Valid inequalities and restrictions for stochastic programming problems with first order stochastic dominance constraints

Stochastic dominance relations are well studied in statistics, decision theory and economics. Recently, there has been significant interest in introducing dominance relations into stochastic optimization problems as constraints. In the discrete case, stochastic optimization models involving second order stochastic dominance constraints can be solved by linear programming. However, problems involving first order stochastic dominance constraints are potentially hard due to the non-convexity of the associated feasible regions. In this paper we consider a mixed 0–1 linear programming formulation of a discrete first order constrained optimization model and present a relaxation based on second order constraints. We derive some valid inequalities and restrictions by employing the probabilistic structure of the problem. We also generate cuts that are valid inequalities for the disjunctive relaxations arising from the underlying combinatorial structure of the problem by applying the lift-and-project procedure. We describe three heuristic algorithms to construct feasible solutions, based on conditional second order constraints, variable fixing, and conditional value at risk. Finally, we present numerical results for several instances of a real world portfolio optimization problem. This research was supported by the NSF awards DMS-0603728 and DMI-0354678.     

A dynamic equivalence principle for systematic longevity risk management

This paper addresses systematic longevity risk in long-term insurance business. We analyze the consequences of working under unknown survival probabilities on the efficiency of the Law of Large Numbers and point out the need for appropriate and feasible risk management techniques. We propose a setting for risk sharing schemes between the insurer and policyholders via a dynamic equivalence principle. We focus on a pure endowment contract and derive conditions for a viable risk sharing scheme which enhances the solvency situation of the insurer while being more favorably priced for the policyholders.     

An aggregate stochastic programming model for air traffic flow management

In this paper, we present an aggregate mathematical model for air traffic flow management (ATFM), a problem of great concern both in Europe and in the United States. The model extends previous approaches by simultaneously taking into account three important issues: (i) the model explicitly incorporates uncertainty in the airport capacities; (ii) it also considers the trade-off between airport arrivals and departures, which is a crucial issue in any hub airport; and (iii) it takes into account the interactions between different hubs.The level of aggregation proposed for the mathematical model allows us to solve realistic size instances with a commercial solver on a PC. Moreover it allows us to compute solutions which are perfectly consistent with the Collaborative Decision-Making (CDM) procedure in ATFM, widely adopted in the USA and which is currently receiving a lot of attention in Europe. In fact, the proposed model suggests the number of flights that should be delayed, a decision that belongs to the ATFM Authority, rather than assigning delays to individual aircraft.     

A dynamic stochastic programming model for international portfolio management

We develop a multi-stage stochastic programming model for international portfolio management in a dynamic setting. We model uncertainty in asset prices and exchange rates in terms of scenario trees that reflect the empirical distributions implied by market data. The model takes a holistic view of the problem. It considers portfolio rebalancing decisions over multiple periods in accordance with the contingencies of the scenario tree. The solution jointly determines capital allocations to international markets, the selection of assets within each market, and appropriate currency hedging levels. We investigate the performance of alternative hedging strategies through extensive numerical tests with real market data. We show that appropriate selection of currency forward contracts materially reduces risk in international portfolios. We further find that multi-stage models consistently outperform single-stage models. Our results demonstrate that the stochastic programming framework provides a flexible and effective decision support tool for international portfolio management.     

On the effectiveness of scenario generation techniques in single-period portfolio optimization

In single-period portfolio selection problems the expected value of both the risk measure and the portfolio return have to be estimated. Historical data realizations, used as equally probable scenarios, are frequently used to this aim. Several other parametric and non-parametric methods can be applied. When dealing with scenario generation techniques practitioners are mainly concerned on how reliable and effective such methods are when embedded into portfolio selection models. In this paper we survey different techniques to generate scenarios for the rates of return. We also compare the techniques by providing in-sample and out-of-sample analysis of the portfolios obtained by using these techniques to generate the rates of return. Evidence on the computational burden required by the different techniques is also provided. As reference model we use the Worst Conditional Expectation model with transaction costs. Extensive computational results based on different historical data sets from London Stock Exchange Market (FTSE) are presented and some interesting financial conclusions are drawn.     

User-model interaction in decision support systems for risk management

This paper describes and evaluates three different approaches to building decision support systems: the Operations Research/Management Science approach, the Decision Analysis/Multiattribute Utility approach, and the Artificial Intelligence/Expert Systems approach. It evaluates the usefulness of the three approaches for risk management. In particular, it defines evaluation objectives of risk analysts, risk managers, and laypeople and provides a subjective assessment how the three approaches stack up against their objectives. The paper concludes that for most risk management applications a combination of the three approaches would be most desirable.This paper was written under contract No. 2709-85-05 ED ISP D of the European Atomic Energy Community, Commission of the European Communities, Joint Research Centre, Ispra Establishment, Ispra, Italy to the Gemeinschaft für Entscheidungs- und Risikoanalyse, Berlin, West Germany. It was prepared for presentation at the Conference on Operations Research and Multiattribute Decision Analysis held in Passau, April 20–26, 1986. The views and opinions expressed in this paper are solely those of the author.     

A multistage linear stochastic programming model for optimal corporate debt management

Large corporations fund their capital and operational expenses by issuing bonds with a variety of indexations, denominations, maturities and amortization schedules. We propose a multistage linear stochastic programming model that optimizes bond issuance by minimizing the mean funding cost while keeping leverage under control and insolvency risk at an acceptable level. The funding requirements are determined by a fixed investment schedule with uncertain cash flows. Candidate bonds are described in a detailed and realistic manner. A specific scenario tree structure guarantees computational tractability even for long horizon problems. Based on a simplified example, we present a sensitivity analysis of the first stage solution and the stochastic efficient frontier of the mean-risk trade-off. A realistic exercise stresses the importance of controlling leverage. Based on the proposed model, a financial planning tool has been implemented and deployed for Brazilian oil company Petrobras.     

A web-based decision support system for waste lube oils collection and recycling

This paper presents a web-based decision support system (DSS) that enables schedulers to tackle reverse supply chain management problems interactively. The focus is on the efficient and effective management of waste lube oils collection and recycling operations. The emphasis is given on the systemic dimensions and modular architecture of the proposed DSS. The latter incorporates intra- and inter-city vehicle routing with real-life operational constraints using shortest path and sophisticated hybrid metaheuristic algorithms. It is also integrated with an Enterprise Resource Planning system allowing the utilization of particular functional modules and the combination with other peripheral planning tools. Furthermore, the proposed DSS provides a framework for on-line monitoring and reporting to all stages of the waste collection processes. The system is developed using a web architecture that enables sharing of information and algorithms among multiple sites, along with wireless telecommunication facilities. The application to an industrial environment showed improved productivity and competitiveness, indicating its applicability on realistic reverse logistical planning problems.     

A stochastic model for risk management in global supply chain networks

With the increasing emphasis on supply chain vulnerabilities, effective mathematical tools for analyzing and understanding appropriate supply chain risk management are now attracting much attention. This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption. We provide a new solution methodology using the Moreau–Yosida regularization, and design an algorithm for treating the multi-stage global supply chain network problem with profit maximization and risk minimization objectives.     

A multi-objective multi-period stochastic programming model for public debt management

While raising debt on behalf of the government, public debt managers need to consider several possibly conflicting objectives and have to find an appropriate combination for government debt taking into account the uncertainty with regard to the future state of the economy. In this paper, we explicitly consider the underlying uncertainties with a complex multi-period stochastic programming model that captures the trade-offs between the objectives. The model is designed to aid the decision makers in formulating the debt issuance strategy. We apply an interactive procedure that guides the issuer to identify good strategies and demonstrate this approach for the public debt management problem of Turkey.     

Conditional value at risk and related linear programming models for portfolio optimization

Many risk measures have been recently introduced which (for discrete random variables) result in Linear Programs (LP). While some LP computable risk measures may be viewed as approximations to the variance (e.g., the mean absolute deviation or the Gini’s mean absolute difference), shortfall or quantile risk measures are recently gaining more popularity in various financial applications. In this paper we study LP solvable portfolio optimization models based on extensions of the Conditional Value at Risk (CVaR) measure. The models use multiple CVaR measures thus allowing for more detailed risk aversion modeling. We study both the theoretical properties of the models and their performance on real-life data.     

A belief rule-based decision support system for clinical risk assessment of cardiac chest pain

This paper describes a prototype clinical decision support system (CDSS) for risk stratification of patients with cardiac chest pain. A newly developed belief rule-based inference methodology-RIMER was employed for developing the prototype. Based on the belief rule-based inference methodology, the prototype CDSS can deal with uncertainties in both clinical domain knowledge and clinical data. Moreover, the prototype can automatically update its knowledge base via a belief rule base (BRB) learning module which can adjust BRB through accumulated historical clinical cases. The domain specific knowledge used to construct the knowledge base of the prototype was learned from real patient data. We simulated a set of 1000 patients in cardiac chest pain to validate the prototype. The belief rule-based prototype CDSS has been found to perform extremely well. Firstly, the system can provide more reliable and informative diagnosis recommendations than manual diagnosis using traditional rules when there are clinical uncertainties. Secondly, the diagnostic performance of the system can be significantly improved after training the BRB through accumulated clinical cases.     

A dynamic binomial expansion technique for credit risk measurement: a Bayesian filtering approach

Credit risk measurement and management are important and current issues in the modern finance world from both the theoretical and practical perspectives. There are two major schools of thought for credit risk analysis, namely the structural models based on the asset value model originally proposed by Merton and the intensity‐based reduced form models. One of the popular credit risk models used in practice is the Binomial Expansion Technique (BET) introduced by Moody's. However, its one‐period static nature and the independence assumption for credit entities' defaults are two shortcomings for the use of BET in practical situations. Davis and Lo provided elegant ways to ease the two shortcomings of BET with their default infection and dynamic continuous‐time intensity‐based approaches. This paper first proposes a discrete‐time dynamic extension to the BET in order to incorporate the time‐dependent and time‐varying behaviour of default probabilities for measuring the risk of a credit risky portfolio. In reality, the ‘true’ default probabilities are unobservable to credit analysts and traders. Here, the uncertainties of ‘true’ default probabilities are incorporated in the context of a dynamic Bayesian paradigm. Numerical studies of the proposed model are provided.     

A prolog-based decision support system for computer capacity planning

This paper describes a project to implement a decision support system for computer capacity planning. The system provides an intelligent interface to the various models needed for this type of planning by assisting the user in model formulation, data manipulation, model execution, interpretation and manipulation of results. The implementation strategy is based on the integration of relational model and database management with logic. A modified version of a Prolog interpreter is utilized as the vehicle for this integrated strategy.This research was supported by Sandia National Laboratories Grant No. 56-3737. Sandia is managed by AT&T Technologies for the U.S. Department of Energy.     

MEDSS: A Multi-Agent Environmental Decision Support System framework for model management

Model Management Systems (MMS) have become increasingly important in handling complicated problems in Decision Support Systems (DSS). The primary goal of MMS is to facilitate the development and the utilization of quantitative models to improve decision performance. Much current research focuses on model construction. Where early research used deductive reasoning approaches to construct new models, more recent efforts use inductive reasoning mechanisms. Both approaches have their drawbacks. Deductive reasoning methods require a strong domain theory (which may not exist or may be too complex to apply) and ignore previous solving experience. Inductive reasoning methods can take advantage of precedents or prototypical cases, but do not employ domain knowledge. Both methods are limited in learning capacity. This study proposes a Multi-Agent Environmental Decision Support System, which integrates an Inductive Reasoning Agent, and an Environmental Learning Agent to perform new model formation and problem solving. New models can be generated by the coordination of both the Inductive Agent and the Deductive Agent. At the same time, a model repair process is undertaken by the Environmental Learning Agent when the prediction resulting from existing knowledge fails.     

A multiobjective optimization model for the waste management of the petrochemical industry

A multiobjective optimization model based on the goal programming approach is proposed in this paper to assist in the proper management of hazardous waste generated by the petrochemical industry. The analytic hierarchy process (AHP), a decision-making approach, incorporating qualitative and quantitative aspects of a problem, is incorporated in the model to prioritize the conflicting goals usually encountered when addressing the waste management problems of the petrochemical industry. The application of the model has been illustrated through a numerical example, using hypothetical but representative data.     

A fuzzy algorithm for continuous capacitated location allocation model with risk consideration

This paper presents a continuous capacitated location-allocation model with fixed cost as a risk management model. In the presented model, the fixed cost consists of production and installation costs. The model considers risk as percent of unsatisfied demands. The fixed cost is assigned to a zone with a predetermined radius from its center. Because of uncertain environment, demand in each zone is investigated as a fuzzy number. The model is solved by a fuzzy algorithm based on α-cut method. After solving the model based on different α-values, the zones with the largest possibilities are determined for locating new facilities and the best locations are calculated based on the obtained possibilities. Then, the model is solved based on different α-values to determine best allocation values. Also, this paper proposes a Cross Entropy (CE) algorithm considering multivariate normal and multinomial density functions for solving large scale instances and is compared with GAMS. Finally, a numerical example is expressed to illustrate the proposed model.     

A multi-level Taguchi-factorial two-stage stochastic programming approach for characterization of parameter uncertainties and their interactions: An application to water resources management

This paper presents a multi-level Taguchi-factorial two-stage stochastic programming (MTTSP) approach for supporting water resources management under parameter uncertainties and their interactions. MTTSP is capable of performing uncertainty analysis, policy analysis, factor screening, and interaction detection in a comprehensive and systematic way. A water resources management problem is used to demonstrate the applicability of the proposed approach. The results indicate that interval solutions can be generated for the objective function and decision variables, and a variety of decision alternatives can be obtained under different policy scenarios. The experimental data obtained from the Taguchi’s orthogonal array design are helpful in identifying the significant factors affecting the total net benefit. Then the findings from the multi-level factorial experiment reveal the latent interactions among those important factors and their curvature effects on the model response. Such a sequential strategy of experimental designs is useful in analyzing the interactions for a large number of factors in a computationally efficient manner.