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The generation maintenance scheduling deals with a time sequence of preventive maintenance outages for a given set of generation units in an electricity market subject to power system restrictions. Incorporating a leader–follower structure in generation maintenance scheduling models is essential because of the inherent conflict between the interests of an independent system operator (ISO) and generation companies (GENCOs). The present paper proposes a new preventive maintenance scheduling model for generation companies facing the risk of involving generation units' disruption and demand variations while ensuring the reliability of the power system. Each GENCO proposes the maintenance schedule of its generation units to the ISO in a non-cooperative manner intending to maximize its net profit. Then ISO reacts to the aggregated schedule according to the power system's reliability index. Thus, a new formula is developed to consider all the interactions between the power system's stakeholders. In this regard, a stochastic multi-leader one-follower approach is applied. The GENCOs are considered independent leaders at the upper-level and the ISO is considered a follower at the lower-level. Then an equivalent single-level counterpart model is presented for each leader. So, the whole problem is converted into multiple individual stochastic single-level models, and then the Nash Equilibrium concept is used to determine GENCO equilibrium strategies. The proposed methodology is evaluated using some modified IEEE reliability test systems. The numerical analysis confirms that the proposed model is more effective in cases with higher uncertainties. Moreover, the performed analysis demonstrated the importance of applying a bi-level approach to the problem. Finally, the superiority of the proposed approach compared to the existing one is confirmed. [ABSTRACT FROM AUTHOR]

The construction and operation of linear infrastructure has major impacts on biodiversity through loss of habitat, increased mortality and loss of connectivity. In particular, minimising the impact of roads which pass through ecologically sensitive areas on surrounding species at the construction and operational phases is critical for conservation. However, potential impacts are rarely known perfectly at the construction phase and early in the operational phase. To address this problem, a company could build flexibility into road operation so that it can respond rapidly to future ecological impacts if necessary. In this paper we analyse the value of this flexibility using stochastic dynamic programming and use the results to guide a global search algorithm to find high value roads in the region. We consider flexibility in terms of the proportion of traffic volume routed along the road, with the remainder passing along an existing higher-cost, lower-impact road. We applied this to an example scenario where a road must be routed through a region with a vulnerable species present. By incorporating flexibility, the proposed model was able to find a road that met a desired ending population of animals and was more valuable than roads found under existing design alternatives. [ABSTRACT FROM AUTHOR]

This paper studies the issue of coordinating equipment maintenance operations with capital investment strategy in the presence of random equipment failures. The traditional approach, developed by Kamien and Schwartz (KS) in their celebrated paper published in 1971, is to formulate the problem as a deterministic optimal control problem with the probability of machine failure as the state variable. With this approach, the optimal policy is deterministic. As a major departure from the KS approach, we explicitly model the underlying stochastic process of machine failures. Our analysis of the stochastic dynamic programming model offers new insights into the problem. Under a long planning horizon with a limited replacement opportunity, each individual machine serves as a revenue generator and contributes a significant amount to the profit of the system. In contrast, when the replacement budget is quite generous over a relatively short planning horizon, adding one extra machine only helps as a backup for unexpected failures of the machines purchased before it. An interesting result derived from this comparison is that a deterministic policy turns out to be optimal for the former, while a state-contingent policy must be applied to the latter. In other words, the deterministic KS approach does not work in general when a chain of machine replacement is considered. We further characterize the effects of the discount rate, productivity deterioration, learning, decision delay, and technology advancement on the optimal policy. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-stage stochastic weekly operating room planning problem with an exponential number of scenarios. The objective function is to minimize the sum of the fixed opening cost of operating rooms and the expected overtime costs that are computed in the second stage. We propose a state-variable model to formulate the two-stage stochastic operating room planning problem and prove its validity. The main advantage of the proposed state-variable model is that it has a pseudo-polynomial number of variables and constraints that are significantly fewer than the number of variables and constraints in an equivalent scenario-based stochastic programming model. We improve the quality of the proposed model by developing an enhanced model that includes remarkably fewer variables and constraints. We also strengthen the model by developing several valid inequalities, including worst-case scenario and symmetry-breaking cuts. We carried out extensive computational experiments to evaluate the performance of the proposed model. The computational results show that the proposed model is capable of finding optimal solutions of instances with 50 surgeries and 1.55E+40 scenarios that is a significant improvement over the state-of-the-art models. The results revealed that the model finds feasible solutions with an average optimality gap of 0.78% for instances with 80 surgeries and 1.48E+64 scenarios. [ABSTRACT FROM AUTHOR]

In this paper, a new production, allocation, location, inventory holding, distribution, and flow problems for a new sustainable-resilient health care network related to the COVID-19 pandemic under uncertainty is developed that also integrated sustainability aspects and resiliency concepts. Then, a multi-period, multi-product, multi-objective, and multi-echelon mixed-integer linear programming model for the current network is formulated and designed. Formulating a new MILP model to design a sustainable-resilience healthcare network during the COVID-19 pandemic and developing three hybrid meta-heuristic algorithms are among the most important contributions of this research. In order to estimate the values of the required demand for medicines, the simulation approach is employed. To cope with uncertain parameters, stochastic chance-constraint programming is proposed. This paper also proposed three meta-heuristic methods including Multi-Objective Teaching–learning-based optimization (TLBO), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA) to find Pareto solutions. Since heuristic approaches are sensitive to input parameters, the Taguchi approach is suggested to control and tune the parameters. A comparison is performed by using eight assessment metrics to validate the quality of the obtained Pareto frontier by the heuristic methods on the experiment problems. To validate the current model, a set of sensitivity analysis on important parameters and a real case study in the United States are provided. Based on the empirical experimental results, computational time and eight assessment metrics proposed methodology seems to work well for the considered problems. The results show that by raising the transportation costs, the total cost and the environmental impacts of sustainability increased steadily and the trend of the social responsibility of staff rose gradually between − 20 and 0%, but, dropped suddenly from 0 to + 20%. Also in terms of the on-resiliency of the proposed network, the trends climbed slightly and steadily. Applications of this paper can be useful for hospitals, pharmacies, distributors, medicine manufacturers and the Ministry of Health. [ABSTRACT FROM AUTHOR]

Planning and scheduling of operating rooms (ORs) is important for hospitals to improve efficiency and achieve high quality of service. Due to significant uncertainty in surgery durations, scheduling of ORs can be very challenging. In this paper, surgical case scheduling problem with uncertain duration of surgeries in multi resource environment is investigated. We present a two-stage stochastic mixed-integer programming model, named SOS, with the objective of total ORs idle time and overtime. Also, in this paper a two-step approach is proposed for solving the model based on the L-shaped algorithm. Proposing the model in a multi resources environment with considering real-life limitations in academic hospitals and developing an approach for solving this stochastic model efficiently form the main contributions of this paper. The model is evaluated through several numerical experiments based on real data from Hasheminejad Kidney Center (HKC) in Iran. The solutions of SOS are compared with the deterministic solutions in several real instances. Numerical results show that SOS enjoys a better performance in 97% of the cases. Furthermore, the results of comparing with actual schedules applied in HKC reveal a notable reduction of OR idle time and over time which illustrate the efficiency of the proposed model in practice. [ABSTRACT FROM AUTHOR]

In the present paper we generalise the classical newsvendor problem for critical perishable commodities having more severe costs than its linear alternative. Piece wise polynomial cost functions are introduced to accommodate the excess severity. Stochastic demand is assumed to follow a completely unknown probability distribution. Non parametric estimator of the optimal order quantity has been developed from an estimating equation using a random sample. Strong consistency of the estimator is proved for unique optimal order quantity and the result is extended for multiple solutions. Simulation results indicate that non parametric estimator is efficient in terms of mean square error. Real life application of the proposed non-parametric estimator has been demonstrated with Avocado demand in the United States of America and Covid-19 test kit demand during second wave of SARS-COV2 pandemic across 86 countries. [ABSTRACT FROM AUTHOR]

This paper investigates the variance reduction techniques Antithetic Variates (AV) and Latin Hypercube Sampling (LHS) when used for sequential sampling in stochastic programming and presents a comparative computational study. It shows conditions under which the sequential sampling with AV and LHS satisfy finite stopping guarantees and are asymptotically valid, discussing LHS in detail. It computationally compares their use in both the sequential and non-sequential settings through a collection of two-stage stochastic linear programs with different characteristics. The numerical results show that while both AV and LHS can be preferable to random sampling in either setting, LHS typically dominates in the non-sequential setting while performing well sequentially and AV gains some advantages in the sequential setting. These results imply that, given the ease of implementation of these variance reduction techniques, armed with the same theoretical properties and improved empirical performance relative to random sampling, AV and LHS sequential procedures present attractive alternatives in practice for a class of stochastic programs. [ABSTRACT FROM AUTHOR]

In the aftermath of a hurricane, humanitarian logistics plays a critical role in delivering relief items to the affected areas in a timely fashion. This paper proposes a novel stochastic look-ahead framework that implements a two-stage stochastic programming model in a rolling horizon approach to address the evolving uncertain logistics system state during the post-hurricane humanitarian logistics operations. The two-stage stochastic programming model that executes in this rolling horizon approach is formulated as a mixed-integer programming problem. The model aims to minimize the total cost incurred in the logistics operations, which consist of transportation cost and social cost. The social cost is measured as a function of deprivation for unsatisfied demand. Our extensive numerical results and sensitivity analysis demonstrate the effectiveness of the proposed approach in reducing the total cost incurred during the post-hurricane relief logistics operations compared to the two-stage stochastic programming model implemented in a static fashion. [ABSTRACT FROM AUTHOR]

Multiple and usually conflicting objectives subject to data uncertainty are main features in many real-world problems. Consequently, in practice, decision-makers need to understand the trade-off between the objectives, considering different levels of uncertainty in order to choose a suitable solution. In this paper, we consider a two-stage bi-objective single source capacitated model as a base formulation for designing a last-mile network in disaster relief where one of the objectives is subject to demand uncertainty. We analyze scenario-based two-stage risk-neutral stochastic programming, adaptive (two-stage) robust optimization, and a two-stage risk-averse stochastic approach using conditional value-at-risk (CVaR). To cope with the bi-objective nature of the problem, we embed these concepts into two criterion space search frameworks, the ϵ -constraint method and the balanced box method, to determine the Pareto frontier. Additionally, a matheuristic technique is developed to obtain high-quality approximations of the Pareto frontier for large-size instances. In an extensive computational experiment, we evaluate and compare the performance of the applied approaches based on real-world data from a Thies drought case, Senegal. [ABSTRACT FROM AUTHOR]

The paper investigates national/regional power generation expansion planning for medium/long-term analysis in the presence of electricity demand uncertainty. A two-stage stochastic programming is designed to determine the optimal mix of energy supply sources with the aim to minimise the expected total cost of electricity generation considering the total carbon dioxide emissions produced by the power plants. Compared to models available in the extant literature, the proposed stochastic generation expansion model is constructed based on sets of feasible slots (schedules) of existing and potential power plants. To reduce the total emissions produced, two approaches are applied where the first one is performed by introducing emission costs to penalise the total emissions produced. The second approach transforms the stochastic model into a multi-objective problem using the ϵ -constraint method for producing the Pareto optimal solutions. As the proposed stochastic energy problem is challenging to solve, a technique that decomposes the problem into a set of smaller problems is designed to obtain good solutions within an acceptable computational time. The practical use of the proposed model has been assessed through application to the regional power system in Indonesia. The computational experiments show that the proposed methodology runs well and the results of the model may also be used to provide directions/guidance for Indonesian government on which power plants/technologies are most feasible to be built in the future. [ABSTRACT FROM AUTHOR]

In the spot market for air cargo, airlines typically adopt dynamic pricing to tackle demand uncertainty, for which it is difficult to accurately estimate the distribution. This study addresses the problem where a dominant airline dynamically sets prices to sell its capacities within a two-phase sales period with only partial information. That partial information may show as the moments (upper and lower bounds and mean) and the median of the demand distribution. We model the problem of dynamic pricing as a distributional robust stochastic programming, which minimizes the expected regret value under the worst-case distribution in the presence of partial information. We further reformulate the proposed non-convex model to show that the closed-form formulae of the second-stage maximal expected regret are well-structured. We also design an efficient algorithm to characterize robust pricing strategies in a polynomial-sized running time. Using numerical analysis, we present several useful managerial insights for airline managers to strategically collect demand information and make prices for their capacities in different market situations. Moreover, we verify that additional information will not compromise the viability of the pricing strategies being implemented. Therefore, the method we present in this paper is easier for airlines to use. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of choosing the optimal pension fund in the second pillar of Lithuanian pension system by providing some guidelines to individuals with defined contribution pension plans. A multistage risk-averse stochastic optimization model is proposed that can be used to plan a long-term pension accrual under two different cases: minimum and maximum accumulation plans as possible options in the system. The investment strategy of personal savings is based on the optimal solutions over possible scenario realizations generated for a particular participant. The concept of the risk-averse decision-maker is implemented by choosing the conditional value at risk as the risk measure defined by a nested formulation that guarantees the time consistency in the multistage model. The paper focuses on three important decision-making moments corresponding to the duration of periods to be modelled. The first period is a short-term accumulation, while the second period is a long-term accumulation with possibly high deviation of objective function value. The third period is designed to implement the concept of target date fund in the second pillar pension scheme as the subsequent need to protect against potential losses at risky pension funds. The experimental findings of this research provide insights for individuals as decision-makers to select pension funds, as well as for policy-makers by revealing the vulnerability of pension system. [ABSTRACT FROM AUTHOR]

Robust multi-stage linear optimization is hard computationally and only small problems can be solved exactly. Hence, robust multi-stage linear problems are typically addressed heuristically through decision rules, which provide upper bounds for the optimal solution costs of the problems. We investigate in this paper lower bounds inspired by the perfect information relaxation used in stochastic programming. Specifically, we study the uncapacitated robust lot-sizing problem, showing that different versions of the problem become tractable whenever the non-anticipativity constraints are relaxed. Hence, we can solve the resulting problem efficiently, obtaining a lower bound for the optimal solution cost of the original problem. We compare numerically the solution time and the quality of the new lower bound with the dual affine decision rules that have been proposed by Kuhn et al. (Math Program 130:177-209, 2011). [ABSTRACT FROM AUTHOR]

Multi-portfolio optimization problems and the incorporation of marginal risk contribution constraints have recently received a sustained interest from academia and financial practitioners. We propose a class of new stochastic risk budgeting multi-portfolio optimization models that impose portfolio as well as marginal risk constraints. The models permit the simultaneous and integrated optimization of multiple sub-portfolios in which the marginal risk contribution of each individual security is accounted for. A risk budget defined with a downside risk measure is allocated to each security. We consider the two cases in which the asset universes of the sub-portfolios are either disjoint (diversification of style) or overlap (diversification of judgment). The proposed models take the form of stochastic programming problems and include each a probabilistic constraint with multi-row random technology matrix. We expand a combinatorial modeling framework to represent the feasible set of the chance constraints first as a set of mixed-integer linear inequalities. The new reformulation proposed in this paper is much sparser than previously presented reformulations and allows the efficient solution of problem instances that could not be solved otherwise. We evaluate the efficiency and scalability of the proposed method that is general enough to be applied to general chance-constrained optimization problems. We conduct a cross-validation study via a rolling-horizon procedure to assess the performance of the models, and understand the impact of the parameters and diversification types on the portfolios. [ABSTRACT FROM AUTHOR]

This paper considers an extension of the common asset universe of a pension fund to investment certificates. Investment certificates are a class of structured products particularly interesting for their special payoff structures and they are acquiring relevancy in the worldwide markets. In fact, some subclasses of certificates offer loss protection and show high liquidity and, thus, they can be very appreciated by pension fund managers. We consider the problem of a pension fund manager who has to implement an Asset and Liability Management model trying to achieve a long-term sustainability. Therefore, we formulate a multi-stage stochastic programming problem adopting a discrete scenario tree and a multi-objective function. We propose a technique to price highly structured products such as investment certificates on a discrete scenario tree. Finally, we solve the investment problem considering some investment certificate types both in term of payoff structure and protection level, and we test whether they are preferred or not to standard hedging contract such as put options. Moreover, we test the inclusion of first-order and second-order stochastic dominance constraints on multiple stages with respect to a benchmark portfolio. Numerical results show that the portfolio composition reacts to the inclusion of the stochastic dominance constraints, and that the optimal portfolio is efficiently able to reach several targets such as liquidity, returns, sponsor's extraordinary contribution and funding gap. [ABSTRACT FROM AUTHOR]

This paper addresses design and planning of an integrated forward/reverse logistics network over a planning horizon with multiple tactical periods. In the network, demand for new products and potential return of used products are stochastic. Furthermore, collection amounts of used products with different quality levels are assumed dependent on offered acquisition prices to customer zones. A uniform distribution function defines the expected price of each customer zone for one unit of each used product. Using two-stage stochastic programming, a mixed-integer linear programming model is proposed. To cope with demand and potential return uncertainty, Latin Hypercube Sampling method is applied to generate fan of scenarios and then, backward scenario reduction technique is used to reduce the number of scenarios. Due to the problem complexity, a novel simulation-based simulated annealing algorithm is developed to address large-sized test problems. Numerical results indicate the applicability of the model as well as the efficiency of the solution approach. In addition, the performance of the scenario generation method and the importance of stochasticity are examined for the optimization problem. Finally, several numerical experiments including sensitivity analysis on main parameters of the problem are performed. [ABSTRACT FROM AUTHOR]

We consider the problem to find a schedule for component replacement in a multi-component system, whose components possess stochastic lives and economic dependencies, such that the expected costs for maintenance during a pre-defined time period are minimized. The problem was considered in Patriksson et al. (Ann Oper Res 224:51–75, 2015b), in which a two-stage approximation of the problem was optimized through decomposition (denoted the optimization policy). The current paper improves the effectiveness of the decomposition approach by establishing a tighter bound on the value of the recourse function (i.e., the second stage in the approximation). A general lower bound on the expected maintenance cost is also established. Numerical experiments with 100 simulation scenarios for each of four test instances show that the tighter bound yields a decomposition generating fewer optimality cuts. They also illustrate the quality of the lower bound. Contrary to results presented earlier, an age-based policy performs on par with the optimization policy, although most simple policies perform worse than the optimization policy. [ABSTRACT FROM AUTHOR]

Multistage stochastic programs serve to make sequential decisions conditional on a gradual realization of some stochastic process. The progressive arrival of new information divides a problem into stages. As the number of stages increases, however, the applicability of stochastic programming is halted by the curse of dimensionality. A commonly used approximation is obtained by replacing the random parameters by their expected values, which results in a problem with fewer stages. The present paper suggests metrics to support the choice of the number of stages: The value of an extended expected value (EV) problem which accounts for stochastic approximations, the Expected result of using the expected value solution (EEV), the value of the stochastic solution, and the values of two Wait-and-See (WS) approximations. We show that for linear minimization problems with random right-hand-side, the value of the EV problem provides a lower bound that improves with the number of stages. The same holds for the WS approximations for general linear minimization problems and with one of the approximations improving the EV bound. In contrast, we show that the upper bound provided by the EV solution may not improve with the number of stages. Finally, we define the marginal benefit of including an additional stage in an EV approximation and demonstrate how to use it in a heuristic. We apply our approach to a hedging problem and confirm that increasing the number of stages does not necessarily foster better decisions. [ABSTRACT FROM AUTHOR]

In this paper, we present bounds for multi-horizon stochastic optimization problems, a class of problems introduced in Kaut et al. (Comput Manag Sci 11:179–193, 2014) relevant in many industry-life applications typically involving strategic and operational decisions on two different time scales. After providing three general mathematical formulations of a multi-horizon stochastic program, we extend the definition of the traditional Expected Value problem and Wait-and-See problem from stochastic programming in a multi-horizon framework. New measures are introduced allowing to quantify the importance of the uncertainty at both strategic and operational levels. Relations among the solution approaches are then determined and chain of inequalities provided. Numerical experiments based on an energy planning application are finally presented. [ABSTRACT FROM AUTHOR]

We present a multi-stage model for determining the optimal production and emissions coverage for an industrial company participating in the European Emissions Trading System. This model is adapted for a real-life European steel company. A mean-multiperiod CVaR is used as a decision criterion. There are two stochastic parameters—market demand for products and emissions allowance price. The aim of this paper is to explore the costs and risk of a company caused by emissions trading. The presented model is solved for various values of the risk aversion parameters and initial price of the allowance. As a result, it is found that the production is little influenced by the price of allowances and it nearly does not depend on risk-aversion. The probability of the company's default, on the other hand, is significantly influenced by the emission prices. Futures on allowances as well as banking (i.e., transferring allowances between periods) are used to reduce the risks of the emissions trading. We further exploit the same situation under different settings, namely, given random price margins, and time-dependent, deterministic and positively contaminated distributions of demand. In all these cases, the results follow patterns similar to those given the original setting. [ABSTRACT FROM AUTHOR]

In this paper a stochastic districting problem is investigated. Demand is assumed to be represented by a random vector with a given joint probability distribution function. A two-stage mixed-integer stochastic programming model is proposed. The first stage comprises the decision about the initial territory design: the districts are defined and all the territory units assigned to one and exactly one of them. In the second stage, i.e., after demand becomes known, balancing requirements are to be met. This is ensured by means of two recourse actions: outsourcing and reassignment of territory units. The objective function accounts for the total expected cost that includes the cost for the first-stage territory design plus the expected cost incurred at the second stage by outsourcing and reassignment. The (re)assignment costs are associated with the distances between territory units, i.e., the focus is put on the compactness of the solution. The model is then extended in different ways to account for aspects of practical relevance such as a maximum desirable dispersion, reallocation constraints, or similarity of the second-stage solution w.r.t. the first-stage one. The new modeling framework proposed is tested computationally using instances built using real geographical data. [ABSTRACT FROM AUTHOR]

In the last century, many infectious diseases have been completely eradicated or significantly reduced because of childhood vaccinations. Ample evidence suggests that low vaccination coverage in developing countries is caused by vaccine stockout and high rates of vaccine wastage. Wastage occurs when a vaccine vial is physically damaged or exposed to extreme temperatures, or when doses from an open vial are discarded after their safe-use time expires. The latter is referred to as open vial wastage (OVW). Clinics can use single-dose vials to reduce OVW; however, such an approach is more expensive than using multi-dose vials. The focus of this research is to develop new policies that support vaccine administration and inventory replenishment. These policies are expected to reduce OVW, reduce the cost of vaccinations, and improve vaccination coverage levels in developing countries. This paper proposes a two-stage stochastic programming model that identifies an optimal combination of differently sized vaccine vials and the corresponding decisions that clinics make about opening vials in the face of uncertain patient arrivals. This work develops a case study with data gathered from Bangladesh. Experimental results indicate that using a combination of vials of different sizes reduces OVW, as opposed to the current practice of using single-sized multi-dose vials. Experimental results also point to simple and economic vaccine administration policies that health care administrators can use to minimize OVW. The model is solved using an extension of the stochastic Benders decomposition algorithm, the L-shaped method (LS). This algorithm uses Gomory mixed integer and mixed-integer rounding cuts to address the problem's non-convexity. Computational results reveal that the solution approach presented here outperforms the standard LS method. [ABSTRACT FROM AUTHOR]

The alternate direction method of multipliers (ADMM) has received significant attention recently as a powerful algorithm to solve convex problems with a block structure. The vast majority of applications focus on deterministic problems. In this paper we show that ADMM can be applied to solve two-stage stochastic programming problems, and we propose an implementation in three blocks with or without proximal terms. We present numerical results for large scale instances, and extend our findings for risk averse formulations using utility functions. [ABSTRACT FROM AUTHOR]

In this paper, we consider capacity expansion for network models subject to uncertainty and budget constraints. We use a scenario tree approach to handle the uncertainty and construct a multi-stage stochastic mixed-integer programming model for the network capacity expansion problem. We assume that permanent capacity and spot market capacity are available, which can be used permanently or temporarily by the decision maker respectively. By relaxing the budget constraints, we propose a heuristic Lagrangian relaxation method to solve the problem. Two algorithms are developed to find tight upper bounds for the Lagrangian relaxation procedure. The experimental results show superior performance of the proposed Lagrangian relaxation method compared with CPLEX. [ABSTRACT FROM AUTHOR]

This paper developed a stochastic modelling framework to determine the locations and transport capacities of drone facilities for effectively coping with a disaster. The developed model is applicable to emergency planning that incorporates drones into humanitarian logistics while taking into account the uncertain characteristics of drone operating conditions. Because of the importance of speedy decision making in disaster management, a heuristic algorithm was developed using Benders decomposition, which generates time-efficient high-quality solutions. The linear programming rounding method was used to make the algorithm efficient. Computational experiments demonstrated the superiority of the developed algorithm, and a sensitivity analysis was carried out to gain additional insights. [ABSTRACT FROM AUTHOR]

Risk budgeting is one of the most recent and successful approaches for the portfolio selection problem. Considering mean-standard-deviation as a risk measure, this paper addresses the risk budgeting problem under the uncertainty of the covariance matrix and the mean vector, assuming that a finite set of scenarios is possible. The problem is formulated as a scenario-based stochastic programming model, and its stability is examined over real-world instances. Then, since investing in all available assets in the market is practically impossible, the stochastic model is extended by incorporating the cardinality constraint so that all selected assets have the same risk contribution while maximizing the expected portfolio return. The extended problem is formulated as a bi-level programming model, and an efficient hybrid algorithm based on the cross-entropy is adopted to solve it. To calibrate the algorithm’s parameters, an effective mechanism is introduced. Numerical experiments on real-world datasets confirm the efficiency of the proposed models and algorithm. [ABSTRACT FROM AUTHOR]

This paper introduces a multistage stochastic mixed-integer programming model designed for a goal-based investing (GBI) problem, incorporating the option of goal postponement. Our model allows individuals to defer the fulfillment of their goals within a predefined timeframe. We emphasize the advantages of incorporating goal postponement into the GBI framework, including its ability to accommodate stage-preference ambiguity, address mistiming issues, and enhance utility for individuals. Theoretical results of a GBI problem with goal postponement are presented, and to tackle large-scale multistage GBI problems, we employ a decomposition algorithm known as stochastic dual dynamic integer programming (SDDiP). Numerical results demonstrate that the option to postpone a goal proves especially advantageous when goals are exposed to high inflation rates, and SDDiP emerges as a computationally efficient approach for handling large-scale GBI problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider a project-based organization that deals with an assignment problem in which a set of projects must be assigned to a group of project managers. This assignment is done based on the relative contributions of projects to the organizational mission and a matching score between each pair of a project and a project manager. We assume that some projects are deterministic, and the organization has signed their corresponding contracts while others are stochastic, i.e. the organization has submitted bids for these projects and may or may not win them in the future. Furthermore, we consider a finite planning horizon and presume a predetermined start time for each deterministic and stochastic project. We develop two models including a multi-stage stochastic integer programming model and a stochastic dynamic programming model to solve the problem. The latter shows better performance for small-size and less complex instances whereas the former gives better performance for more complex instances. We also developed a heuristic algorithm to solve large-size and more complex instances. Computational results indicate that the developed heuristic algorithm can reach near-optimal solutions in reasonable CPU run times and dominates the two other solution approaches particularly for large-size instances. [ABSTRACT FROM AUTHOR]

A multi-product, multi-period, multi-site supply chain production and transportation planning problem, in the textile and apparel industry, under demand and price uncertainties is considered in this paper. The problem is formulated using a two-stage stochastic programming model taking into account the production amount, the inventory and backorder levels as well as the amounts of products to be transported between the different plants and customers in each period. Risk management is addressed by incorporating a risk measure into the stochastic programming model as a second objective function, which leads to a multi-objective optimization model. The objectives aim to simultaneously maximize the expected net profit and minimize the financial risk measured. Two risk measures are compared: the conditional-value-at-risk and the downside risk. As the considered objective functions conflict with each other’s, the problem solution is a front of Pareto optimal robust alternatives, which represents the trade-off among the different objective functions. A case study using real data from textile and apparel industry in Tunisia is presented to illustrate the effectiveness of the proposed model and the robustness of the obtained solutions. [ABSTRACT FROM AUTHOR]

Timely, effective delivery of relief resources to the sufferers in a natural disaster is quite crucial. All governments especially those having high risk of natural disasters must have a comprehensive and implementable plan to suitably manage humanitarian issues after a natural disaster occurs. They should construct sufficient facilities and prepare and store enough relief items (e.g., tents, medical packages, and meals) to be able to quickly respond to necessary needs of injured and homeless people; otherwise, it might lead to humanitarian crises with high numbers of casualties. In this study, we extend the mathematical two-stage stochastic optimization model proposed by Mete and Zabinsky (Int J Prod Econ 126:76-84, 2010) simultaneously considering two phases: pre- and post-disaster. All decisions pertinent to the pre-disaster phase, such as the locations of warehouse and pre-positioned relief items, should be taken in the first stage; however, other decisions pertinent to the post-disaster phase, such as the allocations of warehouses to the demanding points are taken in the second stage. In this study, we consider bi-directional relations between warehouses, which can increase the flexibility of the constructed network to handle the needs of injured people in a shorter time interval. Furthermore, whereas the relief process should be implemented within a specific time interval (e.g., 3 days), our extended optimization model is constructed for a multi-period and multi-product situation. We construct the extended model based on a professional report prepared by the Japanese International Cooperation Agency in a study of the seismic micro zoning of Tehran on April 13, 1999. The respective data in this report has also been updated based on the reports of Tehran Municipality to be matched with the current situation of Tehran. The results of our extended multi-period model for the respective real case study in this paper verify suitable responses and better services to the affected areas compared to what are provided through the respective single-period optimization model. [ABSTRACT FROM AUTHOR]

The literature on portfolio selection mostly concentrates on computational analysis rather than on modelling efforts. In response, this paper provides a comprehensive literature review of multiple objective deterministic and stochastic programming models for the portfolio selection problem. First, we summarize different concepts related to portfolio selection theory, including pricing models and portfolio risk measures. Second, we report the mathematical models that are generally used to solve deterministic and stochastic multiple objective programming problems. Finally, we present how these models can be used to solve the portfolio selection problem. [ABSTRACT FROM AUTHOR]

In this paper, we study risk-averse models for multicriteria optimization problems under uncertainty. We use a weighted sum-based scalarization and take a robust approach by considering a set of scalarization vectors to address the ambiguity and inconsistency in the relative weights of each criterion. We model the risk aversion of the decision makers via the concept of multivariate conditional value-at-risk ( CVaR). First, we introduce a model that optimizes the worst-case multivariate CVaR and show that its optimal solution lies on a particular type of stochastic efficient frontier. To solve this model, we develop a finitely convergent delayed cut generation algorithm for finite probability spaces. We also show that the proposed model can be reformulated as a compact linear program under certain assumptions. In addition, for the cut generation problem, which is in general a mixed-integer program, we give a stronger formulation than the existing ones for the equiprobable case. Next, we observe that similar polyhedral enhancements are also useful for a related class of multivariate CVaR-constrained optimization problems that has attracted attention recently. In our computational study, we use a budget allocation application to benchmark our proposed maximin type risk-averse model against its risk-neutral counterpart and a related multivariate CVaR-constrained model. Finally, we illustrate the effectiveness of the proposed solution methods for both classes of models. [ABSTRACT FROM AUTHOR]

We develop a dynamic stochastic model of military workforce planning that incorporates uncertainties about personnel gains and losses across ranks. We then apply it to determine the probability of not meeting required targets as well as the resulting shortages and overages in the short, medium, and long terms along with the evaluation of policies to mitigate these risks. Our model allows decision makers to adjust recruiting and training practices to minimize the risk of not meeting target personnel levels as well as to value retention and reenlistment policies by calculating the expected marginal value of retaining additional service members. Moreover, it allows us to create a penalty function to optimize recruiting and training levels. The outcome is a tool to evaluate and ensure comprehensive force readiness. [ABSTRACT FROM AUTHOR]

This paper presents a two-stage stochastic programming model to design a green supply chain in a carbon trading environment. The model solves a discrete location problem and determines the optimal material flows and the number of carbon credits/allowances traded. The study contributes to the existing literature by incorporating uncertainty in carbon price and product demand. The proposed model is applied to a real world case study and the numerical results are carefully analyzed and interpreted. We find that the supply chain configuration can be highly sensitive to the probability distribution of the carbon credit price. More importantly, we observe that carbon price and budget availability for supply chain reconfiguration can both have a positive but nonlinear relationship with greening of the supply chain. [ABSTRACT FROM AUTHOR]

The vast majority of the machine scheduling literature focuses on deterministic problems in which all data is known with certainty a priori. In practice, this assumption implies that the random parameters in the problem are represented by their point estimates in the scheduling model. The resulting schedules may perform well if the variability in the problem parameters is low. However, as variability increases accounting for this randomness explicitly in the model becomes crucial in order to counteract the ill effects of the variability on the system performance. In this paper, we consider single-machine scheduling problems in the presence of uncertain parameters. We impose a probabilistic constraint on the random performance measure of interest, such as the total weighted completion time or the total weighted tardiness, and introduce a generic risk-averse stochastic programming model. In particular, the objective of the proposed model is to find a non-preemptive static job processing sequence that minimizes the value-at-risk (VaR) of the random performance measure at a specified confidence level. We propose a Lagrangian relaxation-based scenario decomposition method to obtain lower bounds on the optimal VaR and provide a stabilized cut generation algorithm to solve the Lagrangian dual problem. Furthermore, we identify promising schedules for the original problem by a simple primal heuristic. An extensive computational study on two selected performance measures is presented to demonstrate the value of the proposed model and the effectiveness of our solution method. [ABSTRACT FROM AUTHOR]

The increasing vulnerability of the population from frequent disasters requires quick and effective responses to provide the required relief through effective humanitarian supply chain distribution networks. We develop scenario-robust optimization models for stocking multiple disaster relief items at strategic facility locations for disaster response. Our models improve the robustness of solutions by easing the difficult, and usually impossible, task of providing exact probability distributions for uncertain parameters in a stochastic programming model. Our models allow decision makers to specify uncertainty parameters (i.e., point and probability estimates) based on their degrees of knowledge, using distribution-free uncertainty sets in the form of ranges. The applicability of our generalized approach is illustrated via a case study of hurricane preparedness in the Southeastern United States. In addition, we conduct simulation studies to show the effectiveness of our approach when conditions deviate from the model assumptions. [ABSTRACT FROM AUTHOR]

In the paper we develop a two stage scenario-based stochastic programming model for water management in the Indus Basin Irrigation System (IBIS). We present a comparison between the deterministic and scenario-based stochastic programming model. Our model takes stochastic inputs on hydrologic data i.e. inflow and rainfall. We divide the basin into three rainfall zones which overlap on 44 canal commands. Data on crop characteristics are taken on canal command levels. We then use ten-daily and monthly time intervals to analyze the policies. This system has two major reservoirs and a complex network of rivers, canal head works, canals, sub canals and distributaries. All the decisions on hydrologic aspects are governed by irrigation and agricultural development policies. Storage levels are maintained within the minimum and maximum bounds for every time interval according to a power generation policy. The objective function is to maximize the expected revenue from crops production. We discuss the flexibility of two stochastic optimization models with varying time horizon. [ABSTRACT FROM AUTHOR]

COVID-19 is a highly prevalent disease that has led to numerous predicaments for healthcare systems worldwide. Owing to the significant influx of patients and limited resources of health services, there have been several limitations associated with patients' hospitalization. These limitations can cause an increment in the COVID-19-related mortality due to the lack of appropriate medical services. They can also elevate the risk of infection in the rest of the population. The present study aims to investigate a two-phase approach to designing a supply chain network for hospitalizing patients in the existing and temporary hospitals, efficiently distributing medications and medical items needed by patients, and managing the waste created in hospitals. Since the number of future patients is uncertain, in the first phase, trained Artificial Neural Networks with historical data forecast the number of patients in future periods and generate scenarios. Through the use of the K-Means method, these scenarios are reduced. In the second phase, a multi-objective, multi-period, data-driven two-stage stochastic programming is developed using the acquired scenarios in the previous phase concerning the uncertainty and disruption in facilities. The objectives of the proposed model include maximizing the minimum allocation-to-demand ratio, minimizing the total risk of disease spread, and minimizing the total transportation time. Furthermore, a real case study is investigated in Tehran, the capital of Iran. The results showed that the areas with the highest population density and no facilities near them have been selected for the location of temporary facilities. Among temporary facilities, temporary hospitals can allocate up to 2.6% of the total demand, which puts pressure on the existing hospitals to be removed. Furthermore, the results indicated that the allocation-to-demand ratio can remain at an ideal level when disruptions occur by considering temporary facilities. Our analyses focus on: (1) Examining demand forecasting error and generated scenarios in the first phase, (2) exploring the impact of demand parameters on the allocation-to-demand ratio, total time and total risk, (3) investigating the strategy of utilizing temporary hospitals to address sudden changes in demand, (4) evaluating the effect of disruption to facilities on the supply chain network. [ABSTRACT FROM AUTHOR]