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This paper addresses a dual channel, clicks-and-mortar retailer's problem of determining which among a set of products with seasonal demand will occupy limited retail shelf space, which products will be offered via an online channel, and which items will be available through both channels. Using a consumer choice model in which the set of products offered influences each product's demand in each channel, we consider stocking and price decisions under uncertain demand in a single-period setting with a constraint on the probability of stocking out. The resulting model is a large-scale, chance-constrained, two-stage stochastic programme. We propose a sample average approximation (SAA) method that permits quickly arriving at near-optimal solutions for this complex problem class. We also exercise the proposed model to gain insights on the problem's key tradeoffs and properties of optimal solutions. [ABSTRACT FROM AUTHOR]

Due to the increasingly competitive nature of the global market, the capability of controlling delivery time is becoming a significant advantage for enterprises. A novel fourth-party logistics (4PL) network design problem with the objective of minimizing the overall cost under service time constraint and stochastic demand is proposed in the paper. To address this problem, a two-stage nonlinear stochastic programming model is proposed. The topological structure of the 4PL network is decided in the first stage, while the network flows are determined in the second stage. By using auxiliary variables to linearize the service time constraint and by adopting the sample average approximation (SAA) method to handle the stochastic demand, the two-stage nonlinear stochastic programming model is transformed into a mixed integer linear programming (MILP) model. To overcome the difficulties of solving the MILP model caused by a large number of demand scenarios and integer-valued decision variables, a variable separation (VS) strategy is presented to improve the dual decomposition and Lagrangian relaxation (DDLR) approach to propose a VSDDLR-SAA algorithm. Results of the numerical examples and a real-life case illustrate the effectiveness of the proposed model and VSDDLR-SAA algorithm. Comparison analysis of the 4PL network and the supply chain network shows that 4PL can deliver products within the prescribed time at a lower cost by cooperating with third-party logistics providers. [ABSTRACT FROM AUTHOR]

The implementation of the circular economy is increasingly supported by many governments. It is performed by integrating the activities of reverse supply chain (RSC) into those of forward supply chain. However, many companies that traditionally focus on the activities of forward supply chain have decided to collaborate with third-party reverse logistics providers to manage the RSC. This collaboration motivates the work presented in this paper to propose better decisions for decision makers in the providers under the fact that integrating decisions of the collection of End-of-Life products and their disassembly process proposes a RSC with better performance. In this paper, an integrated problem concerning those decisions is presented and formalised. It also deals with the uncertainty of the quality and the quantity of products as well as the demands of the associated components. Two approximate methods are developed to provide the solutions. [ABSTRACT FROM AUTHOR]

Scheduling-Location (ScheLoc) problem is a new and interesting topic in manufacturing, considering location and scheduling decisions simultaneously. Most existing works focus on the deterministic problems. In practice, however, job-processing times are usually uncertain due to some factors. This paper investigates the stochastic parallel machine ScheLoc problem to minimise the weighted sum of the location cost and the expectation of the total completion time. A two-stage stochastic programming formulation is proposed, then the sample average approximation (SAA) method is adapted to solve the small-size problems. To efficiently address the large-scale problems, a genetic algorithm (GA) and a scenario-based heuristic are designed. Numerical experiments on 450 instances are conducted. Computational results show that the scenario-based heuristic outperforms SAA method and GA in terms of solution quality and computational time. [ABSTRACT FROM AUTHOR]

The resource-constrained project scheduling problem (RCPSP) has been widely studied during the last few decades. In real-world projects, however, not all information is known in advance and uncertainty is an inevitable part of these projects. The chance-constrained resource-constrained project scheduling problem (CC-RCPSP) has been recently introduced to deal with uncertainty in the RCPSP. In this paper, we propose a branch-and-bound (B&B) algorithm and a mixed integer linear programming (MILP) formulation that solve a sample average approximation of the CC-RCPSP. We introduce two different branching schemes and eight different priority rules for the proposed B&B algorithm. The computational results suggest that the proposed B&B procedure clearly outperforms both a proposed MILP formulation and a branch-and-cut algorithm from the literature. [ABSTRACT FROM AUTHOR]

Selective disassembly sequencing is the problem of determining the sequence of disassembly operations to extract one or more target components of a product. This study considers the problem with random operation times in the parallel disassembly environment in which one or more components can be removed at the same time by a single disassembly operation. After representing all possible disassembly sequences using the extended process graph, a stochastic integer programming model is developed for the objective of minimising the sum of disassembly and penalty costs, where the disassembly costs consist of sequence-dependent set-up and operation costs and the penalty cost is the expectation of the costs incurred when the total disassembly time exceeds a threshold value. A sample average approximation-based solution algorithm is proposed that incorporates an optimal algorithm to solve the sample average approximating problem under a given set of scenarios for disassembly operation times. The algorithm is illustrated with a hand-light case and a large-sized random instance, and the results are reported. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of profit-oriented disassembly line design and balancing considering partial disassembly, presence of hazardous parts and uncertainty of task processing times. Few papers have studied the stochastic disassembly line balancing problem and existing approaches have focused on heuristic and metaheuristic methods. Most existing work has concentrated on complete disassembly where task times are assumed to be normal random variables and where AND/OR graphs are not considered. The objective of this paper is the design of a serial line that obtains the maximum revenue and then balances the workload under uncertainty. The processing time of a disassembly task is assumed to be a random variable with any known probability distribution. An AND/OR graph is used to model the precedence relationships among tasks. Stochastic programming models and exact-based solution approaches combining the L-shaped algorithm and Monte Carlo sampling techniques are proposed. The relevance and applicability of the proposed models and solution methods are shown by solving efficiently a set of disassembly problem instances from the literature. [ABSTRACT FROM AUTHOR]

Nowadays, the high penetration of renewable energy, with variable and unpredictable nature, poses major challenges to operation and planning studies of power systems. Employing energy storage plants has been introduced as an effective solution to alleviate these challenges. Several studies have been presented in the literature to provide a framework for planning studies of energy storage plants. However, they usually have two main drawbacks: (i) ignoring the lifetime varying characteristic of energy storage, (ii) inability to model the charge/discharge schedule of energy storage accurately. This paper amends the abovementioned shortcomings by proposing a distributionally robust planning method based on Kullback–Leibler divergence. According to the power function of lifespan of electrochemical energy storage, the lifespan model of energy storage plants with equivalent full cycles times is established. Considering the lifespan model constraints of the energy storage plant and system operating constraints, the planning model of energy storage plants is constructed with the lifespan cycle cost and units’ operation cost as the objective. Furthermore, the ambiguity set of wind farm output based on Kullback–Leibler divergence is embedded into the planning model of energy storage plants, and the distributionally robust planning model of energy storage plant is transformed into mixed integer linear programming model by sample average approximation method. A modified IEEE-30 bus system with two wind farms is studied to demonstrate the effectiveness. The results show distributionally robust planning model reduces about 10% planning cost compared with the traditional robust planning model, and increases the energy storage capacity by 12MW compared with the stochastic planning method. Other, the planning cost of energy storage plants will decrease by 5% ∼23% when the wind abandoned rate increases by 2% and decreases slowly with the increase of abandoned wind rate.

When there are infinitely many scenarios, the current studies of two-stage stochastic programming problems rely on the relatively complete recourse assumption. However, such an assumption can be unrealistic for many real-world problems. This motivates us to study general stochastic programming problems where the sample average approximation (SAA) solutions are not necessarily feasible. When the problems are convex and the true solutions lie in the interior of feasible solutions, we show that the portion of infeasible SAA solutions decays exponentially as the sample size increases. We also study functions with chain-constrained domain and show that the portion of SAA solutions having a low degree of feasibility decays exponentially as the sample size increases. This result is then extended to multistage stochastic programming. [ABSTRACT FROM AUTHOR]

Abstract This paper considers a class of stochastic complementarity problems (SCP). Different from the classical complementarity problems, the SCP contains a mathematical expectation, which may not be evaluated in an explicit form in general. We combine an interior-point algorithm for deterministic cases with the well-known sample average approximation (SAA) techniques to present an SAA-based infeasible interior-point algorithm for the SCP. We investigate the convergence properties and computational complexity of the proposed algorithm under mild assumptions. Then, we extend these results to a class of mixed SCPs. Furthermore, we apply the proposed algorithms to solve a stochastic natural gas transmission problem and a stochastic oligopoly model. Preliminary numerical experiments indicate that the proposed approach is competitive with some existing methods. Highlights • We study a class of stochastic complementarity problems. • We present an infeasible interior-point algorithm for the considered problem. • We investigate convergence properties and computational complexity of the algorithm. • We apply the proposed approach to natural gas transmission and oligopoly problems. [ABSTRACT FROM AUTHOR]

Stochastic variational inequalities (SVI) provide a unified framework for the study of a general class of nonlinear optimization and Nash-type equilibrium problems with uncertain model data. Often the true solution to an SVI cannot be found directly and must be approximated. This paper considers the use of a sample average approximation (SAA), and proposes a new method to compute confidence intervals for individual components of the true SVI solution based on the asymptotic distribution of SAA solutions. We estimate the asymptotic distribution based on one SAA solution instead of generating multiple SAA solutions, and can handle inequality constraints without requiring the strict complementarity condition in the standard nonlinear programming setting. The method in this paper uses the confidence regions to guide the selection of a single piece of a piecewise linear function that governs the asymptotic distribution of SAA solutions, and does not rely on convergence rates of the SAA solutions in probability. It also provides options to control the computation procedure and investigate effects of certain key estimates on the intervals. [ABSTRACT FROM AUTHOR]

Scheduling appointments in a multi-disciplinary clinic is complex, since coordination between disciplines is required. The design of a blueprint schedule for a multi-disciplinary clinic with open access requirements requires an integrated optimization approach, in which all appointment schedules are jointly optimized. As this currently is an open question in the literature, our research is the first to address this problem. This research is motivated by a Dutch hospital, which uses a multi-disciplinary cancer clinic to communicate the diagnosis and to explain the treatment plan to their patients. Furthermore, also regular patients are seen by the clinicians. All involved clinicians therefore require a blueprint schedule, in which multiple patient types can be scheduled. We design these blueprint schedules by optimizing the patient waiting time, clinician idle time, and clinician overtime. As scheduling decisions at multiple time intervals are involved, and patient routing is stochastic, we model this system as a stochastic integer program. The stochastic integer program is adapted for and solved with a sample average approximation approach. Numerical experiments evaluate the performance of the sample average approximation approach. We test the suitability of the approach for the hospital's problem at hand, compare our results with the current hospital schedules, and present the associated savings. Using this approach, robust blueprint schedules can be found for a multi-disciplinary clinic of the Dutch hospital. [ABSTRACT FROM AUTHOR]

In real-world project scheduling applications, activity durations are often uncertain. Proactive scheduling can effectively cope with the duration uncertainties, by generating robust baseline solutions according to a priori stochastic knowledge. However, most of the existing proactive approaches assume that the duration uncertainty of an activity is not related to its scheduled start time, which may not hold in many real-world scenarios. In this paper, we relax this assumption by allowing the duration uncertainty to be time-dependent, which is caused by the uncertainty of whether the activity can be executed on each time slot. We propose a stochastic optimization model to find an optimal Partial-order Schedule (POS) that minimizes the expected makespan. This model can cover both the time-dependent uncertainty studied in this paper and the traditional timeindependent duration uncertainty. To circumvent the underlying complexity in evaluating a given solution, we approximate the stochastic optimization model based on Sample Average Approximation (SAA). Finally, we design two efficient branch-and-bound algorithms to solve the NP-hard SAA problem. Empirical evaluation confirms that our approach can generate high-quality proactive solutions for a variety of uncertainty distributions. [ABSTRACT FROM AUTHOR]

In Ban and Rudin's (2018) "The Big Data Newsvendor: Practical Insights from Machine Learning," the authors take an innovative machine-learning approach to a classic problem solved by almost every company, every day, for inventory management. By allowing companies to use large amounts of data to predict the correct answers to decisions directly, they avoid intermediate questions, such as "how many customers will we get tomorrow?" and instead can tell the company how much inventory to stock for these customers. This has implications for almost all other decision-making problems considered in operations research, which has traditionally considered data estimation separately from the decision optimization. Their proposed methods are shown to work both analytically and empirically with the latter explored in a hospital nurse staffing example in which the best one-step, feature-based newsvendor algorithm (the kernel-weights optimization method) is shown to beat the best-practice benchmark by 24% in the out-of-sample cost at a fraction of the speed. We investigate the data-driven newsvendor problem when one has n observations of p features related to the demand as well as historical demand data. Rather than a two-step process of first estimating a demand distribution then optimizing for the optimal order quantity, we propose solving the "big data" newsvendor problem via single-step machine-learning algorithms. Specifically, we propose algorithms based on the empirical risk minimization (ERM) principle, with and without regularization, and an algorithm based on kernel-weights optimization (KO). The ERM approaches, equivalent to high-dimensional quantile regression, can be solved by convex optimization problems and the KO approach by a sorting algorithm. We analytically justify the use of features by showing that their omission yields inconsistent decisions. We then derive finite-sample performance bounds on the out-of-sample costs of the feature-based algorithms, which quantify the effects of dimensionality and cost parameters. Our bounds, based on algorithmic stability theory, generalize known analyses for the newsvendor problem without feature information. Finally, we apply the feature-based algorithms for nurse staffing in a hospital emergency room using a data set from a large UK teaching hospital and find that (1) the best ERM and KO algorithms beat the best practice benchmark by 23% and 24%, respectively, in the out-of-sample cost, and (2) the best KO algorithm is faster than the best ERM algorithm by three orders of magnitude and the best practice benchmark by two orders of magnitude. The online appendices are available at https://doi.org/10.1287/opre.2018.1757. [ABSTRACT FROM AUTHOR]

This paper, develop a linear stochastic programming model. The objective of model is planning for power energy capacity for facing with demand. In this model, capacity decisions are made to select the time, the location and the type of equipment for power transmission and generation expansion and also try to demand side management. The purpose of model is making decision for construction and expansion of region’s capacity by an incorporated pattern. In this study, planning horizon is 10 years. Demand and outage are considered as an uncertain factor. Attention to different way of facing with demand, demand side management and outage together are the innovations of this research. Designed model centralize in economic, environmental and sociable factors. The results are anticipation of needed capacity, planning for making power plant, providing transmission base and development of demand side management in order to increase social satisfaction. However the remaining sections described the review of capacity planning and assigned the affecting factors on it. Then formulated a linear multi-objective stochastic optimization model and optimal solutions are founded base on sample average approximation.

Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees, however, do not typically hold in finite samples. In this paper, we propose a modification of SAA, which we term Robust SAA, which retains SAA’s tractability and asymptotic properties and, additionally, enjoys strong finite-sample performance guarantees. The key to our method is linking SAA, distributionally robust optimization, and hypothesis testing of goodness-of-fit. Beyond Robust SAA, this connection provides a unified perspective enabling us to characterize the finite sample and asymptotic guarantees of various other data-driven procedures that are based upon distributionally robust optimization. This analysis provides insight into the practical performance of these various methods in real applications. We present examples from inventory management and portfolio allocation, and demonstrate numerically that our approach outperforms other data-driven approaches in these applications. [ABSTRACT FROM AUTHOR]

In this work we consider the shortest path problem with uncertainty in arc lengths and convex risk measure objective.We explore efficient implementations of sample average approximation (SAA) methods to solve shortest path problems when the conditional value at risk and entropic risk measures are used and there is correlation present in the uncertain arc lengths. Ourwork explores the use of different decomposition techniques to achieve an efficient implementation of SAA methods for these nonlinear convex integer optimization problems. A computational study shows the effect of geometry, uncertainty correlation and variance, and risk measure parameters on efficiency and accuracy of the methods developed. [ABSTRACT FROM AUTHOR]

We consider a stochastic single item production‐inventory‐routing problem with a single producer, multiple clients, and multiple vehicles. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented, and valid inequalities are introduced to enhance the model. A new general approach that explores the sample average approximation (SAA) method is introduced. In the sample average approximation method, several sample sets are generated and solved independently in order to obtain a set of candidate solutions. Then, the candidate solutions are tested on a larger sample, and the best solution is selected among the candidates. In contrast to this approach, called static, we propose an adjustable approach that explores the candidate solutions in order to identify common structures. Using that information, part of the first‐stage decision variables is fixed, and the resulting restricted problem is solved for a larger size sample. Several heuristic algorithms based on the mathematical model are considered within each approach. Computational tests based on randomly generated instances are conducted to test several variants of the two approaches. The results show that the new adjustable SAA heuristic performs better than the static one for most of the instances. [ABSTRACT FROM AUTHOR]

Selective disassembly sequencing is the problem of determining the sequence of disassembly operations to extract one or more target components of a product. This study addresses a stochastic version of the problem in which abnormal disassembly operations and random operation times are considered under the parallel disassembly environment, i.e., one or more components that can be disassembled further remain after a disassembly operation is done. Abnormal disassembly operations are defined as those in which fasteners can be removed by additional random destructive operations without damaging to target components. After representing all possible sequences using the extended process graph, a stochastic integer programming model is developed that minimizes the sum of disassembly and penalty costs, where the disassembly cost consists of sequence-dependent setup and operation costs, and the penalty cost is the expectation of the costs incurred when the total disassembly time exceeds a given threshold value. A sample average approximation algorithm is proposed that incorporates a branch and bound algorithm to solve the deterministic problem under a scenario for abnormal operations and operation times optimally. Finally, the algorithm is illustrated with a hand-light example and a larger instance. [ABSTRACT FROM AUTHOR]

The objective of this study was to develop stochastic optimization tools for determining the best strategy of photovoltaic installations in a campus environment with consideration of uncertainties in load, power generation and system performance. In addition to a risk neutral approach, we used Conditional Value-at-Risk to estimate the risk in our problem. The resulting Mixed Integer Programming models were formulated using a scenario-based approach. To minimize the mismatch between supply and demand, hourly solar resource and electricity demand levels were characterized via refined models. A sample-average approximation (SAA) method was proposed to provide high-quality solutions efficiently. The SAA problems were solved using exact and heuristic methods. A complete numerical study was conducted to examine the performance of the proposed solution methods, identify optimal selection strategies and consider the sensitivity of the solution to varying levels of risk. [ABSTRACT FROM AUTHOR]

Background: Scientific management methods are urgently needed to balance the demand and supply of heath care services in Chinese hospitals. Operating theatre is the bottleneck and costliest department. Therefore, the surgery scheduling is crucial to hospital management.Objective: To increase the utilization and reduce the cost of operating theatre, and to improve surgeons' satisfaction in the meantime, a practical surgery scheduling which could assign the operating room (OR) and surgeon for the surgery and sequence surgeries in each OR was provided for hospital managers.Methods: Surgery durations were predicted by fitting the distributions. A two-step mixed integer programming model considering surgery duration uncertainty was proposed, and sample average approximation (SAA) method was applied to solve the model.Results: Durations of various surgeries were log-normal distributed respectively. Numerical experiments showed the model and method could get good solutions with different sample sizes.Conclusions: Real-life constraints and duration uncertainty were considered in the study, and the model was also very applicable in practice. Average overtime of each OR was reducing and tending to be stable with the number of surgeons increasing, which is a discipline for OR management. [ABSTRACT FROM AUTHOR]

The portfolio optimization model has limited impact in practice because of estimation issues when applied to real data. To address this, we adapt two machine learning methods, regularization and cross-validation, for portfolio optimization. First, we introduce performance-based regularization (PBR), where the idea is to constrain the sample variances of the estimated portfolio risk and return, which steers the solution toward one associated with less estimation error in the performance. We consider PBR for both mean-variance and mean-conditional value-at-risk (CVaR) problems. For the mean-variance problem, PBR introduces a quartic polynomial constraint, for which we make two convex approximations: one based on rank-1 approximation and another based on a convex quadratic approximation. The rank-1 approximation PBR adds a bias to the optimal allocation, and the convex quadratic approximation PBR shrinks the sample covariance matrix. For the mean-CVaR problem, the PBR model is a combinatorial optimization problem, but we prove its convex relaxation, a quadratically constrained quadratic program, is essentially tight. We show that the PBR models can be cast as robust optimization problems with novel uncertainty sets and establish asymptotic optimality of both sample average approximation (SAA) and PBR solutions and the corresponding efficient frontiers. To calibrate the right-hand sides of the PBR constraints, we develop new, performance-based k-fold cross-validation algorithms. Using these algorithms, we carry out an extensive empirical investigation of PBR against SAA, as well as L1and L2regularizations and the equally weighted portfolio. We find that PBR dominates all other benchmarks for two out of three Fama-French data sets. [ABSTRACT FROM AUTHOR]

An algorithm is presented for solving nonlinear optimization problems with chance constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained nonlinear optimization problems that arise in sample average approximations of chance-constrained problems, as well as in other applications in which it is only desired to enforce a minimum number of constraints. The algorithm employs a novel exact penalty function which is minimized sequentially by solving quadratic optimization subproblems with linear cardinality constraints. Properties of minimizers of the penalty function in relation to minimizers of the corresponding nonlinear optimization problem are presented, and convergence of the proposed algorithm to stationarity with respect to the penalty function is proved. The effectiveness of the algorithm is demonstrated through numerical experiments with a nonlinear cash ow problem. [ABSTRACT FROM AUTHOR]

This paper considers a class of vector variational inequalities. First, we present an equivalent formulation, which is a scalar variational inequality, for the deterministic vector variational inequality. Then we concentrate on the stochastic circumstance. By noting that the stochastic vector variational inequality may not have a solution feasible for all realizations of the random variable in general, for tractability, we employ the expected residual minimization approach, which aims at minimizing the expected residual of the so-called regularized gap function. We investigate the properties of the expected residual minimization problem, and furthermore, we propose a sample average approximation method for solving the expected residual minimization problem. Comprehensive convergence analysis for the approximation approach is established as well. [ABSTRACT FROM AUTHOR]

Urban rail planning is extremely complex, mainly because it is a decision problem under different uncertainties. In practice, travel demand is generally uncertain, and therefore, the timetabling decisions must be based on accurate estimation. This research addresses the optimization of train timetable at public transit terminals of an urban rail in a stochastic setting. To cope with stochastic fluctuation of arrival rates, a two-stage stochastic programming model is developed. The objective is to construct a daily train schedule that minimizes the expected waiting time of passengers. Due to the high computational cost of evaluating the expected value objective, the sample average approximation method is applied. The method provided statistical estimations of the optimality gap as well as lower and upper bounds and the associated confidence intervals. Numerical experiments are performed to evaluate the performance of the proposed model and the solution method. [ABSTRACT FROM AUTHOR]

We discuss a general approach to building non-asymptotic confidence bounds for Stochastic Optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than ‘standard’ confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a simulation study illustrating the numerical behaviour of the proposed bounds. [ABSTRACT FROM PUBLISHER]

In this paper a general methodology is proposed based on robust optimization for an inventory control problem subject to uncertain demands and uncertain lead times. Several lead time uncertainty sets are proposed based on the budget uncertainty set, and a set based on the central limit theorem. Robust optimization models are developed for a periodic review, finite horizon inventory control problem subject to uncertain demands and uncertain lead times. We develop an approach based on Benders' decomposition to compute optimal robust (i.e., best worst-case) policy parameters. The proposed approach does not assume distributional knowledge, makes no assumption regarding order crossovers, and is tractable in a practical sense. Comparing the new approach to an epigraph reformulation method, we demonstrate that the epigraph reformulation approach is overly conservative even when costs are stationary. The approach is benchmarked against the sample average approximation (SAA) method. Computational results indicate that the approach provides more stable and robust solutions compared to SAA in terms of standard deviation and worst-case solution, especially when the realized distribution is different than the sampled distribution. [ABSTRACT FROM AUTHOR]

This paper considers a stochastic location-allocation problem for a capacitated bike sharing system (S-L&A-CBSS), in which bike demand is uncertain. To tackle this uncertainty, a Sample Average Approximation (SAA) method is used. Because this problem is an NP-hard problem, a hybrid greedy/evolutionary algorithm based on Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), namely greedy GA-PSO, is embedded in the SAA method in order to solve the given large-sized problems. The performance of the proposed hybrid algorithm is tested by a number of numerical examples and used for empirical test based on Tehran business zone. Furthermore, the associated results show its efficiency in comparison to an exact solution method in solving small-sized problems. Finally, the conclusion is provided. [ABSTRACT FROM AUTHOR]

Utility-based choice models are often used to determine a consumer's purchase decision among a list of available products; to provide an estimate of product demands; and, when data on purchase decisions or market shares are available, to infer consumers' preferences over observed product characteristics. These models also serve as a building block in modeling firms' pricing and assortment optimization problems. We consider a firm's multiproduct pricing problem, in which product demands are determined by a pure characteristics model. A sample average approximation (SAA) method is used to approximate the expected market share of products and the firm profit. We propose an SAA-regularized method for the multiproduct price optimization problem. We present convergence analysis and numerical examples to show the efficiency and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Traditionally, most stochastic approximation (SA) schemes for stochastic variational inequality (SVI) problems have required the underlying mapping to be either strongly monotone or monotone and Lipschitz continuous. In contrast, we consider SVIs with merely monotone and non-Lipschitzian maps. We develop a regularized smoothed SA (RSSA) scheme wherein the stepsize, smoothing, and regularization parameters are reduced after every iteration at a prescribed rate. Under suitable assumptions on the sequences, we show that the algorithm generates iterates that converge to the least norm solution in an almost sure sense, extending the results in Koshal et al. (IEEE Trans Autom Control 58(3):594-609, 2013) to the non-Lipschitzian regime. Additionally, we provide rate estimates that relate iterates to their counterparts derived from a smoothed Tikhonov trajectory associated with a deterministic problem. To derive non-asymptotic rate statements, we develop a variant of the RSSA scheme, denoted by aRSSA $$_r$$ , in which we employ a weighted iterate-averaging, parameterized by a scalar r where $$r = 1$$ provides us with the standard averaging scheme. The main contributions are threefold: (i) when $$r<1$$ and the parameter sequences are chosen appropriately, we show that the averaged sequence converges to the least norm solution almost surely and a suitably defined gap function diminishes at an approximate rate $$\mathcal{O}({1}\slash {\root 6 \of {k}})$$ after k steps; (ii) when $$r<1$$ , and smoothing and regularization are suppressed, the gap function admits the rate $$\mathcal{O}({1}\slash {\sqrt{k}})$$ , thus improving the rate $$\mathcal{O}(\ln (k)/\sqrt{k})$$ under standard averaging; and (iii) we develop a window-based variant of this scheme that also displays the optimal rate for $$r < 1$$ . Notably, we prove the superiority of the scheme with $$r < 1$$ with its counterpart with $$r=1$$ in terms of the constant factor of the error bound when the size of the averaging window is sufficiently large. We present the performance of the developed schemes on a stochastic Nash-Cournot game with merely monotone and non-Lipschitzian maps. [ABSTRACT FROM AUTHOR]

Stochastic variational inequalities (SVIs) provide a means for modeling various optimization and equilibrium problems where data are subject to uncertainty. Often the SVI cannot be solved directly and requires a numerical approximation. This paper considers the use of a sample average approximation and proposes three methods for computing confidence intervals for components of the true solution. The first two methods use an 'indirect approach' that requires initially computing asymptotically exact confidence intervals for the solution to the normal map formulation of the SVI. The third method directly constructs confidence intervals for the true SVI solution; intervals produced with this method meet a minimum specified level of confidence in the same situations for which the first two methods are applicable. We justify the three methods theoretically with weak convergence results, discuss how to implement these methods, and test their performance using three numerical examples. [ABSTRACT FROM AUTHOR]

The sample average approximation (SAA) approach is a widely used technique, based on Monte-Carlo simulation, often applied to large-scale stochastic optimization problems. In this approach, a set of sample average problems with multiple copies of sampled scenarios are generated and solved exactly. In other words, there is an implicit assumption that the sample average problems are solvable to optimality. In some instances, however, the sample average problems might be NP-hard problems, often difficult or impractical to solve to optimality. In this article, we broaden the scope of the SAA approach and show that even without solving the sample problems to optimality, by combining a heuristic and a lower bounding approach, high-quality solutions with tight confidence bounds on the optimal solution value can be obtained. We demonstrate this 'inexact SAA approach' on two problems. First, we apply it to the Stochastic Connected Facility Location (SConFL) problem, the motivating application for this article, that arises in the design of telecommunications networks. As an additional application, we also use it for the Stochastic Uncapacitated Facility Location (SUFL) problem. Our computational results demonstrate the effectiveness of the inexact SAA approach. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 19-33 2017 [ABSTRACT FROM AUTHOR]

In this paper, we consider the stochastic second-order cone complementarity problems (SSOCCP). We first formulate the SSOCCP contained expectation as an optimization problem using the so-called second-order cone complementarity function. We then use sample average approximation method and smoothing technique to obtain the approximation problems for solving this reformulation. In theory, we show that any accumulation point of the global optimal solutions or stationary points of the approximation problems are global optimal solution or stationary point of the original problem under suitable conditions. Finally, some numerical examples are given to explain that the proposed methods are feasible. [ABSTRACT FROM PUBLISHER]

In air cargo transportation, capacity can be reserved via allotment, which are long-term contracts with fixed price, and free, which is the space not assigned to allotment contracts. In this later case, reservations are made closer to the departure date, and normally higher tariffs are charged. The demand, the tariff, and the show-up rate for the free mode are stochastic. We consider risk neutral and risk averse formulations, using the Conditional Value-at-Risk as a risk measure. We solve the resulting problems using the Sample Average Approximation and test our models with nine experiments representing different demand patterns using real data from a major airline. [ABSTRACT FROM AUTHOR]

This work proposes a multi-objective optimization model to design a sustainable multi-period second generation biomass-to-bioethanol supply chain under multiple uncertainties. The objective is to simultaneously maximize the economic, environmental, and social performance. The strategic decisions such as land allocation for switchgrass cultivation, biorefinery locations and capacities, and the biomass-to-bioethanol conversion pathway are determined for each planning period which are staggered across the entire planning horizon. The augmented ε –constraint method is used to trade-off among the competing objectives and to obtain feasible solutions that achieve desired levels of sustainability. In order to solve the proposed stochastic optimization model efficiently and effectively, this work proposes a solution approach involving sequential application of a modified Sample Average Approximation method and Benders decomposition. A case study is presented to demonstrate the effectiveness of the proposed mathematical model and its impact on land usage and sustainability. [ABSTRACT FROM AUTHOR]

In many applications, the clustered count data often contain excess zeros and the zero-inflated generalized Poisson mixed (ZIGPM) regression model may be suitable. However, dispersion in ZIGPM is often treated as fixed unknown parameter, and this assumption may be not appropriate in some situations. In this article, a score test for homogeneity of dispersion parameter in ZIGPM regression model is developed and corresponding test statistic is obtained. Sampling distribution and power of the score test statistic are investigated through Monte Carlo simulation. Finally, results from a biological example illustrate the usefulness of the diagnostic statistic. [ABSTRACT FROM AUTHOR]

A new method for dealing with systematic effects in laser scanning and visualizing them by confidence regions is derived. The standard deviations of the systematic effects are obtained by repeatedly measuring three- dimensional coordinates by the laser scanner. In addition, autocovariance and cross-covariance functions are computed by the repeated measurements and give the correlations of the systematic effects. The normal distribution for the measurements and the multivariate uniform distribution for the systematic effects are applied to generate random variates for the measurements and random variates for the measurements plus systematic effects. Monte Carlo estimates of the expectations and the covariance matrix of the measurements with systematic effects are computed. The densities for the confidence ellipsoid for the measurements and the confidence region for the measurements with systematic effects are obtained by relative frequencies. They only depend on the size of the rectangular volume elements for which the densities are determined. The problem of sorting the densities is solved by sorting distances together with the densities. This allows a visualization of the confidence ellipsoid for the measurements and the confidence region for the measurements with systematic effects. [ABSTRACT FROM AUTHOR]

In a more and more competitive and global world, freight transports have to overcome increasingly long distances while at the same time becoming more reliable. In addition, a raising awareness of the need for environmentally friendly solutions increases the importance of transportation modes other than road. Intermodal transportation, in that regard, allows for the combination of different modes in order to exploit their individual advantages. Intermodal transportation networks offer flexible, robust and environmentally friendly alternatives to transport high volumes of goods over long distances. In order to reflect these advantages, it is the challenge to develop models which both represent multiple modes and their characteristics (e.g., fixed-time schedules and routes) as well as the transhipment between these transportation modes. In this paper, we introduce a Green Intermodal Service Network Design Problem with Travel Time Uncertainty (GISND-TTU) for combined offline intermodal routing decisions of multiple commodities. The proposed stochastic approach allows for the generation of robust transportation plans according to different objectives (i.e., cost, time and greenhouse gas (GHG) emissions) by considering uncertainties in travel times as well as demands with the help of the sample average approximation method. The proposed methodology is applied to a real-world network, which shows the advantages of stochasticity in achieving robust transportation plans. [ABSTRACT FROM AUTHOR]

In this letter, we study the problem of estimating the long-run mean of the Ornstein–Uhlenbeck (OU) stochastic process and its effect on the long-term prediction of future vessel states, which is a crucial problem for Maritime Situational Awareness (MSA). We employ a sample mean estimator (SME) to estimate the key OU parameter from the observations, computing the closed-form SME covariance error in both the random and constant sampling time regimes, providing a fundamental building block of the overall long-term state prediction covariance. We show also that the SME is: \sqrtn-consistent when the sampling time is random; asymptotically efficient when the sampling time is constant; and very close to the Cramér–Rao lower bound in the cases of practical interest for MSA. [ABSTRACT FROM PUBLISHER]

An approach to the de novo structure prediction of proteins is described that relies on surface accessibility data from NMR paramagnetic relaxation enhancements by a soluble paramagnetic compound (sPRE). This method exploits the distance-to-surface information encoded in the sPRE data in the chemical shift-based CS-Rosetta de novo structure prediction framework to generate reliable structural models. For several proteins, it is demonstrated that surface accessibility data is an excellent measure of the correct protein fold in the early stages of the computational folding algorithm and significantly improves accuracy and convergence of the standard Rosetta structure prediction approach. [ABSTRACT FROM AUTHOR]

The sample mean is sometimes depicted as a fulcrum placed under the Dot plot. We provide an alternative geometric visualization of the sample mean using the empirical cumulative distribution function or the cumulative histogram data. [ABSTRACT FROM AUTHOR]

In this paper we apply modified Newton method based on sample average approximation (SAA) to solve stochastic variational inequality with stochastic second-order cone constraints (SSOCCVI). Under some moderate conditions, the SAA solution converges to its true counterpart with probability approaching one at exponential rate as sample size increases. We apply the theoretical results for solving a class of stochastic second order cone complementarity problems and stochastic programming problems with stochastic second order cone constraints. Some illustrative examples are given to show how the globally convergent method works and the comparison results between our method and other methods. Furthermore, we apply this method to portfolio optimization with loss risk constraints problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new reformulation for stochastic complementarity problems (SCPs). The new formulation is based on the minimum mean-squared deviation rule in statistics. Under mild conditions, we prove the existence of the solution of the new reformulation for SCP. Furthermore, we present a smoothing sample average approximation method for solving the problems. The convergence properties of the optimal solutions of the approximation problems are studied under mild conditions. Finally, some numerical results are listed as well. [ABSTRACT FROM AUTHOR]

A new and efficient improved maximum scatter difference (MSD) model is introduced in this paper. The main weakness of the MSD model is that the class mean vector is constructed via class sample average when the within-class and between-class scatter matrices are formed. For a few of given samples with non-ideal conditions (e.g., variations of expression, pose and noisy environment), the assessment result is very weak by using the class sample average. That is because there will be some outliers in these samples. Therefore, the recognition performance of maximum scatter difference criterion will decline significantly. To solve the problem, in the traditional MSD model, we use within-class maximum–minimum–median average vector to construct within-class scatter matrix ( S w ) and between-class scatter matrix ( S b ) instead of within-class mean vector. The experimental results show that an improvement of the MSD model is possible with the proposed technique in ORL and Yale face database recognition problems. [ABSTRACT FROM AUTHOR]

In many engineering practices, only a small sample data is collected due to the cost restrictions and limiting conditions. In allusion to the evaluation problem of the small sample, interval estimation approach with the improved grey confidence degree is proposed. On the basis of the definition of grey distance, a new definition of the grey weight for every sample element in grey estimated value and a new definition of grey' confidence degree are put forward. In accordance with the new concept, more accurate grey interval estimation for small samples is deduced. In addition, according to the new' definition, grey interval estimation method for two samples are defined. The grey unilateral confidence interval of small samples based on grey confidence level is also introduced. Finally, several example simulations are conducted. The simulation results show that the reasonable confidence interval is achieved, which demonstrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Consider the problem of minimizing the expected value of a cost function parameterized by a random variable. The classical sample average approximation method for solving this problem requires minimization of an ensemble average of the objective at each step, which can be expensive. In this paper, we propose a stochastic successive upper-bound minimization method (SSUM) which minimizes an approximate ensemble average at each iteration. To ensure convergence and to facilitate computation, we require the approximate ensemble average to be a locally tight upper-bound of the expected cost function and be easily optimized. The main contributions of this work include the development and analysis of the SSUM method as well as its applications in linear transceiver design for wireless communication networks and online dictionary learning. Moreover, using the SSUM framework, we extend the classical stochastic (sub-)gradient method to the case of minimizing a nonsmooth nonconvex objective function and establish its convergence. [ABSTRACT FROM AUTHOR]

The main theme of this research is to introduce a new technique for quality improvement in industries and services environment. The technique is called as quality variation minimizer (QVM), which is used to test and compare product quality among multiple data groups, i.e. machines, operators, and material etc. For the significant application, QVM is applied at Card department in spinning industry to determine yarn grains quality by different machines. Then comparison of QVM is made with other already developed techniques, i.e., coefficient variation (CV), sigma level etc. to determine yarn grains quality. From the results determined by t-test and chi square test, it has been found that QVM is an effective method to determine yarn grains quality with sample average near the target/demanded value as well as minimum variation. [ABSTRACT FROM AUTHOR]

Developing a plan of action for the future use of forest resources requires a way to predict the development of the forest through time. These predictions require the use of inventory data and growth models that contain a large number of uncertainties. These uncertainties impact the quality of the predictions, and if not accounted for, they can lead to the selection of a suboptimal management plan. To account for and manage the uncertainties and associated risk, we have explored the use of stochastic programming. Stochastic programming can integrate uncertainty into the optimization process by solving the problem for a large number of potential scenarios of the forests future development. The selection of an appropriately sized set of scenarios involves a trade-off between tractability issues and problem representation issues. In this paper, an analysis of the trade-offs is conducted. Two cases are studied, one in which only the uncertainty of the inventory data is included and a second in which both growth model and inventory data uncertainties are included. The impact of increasing the number of scenarios on the problem representation is examined through a simple even-flow problem. [ABSTRACT FROM AUTHOR]