate flood conditions when capacity constraints are not likely to become binding the methodology has been applied and tested in a real world case

new bounding and decomposition approaches for milp investment problems multi area transmission and generation planning under policy constraints abstract we propose a novel two phase bounding and decomposition approach to compute optimal and near optimal solutions to large scale mixed integer investment planning problems that have to consider a large number of operating subproblems each of which is a convex optimization our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems the bounding phase exploits jensen s inequality to define a lower bound which we extend to stochastic programs that use expected value constraints to enforce policy objectives the decomposition phase in which the bounds are tightened improves upon the standard benders algorithm by accelerating the convergence of the bounds the lower bound is tightened by using a jensen s inequality based approach to introduce an auxiliary lower bound into the benders master problem upper bounds for both phases are computed using a sub sampling approach executed on a parallel computer system numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable however the decomposition phase is required to attain optimality gaps use of both phases performs better in terms of convergence speed than attempting to solve the problem using just the bounding phase or regular benders decomposition separately

stochastic control of reservoir systems using indicator functions new enhancements 1 in our previous works deterministic release policies were considered for the development of approximations of the two lower moments of the storage volume defined by the dynamic equation of the reservoir in discrete time but in continuous state space important innovation in that work was the incorporation of the lower and upper bounds of reservoir systems into the dynamic equation for the storage volume using indicator functions the current work which also does not use discretization looks at an extension of previous developments that incorporates standard operating policies and also a new randomized release policy both of which make the moments calculations exact under the assumptions that 1 the sum of current random inflow and the previous storage volume can be described by just the two lower moments and 2 only the means and variances of the inflows are known first and second moment expressions are derived for the stochastic storage state variable and include terms for the failure probabilities probabilities of spills or deficits expected values of the storage state variances of storage release policies and failure probabilities are obtained by solving the optimal reservoir operations problem using nonlinear programming the various statistics thus obtained from this optimization compare extremely well with those obtained from simulation for the single reservoir monthly operations problem studied the exact characterization of the mean and variance of the storage state variable is derived which is a difficulty in existing formulations based on linear quadratic gaussian methods for example the latter methods have been unable to estimate these moments reasonably accurately especially for long term operations whereas the traditional storage theory based on discretization brings on the curse of dimensionality the presentation herein is directed to both traditional reservoir storage theorists who are interested in the design of a reservoir where estimating the probabilities of spills and deficits is important and modern reservoir analysts who are interested in multiperiod optimal release decisions in the operations of reservoirs

tight bounds for stochastic convex programs variable and row aggregation as a technique of simplifying a mathematical program is utilized to develop bounds for two stage stochastic convex programs with random right hand sides if one is able to utilize the problem structure along with only first moment information a tighter bound than the usual mean model bound based on jensen s inequality may be obtained moreover it is possible to construct examples for which the mean model bound will be arbitrarily poor consequently one can tighten jensen s bound for stochastic programs when the distribution has a compact support this bound may be improved further by partitioning the support using conditional first moments with regard to first moment upper bounds the gassmann ziemba inequality is used for the stochastic convex program to seek a model which can be solved using standard convex programming techniques moreover it allows one to easily construct upper bounds using the solution of the lower bounding problem finally the results are extended to multistage stochastic convex programming problems

l shaped decomposition of two stage stochastic programs with integer recourse we consider two stage stochastic programming problems with integer recourse the l shaped method of stochastic linear programming is generalized to these problems by using generalized benders decomposition nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques finite convergence of the method is established when gomory s fractional cutting plane algorithm or a branch and bound algorithm is applied

risk based factorial probabilistic inference for optimization of flood control systems with correlated uncertainties abstract in this paper a risk based factorial probabilistic inference method is proposed to address the stochastic objective function and constraints as well as their interactions in a systematic manner to tackle random uncertainties decision makers risk preferences are taken into account in the decision process statistical significance for each of the linear nonlinear and interaction effects of risk parameters is uncovered through conducting a multi factorial analysis the proposed methodology is applied to a case study of flood control to demonstrate its validity and applicability a number of decision alternatives are obtained under various combinations of risk levels associated with the objective function and chance constraints facilitating an in depth analysis of trade offs between economic outcomes and associated risks dynamic complexities are addressed through a two stage decision process as well as through capacity expansion planning for flood diversion within a multi region multi flood level and multi option context findings from the factorial experiment reveal the multi level interactions between risk parameters and quantify their contributions to the variability of the total system cost the proposed method is compared against the fractile criterion optimization model and the chance constrained programming technique respectively

optimal short term hydro scheduling from the principle of progressive optimality this paper presents an algorithm based on the principle of progressive optimality for determining the optimal short term scheduling of multireservoir power systems the method takes into account water head variations spilling and time delays between upstream and downstream reservoirs the method is computationally efficient and has minimal storage requirements the convergence is monotonic and a global solution is reached contrary to dynamic programing the state variables do not have to be discretized with this method an example consisting of four hydroplants in series is solved and the results are presented

applying the minimax criterion in stochastic recourse programs we consider an optimization problem in which some uncertain parameters are replaced by random variables the minimax approach to stochastic programming concerns the problem of minimizing the worst expected value of the objective function with respect to the set of probability measures that are consistent with the available information on the random data only very few practicable solution procedures have been proposed for this problem and the existing ones rely on simplifying assumptions in this paper we establish a number of stability results for the minimax stochastic program justifying in particular the approach of restricting attention to probability measures with support in some known finite set following this approach we elaborate solution procedures for the minimax problem in the setting of two stage stochastic recourse models considering the linear recourse case as well as the integer recourse case since the solution procedures are modifications of well known algorithms their efficacy is immediate from the computational testing of these procedures and we do not report results of any computational experiments

risk decision making method using interval numbers and its application based on the prospect value with multiple reference points a risk decision making method with multiple reference points is proposed two reference points and three reference points are set in the prospect theory two weighting optimization models are established two cases are applied to illustrate the importance of multiple reference points a multi attribute risk decision making problem using interval numbers is studied based on the prospect theory a decision making process often involves various reference standards resulting from different decision making mentalities and contexts to solve these kinds of decision making problems we propose a risk decision making method with multiple reference points for both static and dynamic situations first the guidelines for setting reference points under both static and dynamic conditions are provided based on the nature of the decision making problem second both expected values and positive ideal points for alternatives are set for the static decision making strategy and three reference points are provided for the dynamic strategy including expected values positive ideal points and the development status of alternatives according to the guidelines third characterization techniques used to solve prospect values of decision making alternatives are proposed for both static and dynamic decision making problems then a detailed analysis is provided in terms of weighting functions and prospect values in addition two optimization models using the attribute weight and multi stage weight are established by considering the sensitivity of these two weights to the decision making problem with the aim of maximizing the differentiation degree of alternatives on that basis a ranking analysis is provided for the alternatives finally the proposed method is applied to two cases including supplier selection of key components for large aircraft and an emergency event to illustrate the application and feasibility of the method

decomposition methods in stochastic programming stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition we review basic ideas of cutting plane methods augmented lagrangian and splitting methods and stochastic decomposition methods for convex polyhedral multi stage stochastic programming problems

interactive multiobjective fuzzy random linear programming maximization of possibility and probability this paper considers multiobjective linear programming problems with fuzzy random variables coefficients a new decision making model is proposed to maximize both possibility and probability which is based on possibilistic programming and stochastic programming an interactive algorithm is constructed to obtain a satisficing solution satisfying at least weak pareto optimality

dimension length profiles and trellis complexity of linear block codes this semi tutorial paper discusses the connections between the dimension length profile dlp of a linear code which is essentially the same as its generalized hamming weight hierarchy and the complexity of its minimal trellis diagram these connections are close and deep dlp duality is closely related to trellis duality the dlp of a code gives tight bounds on its state and branch complexity profiles under any coordinate ordering these bounds can often be met a maximum distance separable mds code is characterized by a certain extremal dlp from which the main properties of mds codes are easily derived the simplicity and generality of these interrelationships are emphasized

error analysis of conventional discrete and gradient dynamic programming an asymptotic error analysis of the conventional discrete dynamic programming ddp method is presented and upper bounds of the error in the control policy i e the difference of the estimated and true optimal control at each operation period are computed this error is shown to be of the order of the state discretization interval as a result with significant implications in the optimization of multistate systems where the curse of dimensionality restricts the number of states to a relatively small number the error in the optimal cost varies with as 2 the analysis provides useful insights into the effects of state discretization on calculated control and cost functions the comparability of results from different discretizations and criteria about the required number of nodes in an effort to reduce the discretization error in the case of smooth cost functions a new discrete dynamic programming method termed gradient dynamic programming gdp is proposed gdp uses a piecewise hermite interpolation of the cost to go function at each stage which preserves the values of the cost to go function and of its first derivatives at the discretization nodes the error in the control policy is shown to be of the order of as 3 and the error in the cost to vary with as thus as as decreases gdp converges to the true optimum much more rapidly than ddp another major advantage of the new methodology is that it facilitates the use of newton type iterative methods in the solution of the nonlinear optimization problems at each stage the linear convergence of ddp and the superlinear convergence of gdp are illustrated in an example

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

an improved benders decomposition algorithm for the tree of hubs location problem abstract the tree of hubs location problem is a particularly hard variant of the so called hub location problems when solving this problem by a benders decomposition approach it is necessary to deal with both optimality and feasibility cuts while modern implementations of the benders decomposition method rely on pareto optimal optimality cuts or on rendering feasibility cuts based on minimal infeasible subsystems a new cut selection scheme is devised here under the guiding principle of extracting useful information even when facing infeasible subproblems the proposed algorithm outperforms two other modern variants of the method and it is capable of optimally solving instances five times larger than the ones previously reported on the literature

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

an arc exchange decomposition method for multistage dynamic networks with random arc capacities abstract multistage dynamic networks with random arc capacities mdnrac have been successfully used for modeling various resource allocation problems in the transportation area however solving these problems is generally computationally intensive and there is still a need to develop more efficient solution approaches in this paper we propose a new heuristic approach that solves the mdnrac problem by decomposing the network at each stage into a series of subproblems with tree structures each subproblem can be solved efficiently the main advantage is that this approach provides an efficient computational device to handle the large scale problem instances with fairly good solution quality we show that the objective value obtained from this decomposition approach is an upper bound for that of the mdnrac problem numerical results demonstrate that our proposed approach works very well

risk averse two stage stochastic linear programming modeling and decomposition we formulate a risk averse two stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage the objective function is formulated as a composition of conditional risk measures we analyze properties of the problem and derive necessary and sufficient optimality conditions next we construct a new decomposition method for solving the problem that exploits the composite structure of the objective function we illustrate its performance on a portfolio optimization problem

a loose benders decomposition algorithm for approximating two stage mixed integer recourse models we propose a new class of convex approximations for two stage mixed integer recourse models the so called generalized alpha approximations the advantage of these convex approximations over existing ones is that they are more suitable for efficient computations indeed we construct a loose benders decomposition algorithm that solves large problem instances in reasonable time to guarantee the performance of the resulting solution we derive corresponding error bounds that depend on the total variations of the probability density functions of the random variables in the model the error bounds converge to zero if these total variations converge to zero we empirically assess our solution method on several test instances including the sizes and sslp instances from siplib we show that our method finds near optimal solutions if the variability of the random parameters in the model is large moreover our method outperforms existing methods in terms of computation time especially for large problem instances

new control concepts for uncertain water resources systems 1 theory a major complicating factor in water resources systems management is handling unknown inputs stochastic optimization provides a sound mathematical framework but requires that enough data exist to develop statistical input representations in cases where data records are insufficient e g extreme events or atypical of future input realizations stochastic methods are inadequate this article presents a control approach where input variables are only expected to belong in certain sets the objective is to determine sets of admissible control actions guaranteeing that the system will remain within desirable bounds the solution is based on dynamic programming and derived for the case where all sets are convex polyhedra a companion paper yao and georgakakos this issue addresses specific applications and problems in relation to reservoir system management

a covariance estimator for gee with improved small sample properties summary in this paper we propose an alternative covariance estimator to the robust covariance estimator of generalized estimating equations gee hypothesis tests using the robust covariance estimator can have inflated size when the number of independent clusters is small resampling methods such as the jackknife and bootstrap have been suggested for covariance estimation when the number of clusters is small a drawback of the resampling methods when the response is binary is that the methods can break down when the number of subjects is small due to zero or near zero cell counts caused by resampling we propose a bias corrected covariance estimator that avoids this problem in a small simulation study we compare the bias corrected covariance estimator to the robust and jackknife covariance estimators for binary responses for situations involving 10 40 subjects with equal and unequal cluster sizes of 16 64 observations the bias corrected covariance estimator gave tests with sizes close to the nominal level even when the number of subjects was 10 and cluster sizes were unequal whereas the robust and jackknife covariance estimators gave tests with sizes that could be 2 3 times the nominal level the methods are illustrated using data from a randomized clinical trial on treatment for bone loss in subjects with periodontal disease

a possibilistic programming approach for closed loop supply chain network design under uncertainty the design of closed loop supply chain networks has attracted more attention in recent years according to business and environmental factors the significance of accounting for uncertainty and risk in such networks spurs an interest to develop appropriate decision making tools to cope with uncertain and imprecise parameters in closed loop supply chain network design problems this paper proposes a bi objective possibilistic mixed integer programming model to deal with such issues the proposed model integrates the network design decisions in both forward and reverse supply chain networks and also incorporates the strategic network design decisions along with tactical material flow ones to avoid the sub optimalities led from separated design in both parts to solve the proposed possibilistic optimization model an interactive fuzzy solution approach is developed by combining a number of efficient solution approaches from the recent literature numerical experiments are conducted to demonstrate the significance and applicability of the developed possibilistic model as well as the usefulness of the proposed solution approach

interactive fuzzy random two level linear programming based on level sets and fractile criterion optimization in this paper assuming cooperative behavior of the decision makers two level linear programming problems under fuzzy random environments are considered by introducing a level sets of fuzzy random variables and defining an a stochastic two level linear programming problem for guaranteeing the degree of realization of the problem through a new decision making model proposed based on the fractile criterion optimization model considering fuzzy goals the a stochastic two level programming problem can be equivalently transformed into a deterministic problem interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented an illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method

efficiency of regression estimates for clustered data statistical methods for clustered data such as generalized estimating equations gee and generalized least squares gls require selecting a correlation or convariance structure to specify the dependence between observations within a cluster valid regression estimates can be obtained that do not depend on correct specification of the true correlation but inappropriate specifications can result in a loss of efficiency we derive general expressions for the asymptotic relative efficiency of gee and gls estimators under nested correlation structures efficiency is shown to depend on the covariate distribution the cluster sizes the response variable correlation and the regression parameters the results demonstrate that efficiency is quite sensitive to the between and within cluster variation of the covariates and provide useful characterizations of models for which upper and lower efficiency bounds are attained efficiency losses for simple working correlation matrices such as independence can be large even for small to moderate correlations and cluster sizes

sample size calculations for studies with correlated observations correlated data occur frequently in biomedical research examples include longitudinal studies family studies and ophthalmologic studies in this paper we present a method to compute sample sizes and statistical powers for studies involving correlated observations this is a multivariate extension of the work by self and mauritsen 1988 biometrics 44 79 86 who derived a sample size and power formula for generalized linear models based on the score statistic for correlated data we appeal to a statistic based on the generalized estimating equation method liang and zeger 1986 biometrika 73 13 22 we highlight the additional assumptions needed to deal with correlated data some special cases that are commonly seen in practice are discussed followed by simulation studies

assessing solution quality in stochastic programs determining whether a solution is of high quality optimal or near optimal is fundamental in optimization theory and algorithms in this paper we develop monte carlo sampling based procedures for assessing solution quality in stochastic programs quality is defined via the optimality gap and our procedures output is a confidence interval on this gap we review a multiple replications procedure that requires solution of say 30 optimization problems and then we present a result that justifies a computationally simplified single replication procedure that only requires solving one optimization problem even though the single replication procedure is computationally significantly less demanding the resulting confidence interval might have low coverage probability for small sample sizes for some problems we provide variants of this procedure that require two replications instead of one and that perform better empirically we present computational results for a newsvendor problem and for two stage stochastic linear programs from the literature we also discuss when the procedures perform well and when they fail and we propose using optimal solutions to strengthen the performance of our procedures

on the macwilliams identity for convolutional codes the adjacency matrix associated with a convolutional code collects in a detailed manner information about the weight distribution of the code a macwilliams identity conjecture stating that the adjacency matrix of a code fully determines the adjacency matrix of the dual code will be formulated and an explicit formula for the transformation will be stated the formula involves the macwilliams matrix known from complete weight enumerators of block codes the conjecture will be proven for the class of convolutional codes where either the code itself or its dual does not have forney indices bigger than one for the general case the conjecture is backed up by many examples and a weaker version will be established

parallel decomposition of multistage stochastic programming problems a new decomposition method for multistage stochastic linear programming problems is proposed a multistage stochastic problem is represented in a tree like form and with each node of the decision tree a certain linear or quadratic subproblem is associated the subproblems generate proposals for their successors and some backward information for their predecessors the subproblems can be solved in parallel and exchange information in an asynchronous way through special buffers after a finite time the method either finds an optimal solution to the problem or discovers its inconsistency an analytical illustrative example shows that parallelization can speed up computation over every sequential method computational experiments indicate that for large problems we can obtain substantial gains in efficiency with moderate numbers of processors

a macwilliams identity for convolutional codes the general case a macwilliams identity for convolutional codes will be established it makes use of the weight adjacency matrices of the code and its dual based on state space realizations the controller canonical form of the codes in question the macwilliams identity applies to various notions of duality appearing in the literature on convolutional coding theory

an approximation approach for representing s shaped membership functions in general to formulate a fuzzy linear programming problem with n s shaped utility membership functions traditional methods require n or more extra binary variables because s shaped curves are neither convex nor concave in all places adding binary variables does not improve the bound of the linear programming relaxation on the contrary added binary variables increase the computational burden in the solution process if problems get large therefore a formulation without binary variables should be more efficient accordingly this study proposes a piecewise linear approach to formulate an s shaped membership function mf without adding any extra binary variables which improves the efficiency of fuzzy linear programming in solving decision management problems with s shaped mfs finally a computational experiment is provided to demonstrate the superiority of the proposed models an illustrative example is also provided to show the usefulness of the proposed method

shadow bounds for self dual codes conway and sloane 1990 have previously given an upper bound on the minimum distance of a singly even self dual binary code using the concept of the shadow of a self dual code we improve their bound finding that the minimum distance of a self dual binary code of length n is at most 4 n 24 4 except when n mod 24 22 when the bound is 4 n 24 6 we also show that a code of length a multiple of 24 meeting the bound cannot be singly even the same technique gives similar results for additive codes over gf 4 relevant to quantum coding theory

an interval parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty planning for water quality management systems is complicated by a variety of uncertainties and nonlinearities where difficulties in formulating and solving the resulting inexact nonlinear optimization problems exist with the purpose of tackling such difficulties this paper presents the development of an interval fuzzy nonlinear programming ifnp model for water quality management under uncertainty methods of interval and fuzzy programming were integrated within a general framework to address uncertainties in the left and right hand sides of the nonlinear constraints uncertainties in water quality pollutant loading and the system objective were reflected through the developed ifnp model the method of piecewise linearization was developed for dealing with the nonlinearity of the objective function a case study for water quality management planning in the changsha section of the xiangjiang river was then conducted for demonstrating applicability of the developed ifnp model the results demonstrated that the accuracy of solutions through linearized method normally rises positively with the increase of linearization levels it was also indicated that the proposed linearization method was effective in dealing with ifnp problems uncertainties can be communicated into optimization process and generate reliable solutions for decision variables and objectives the decision alternatives can be obtained by adjusting different combinations of the decision variables within their solution intervals it also suggested that the linearized method should be used under detailed error analysis in tackling ifnp problems

benders decomposition for large scale uncapacitated hub location this paper describes an exact algorithm capable of solving large scale instances of the well known uncapacitated hub location problem with multiple assignments the algorithm applies benders decomposition to a strong path based formulation of the problem the standard decomposition algorithm is enhanced through the inclusion of several features such as the use of a multicut reformulation the generation of strong optimality cuts the integration of reduction tests and the execution of a heuristic procedure extensive computational experiments were performed to evaluate the efficiency and robustness of the algorithm computational results obtained on classical benchmark instances with up to 200 nodes and on a new and more difficult set of instances with up to 500 nodes confirm the efficiency of the algorithm

new rate 1 2 1 3 and 1 4 binary convolutional encoders with an optimum distance profile tabulations of binary systematic and nonsystematic polynomial convolutional encoders with an optimum distance profile for rate 1 2 1 3 and 1 4 are given the reported encoders are found by computer searches that optimize over the weight spectra the free distances for rate 1 3 and 1 4 are compared with heller s 1968 and griesmer s 1960 upper bounds

computing block angular karmarkar projections with applications to stochastic programming we present a variant of karmarkar s algorithm for block angular structured linear programs such as stochastic linear programs by computing the projection efficiently we give a worst case bound on the order of the running time that can be an order of magnitude better than that of karmarkar s standard algorithm further implications for approximations and very large scale problems are given

on the pless construction and ml decoding of the 48 24 12 quadratic residue code we present a method for maximum likelihood decoding of the 48 24 12 quadratic residue code this method is based on projecting the code onto a subcode with an acyclic tanner graph and representing the set of coset leaders by a trellis diagram this results in a two level coset decoding which can be considered a systematic generalization of the wagner rule we show that unlike the 24 12 8 golay code the 48 24 12 code does not have a pless construction which has been an open question in the literature it is determined that the highest minimum distance of a 48 24 binary code having a pless 1986 construction is 10 and up to equivalence there are three such codes

a multicut algorithm for two stage stochastic linear programs outer linearization methods such as van slyke and wets s l shaped method for stochastic linear programs generally apply a single cut on the nonlinear objective at each major iteration the structure of stochastic programs allows for several cuts to be placed at once this paper describes a multicut algorithm to carry out this procedure it presents experimental and theoretical justification for reductions in major iterations

sample size calculations for randomised trials including both independent and paired data randomised trials including a mixture of independent and paired data arise in many areas of health research yet methods for determining the sample size for such trials are lacking we derive design effects algebraically assuming clustering because of paired data will be taken into account in the analysis using generalised estimating equations with either an independence or exchangeable working correlation structure continuous and binary outcomes are considered along with three different methods of randomisation cluster randomisation individual randomisation and randomisation to opposite treatment groups the design effect is shown to depend on the intracluster correlation coefficient proportion of observations belonging to a pair working correlation structure type of outcome and method of randomisation the derived design effects are validated through simulation and example calculations are presented to illustrate their use in sample size planning these design effects will enable appropriate sample size calculations to be performed for future randomised trials including both independent and paired data copyright 2017 john wiley sons ltd

stochastic programming with simple integer recourse stochastic integer programs are notoriously difficult very few properties are known and solution algorithms are very scarce in this paper we introduce the class of stochastic programs with simple integer recourse a natural extension of the simple recourse case extensively studied in stochastic continuous programs analytical as well as computational properties of the expected recourse function of simple integer recourse problems are studied this includes sharp bounds on this function and the study of the convex hull finally a finite termination algorithm is obtained that solves two classes of stochastic simple integer recourse problems

a family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations summary we introduce a family of multivariate binary distributions with certain conditional linear property this family is particularly useful for efficient and easy simulation of correlated binary variables with a given marginal mean vector and correlation matrix

stochastic uncapacitated hub location we study stochastic uncapacitated hub location problems in which uncertainty is associated to demands and transportation costs we show that the stochastic problems with uncertain demands or dependent transportation costs are equivalent to their associated deterministic expected value problem evp in which random variables are replaced by their expectations in the case of uncertain independent transportation costs the corresponding stochastic problem is not equivalent to its evp and specific solution methods need to be developed we describe a monte carlo simulation based algorithm that integrates a sample average approximation scheme with a benders decomposition algorithm to solve problems having stochastic independent transportation costs numerical results on a set of instances with up to 50 nodes are reported

benders decomposition for production routing under demand uncertainty the production routing problem prp is a generalization of the inventory routing problem and concerns the production and distribution of a single product from a production plant to multiple customers using capacitated vehicles in a discrete and finite time horizon in this study we consider the stochastic prp with demand uncertainty in two stage and multistage decision processes the decisions in the first stage include production setups and customer visit schedules while the production and delivery quantities are determined in the subsequent stages we introduce formulations for the two problems which can be solved by a branch and cut algorithm to handle a large number of scenarios we propose a benders decomposition approach which is implemented in a single branch and bound tree and enhanced through lower bound lifting inequalities scenario group cuts and pareto optimal cuts for the multistage problem we also use a warm start procedure that relies on the solution of the simpler two stage prob

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures