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Multiple projects are increasingly managed in a decentralized environment, resulting in an inapplicable centralized resource-constrained multi-project scheduling problem (CRCMPSP). A decentralized resource-constrained multi-project scheduling problem (DRCMPSP) is proposed to ensure the timely delivery of products and services within budget. DRCMPSP often faces difficulty in effectively addressing resource conflict. Moreover, activity durations are hard to determine in advance due to various unpredictable events. Therefore, this paper investigates the performance of priority rules (PRs) for global resource allocation of stochastic DRCMPSP. A two-stage heuristic based on PR is then developed to resolve global resource contention under a stochastic environment. 25 PRs from the literature were selected and incorporated into our approach to explore their efficiency on global resource allocation in different global objectives, that is, the expected average project delay (EAPD) and expected total makespan (ETMS). Computational experiments based on the Multi-Project Scheduling Problem LIBrary (MPSPLIB) dataset show that more efficient PRs always favor activities that try to obtain a low delay for each project for EAPD, whereas for ETMS, more efficient PRs tend to favor the longest projects. Furthermore, the hybrid PRs based on more efficient PRs are designed to allocate global resources, and experimental results show that the average percentage of 3 hybrid PRs better than that of their components is 1.14% for EAPD and 0.81% for ETMS, respectively.

This study investigates a due date quoting problem for a project with stochastic duration, taking the decision-maker's risk attitude into consideration. The project profit is defined as the difference between the price and the cost that is comprised of production cost and earliness-tardiness penalties. In this situation, the due date determination has to be modelled as a stochastic optimisation due to stochastic duration. Conditional value at risk is thus employed as a performance measure to describe the decision-maker's risk attitude. In fixed price contract, when the unit production cost is not smaller than the unit penalty on earliness, the optimal due date increases with the increase of the degree of a decisionmaker's risk aversion, the unit penalty on delay, and the decrease of the unit penalty on earliness. Besides, when the price is proportional to the due date and the slope is no bigger than the unit penalty on tardiness, the optimal due date is smaller than the result in fixed price. This is because high price for a short due date encourages a decision-maker to quote a small due date. Further, we compare the optimal due date in different parameter setting where the penalty coefficient of earliness is negative or zero, which means there is reward or no penalty on earliness, respectively. Finally, a case study is conducted to validate the effectiveness and efficiency of the proposed model. [ABSTRACT FROM AUTHOR]

Purpose: The goal of this article is to provide an extensive literature review of the models and solution procedures proposed by many researchers interested on the Project Scheduling Problem with nondeterministic activities duration. Design/methodology/approach: This paper presents an exhaustive literature review, identifying the existing models where the activities duration were taken as uncertain or random parameters. In order to get published articles since 1996, was employed the Scopus database. The articles were selected on the basis of reviews of abstracts, methodologies, and conclusions. The results were classified according to following characteristics: year of publication, mathematical representation of the activities duration, solution techniques applied, and type of problem solved. Findings: Genetic Algorithms (GA) was pointed out as the main solution technique employed by researchers, and the Resource-Constrained Project Scheduling Problem (RCPSP) as the most studied type of problem. On the other hand, the application of new solution techniques, and the possibility of incorporating traditional methods into new PSP variants was presented as research trends. Originality/value: This literature review contents not only a descriptive analysis of the published articles but also a statistical information section in order to examine the state of the research activity carried out in relation to the Project Scheduling Problem with non-deterministic activities duration. [ABSTRACT FROM AUTHOR]

The efficiency of traditional and stochastic interest rate risk measures is compared under one-, two-, and three-factor no-arbitrage Gauss-Markov term structure models, and for different immunization periods. The empirical analysis, run on the German Treasury bond market from January 2000 to December 2010, suggests that: i) Stochastic interest rate risk measures provide better portfolio immunization than the Fisher-Weil duration; and ii) The superiority of the stochastic risk measures is more evident for multi-factor models and for longer investment horizons. These findings are supported by a first-order stochastic dominance analysis, and are robust against yield curve estimation errors. [ABSTRACT FROM AUTHOR]

Several approximations have been proposed in the literature for the pricing of European-style swaptions under multifactor term structure models. However, none of them provides an estimate for the inherent approximation error. Until now, only the Edgeworth expansion technique of Collin-Dufresne and Goldstein is able to characterize the order of the approximation error. Under a multifactor HJM Gaussian framework, this paper proposes a new approximation for European-style swaptions, which is able to set bounds on the magnitude of the approximation error and is based on the conditioning approach initiated by Curran and Rogers and Shi. All the proposed pricing bounds will arise as a simple by-product of the Nielsen and Sandmann setup, and will be shown to provide a better accuracy-efficiency trade-off than all the approximations already proposed in the literature. [ABSTRACT FROM AUTHOR]

Droughts, as many climatic and environmental phenomena, are events with a random duration. In the monitoring and risk management of this type of phenomena, it is important the development of measures of the risk that an ongoing event ends. This work develops a risk measure conditional on the current state of the event, that can be easily updated in real time. The measure is based on the hazard function of the duration of an event, that is modeled as a parametric function of covariates describing the current state of the process. The use of (time-dependent) internal covariates is often required to describe that state, and maximum likelihood methods cannot be used to estimate the model. Therefore, an approach based on partial likelihood functions that permit the inclusion of both external and internal covariates is suggested. This approach is very general but it has the drawback of requiring some programming to be implemented. However, it is proved that for durations with a geometric distribution, an equivalent and easily implemented approach based on generalized linear models can be used to estimate the hazard function. This methodology is applied to develop a risk measure in drought analysis. The approach is exemplified using the drought series from a Spanish location (Huesca) and internal covariates derived from the rainfall series. The whole modeling process is thoroughly described, including the covariate selection procedure and some new validation tools. [ABSTRACT FROM AUTHOR]

In this paper, we introduce for interest rate sensitive assets the natural analogs of delta and gamma for equity options by considering the derivatives of asset prices with respect to the directions along which the forward rate curve may evolve. Macaulay duration and convexity, as well as stochastic duration considered in Cox et al. (J Business 52:51–61, 1979) and Munk (Rev Derivat Res 3:157–181, 1999), are easily obtained as special cases of these in which the derivatives are computed along parallel shifts and the direction of the forward rate volatilities, respectively. Moreover, we demonstrate using the example of the Ritchken and Sankarasubramanian (Math Financ 5:55–72, 1995) model that the hedging strategy based on these sensitivity measures provides a superior performance in comparison to the traditional duration based hedging approaches. [ABSTRACT FROM AUTHOR]

We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include the stochastic duration approach, Edgeworth expansion, and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon-bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and the computational efficiency of these approximation methods are analyzed. We also investigate the value sensitivity of the guaranteed annuity option with respect to different parameters in the pricing model. [ABSTRACT FROM AUTHOR]

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. [ABSTRACT FROM AUTHOR]