Analysis of critical paths in a project network with fuzzy activity times

This paper proposes an approach to critical path analysis for a project network with activity times being fuzzy numbers, in that the membership function of the fuzzy total duration time is constructed. The basic idea is based on the extension principle and linear programming formulation. A pair of linear programs parameterized by possibility level α is formulated to calculate the lower and upper bounds of the fuzzy total duration time at α. By enumerating different values of α, the membership function of the fuzzy total duration time is constructed, and the fuzzy critical paths are identified at the same time. Moreover, by applying the Yager ranking method, definitions of the most critical path and the relative degree of criticality of paths are developed; and these definitions are theoretically sound and easy to use in practice. Two examples with activity times being fuzzy numbers of L-R and L-L types discussed in previous studies are solved successfully to demonstrate the validity of the proposed approach. Since the total duration time is completely expressed by a membership function rather than by a crisp value, the fuzziness of activity times is conserved completely, and more information is provided for critical path analysis.     

Expanded models of the project portfolio selection problem with loss in divisibility

This research develops three new models for the project portfolio selection problem with multiple periods. To reflect some real situations, three loss assumptions are considered for the interruption of project execution for the first time. The mathematical representations of the loss assumptions are provided and proved. Besides, the workload constraint, capital flow constraint, cardinality constraint, and precedence relationship are incorporated into the models. One benchmark example and one real-world application case are used to demonstrate the capability and characteristics of the proposed models.     

Regulation of a single-server queue with customers who dynamically choose their service durations

Queueing Systems - In recent years, there is a growing attention towards queueing models with customers who choose their service durations. The model assumptions in the existing literature imply...     

On the impact of independence of risks on stop loss premiums

It is demonstrated that stop loss premiums may increase considerably if the usual assumption of independence of the risks in the reinsured portfolio is dropped.     

On the latest starting times and criticality of activities in a network with imprecise durations

This paper deals with problems of computing possible values of latest starting times and determining types of criticality for all activities in a network with interval or fuzzy activity durations. Although the problem of computing the latest starting times has been solved, a novel polynomial algorithm which is easy to understand and improves complexity is proposed.     

Optimal control of impulsive switched systems with minimum subsystem durations

This paper presents a new computational approach for solving optimal control problems governed by impulsive switched systems. Such systems consist of multiple subsystems operating in succession, with possible instantaneous state jumps occurring when the system switches from one subsystem to another. The control variables are the subsystem durations and a set of system parameters influencing the state jumps. In contrast with most other papers on the control of impulsive switched systems, we do not require every potential subsystem to be active during the time horizon (it may be optimal to delete certain subsystems, especially when the optimal number of switches is unknown). However, any active subsystem must be active for a minimum non-negligible duration of time. This restriction leads to a disjoint feasible region for the subsystem durations. The problem of choosing the subsystem durations and the system parameters to minimize a given cost function is a non-standard optimal control problem that cannot be solved using conventional techniques. By combining a time-scaling transformation and an exact penalty method, we develop a computational algorithm for solving this problem. We then demonstrate the effectiveness of this algorithm by considering a numerical example on the optimization of shrimp harvesting operations.     

Properties of multi-mode resource-constrained project scheduling problems with resource vacations and activity splitting

This paper presents results from an extensive computational study of the multi-mode resource-constrained project scheduling problem when activities can be split during scheduling under situations where resources may be temporarily not available. All resources considered are renewable and each resource unit may not be available at all times due to resource vacations, which are known in advance, and assignment to other finite duration activities. A designed experiment is conducted that investigates project makespan improvement when activity splitting is permitted in various project scenarios, where different project scenarios are defined by parameters that have been used in the research literature. A branch-and-bound procedure is applied to solve a number of small project scheduling problems with and without activity splitting. The results show that, in the presence of resource vacations and temporary resource unavailability, activity splitting can significantly improve the optimal project makespan in many scenarios, and that the makespan improvement is primarily dependent on those parameters that impact resource utilization.     

Prediction with a Generalized Cost of Error Function

Classical prediction theory limits itself to quadratic cost functions, and hence least-square predictors. However, the cost functions that arise in practice in economics and management situations are not likely to be quadratic in form, and frequently will be non-symmetric. It is the object of this paper to throw light on prediction in such situations and to suggest some practical implications. It is suggested that a useful, although sub-optimal, manner of taking into account generalized cost functions is to add a constant bias term to the predictor. Two theorems are proved showing that under fairly general conditions the bias term can be taken to be zero when one uses a symmetric cost function. If the cost function is a non-symmetric linear function, an expression for the bias can be simply obtained.     

Submodular Flow Problem with a Nonseparable Cost Function

Received: February 19, 1996     

Control of a Heat Conduction Process with a Quadratic Cost Functional

Two control problems with a quadratic cost functional for a parabolic equation with Robin boundary conditions are investigated.     

On a loss system with a given number of customers

A one-server loss system with Poisson arrival stream and deterministic service times is considered conditional on the number of customers who appeared up to a givenT. This condition implies that the arrival times form a sample of the uniform distribution on (0,T]. We derive several characteristics of interest, such as the blocking probability at any given timet (0,T], the probability that exactlyi of the customers in (0,T] are served and, as a generalization, the distribution of the number of served customers arriving in any subinterval of (0,T].     

Pricing of catastrophe insurance options written on a loss index with reestimation

We propose a valuation model for catastrophe insurance options written on a loss index. This kind of options distinguishes between a loss period [0,T₁], during which the catastrophes may happen, and a development period [T₁,T₂], during which losses entered before T₁ are reestimated. Here we suppose that the underlying loss index is given by a time inhomogeneous compound Poisson process before T₁ and that losses are reestimated by a common factor given by an exponential time inhomogeneous Lévy process after T₁. In this setting, using Fourier transform techniques, we are able to provide analytical pricing formulas for catastrophe options written on this kind of index.     

Optimal Control of a Stochastic Hybrid System with Discounted Cost

We address the optimal control problem of a very general stochastic hybrid system with both autonomous and impulsive jumps. The planning horizon is infinite and we use the discounted-cost criterion for performance evaluation. Under certain assumptions, we show the existence of an optimal control. We then derive the quasivariational inequalities satisfied by the value function and establish well-posedness. Finally, we prove the usual verification theorem of dynamic programming.     

Quantum Optimal Control Problems with a Sparsity Cost Functional

In this article, the investigation of a class of quantum optimal control problems with L¹ sparsity cost functionals is presented. The focus is on quantum systems modeled by Schrödinger-type equations with a bilinear control structure as it appears in many applications in nuclear magnetic resonance spectroscopy, quantum imaging, quantum computing, and in chemical and photochemical processes. In these problems, the choice of L¹ control spaces promotes sparse optimal control functions that are conveniently produced by laboratory pulse shapers. The characterization of L¹ quantum optimal controls and an efficient numerical semi-smooth Newton solution procedure are discussed.     

Infinite Time-Dependent Network Equilibria with a Multivalued Cost Function

In this paper, we consider the dynamic traffic network equilibria with possibly an infinite number of routes, a possibly multivalued cost function, and a not necessarily reflexive Banach space of flow trajectories. We investigate the existence of equilibria under a monotonicity assumption on the cost function, as well as an equivalent condition for equilibria under additional constraints. Finally, we give an iterative method for the computation of equilibria. Our results generalize and extend previous results in Refs. 1–2.Communicated by F. GiannessiThe authors are thankful to the referee and Professor F. Giannessi for valuable suggestions and comments leading the paper to its present form.All correspondence should be sent to the first author.     

dagen: A generator of testsets for project activity nets

We offer a methodology, and the relevant software, to generate source-terminal directed project nets of specified number of nodes, number of activities, complexity index, and ranges of costs and resources utilization.     

Median Predictive Cost of Error with an Asymmetric Cost Function

The problem of reducing predictive cost is considered in the case when the cost of error function is not symmetric and the optimality criterion is the minimization of the median cost of the error of prediction. Examples are given and comparisons made with the usual solution based on the minimization of the mean cost. In the case of a Gaussian process, the median solution is found to be a simple additive adjustment to the predictive mean, and far easier to compute than the solution based on expected cost.     

Data-driven estimation of diurnal patterns of durations between trades on financial markets

We propose a data-driven local linear estimator for diurnal patterns of transaction durations with a brief discussion on its asymptotics. The standardized durations are modeled by the EACD. Codes in R are developed for practical implementation. Application is illustrated by data examples.