scholarly journals Some Special Cases of a Continuous Time-Cost Tradeoff Problem with Multiple Milestones under a Chain Precedence Graph

2016 ◽  
Vol 22 (1) ◽  
pp. 5-12 ◽  
Author(s):  
Byung-Cheon Choi ◽  
Jibok Chung
Keyword(s):  
Continuous Time ◽  
Time Cost ◽  
Special Cases ◽  
Precedence Graph ◽  
A Chain

A Time–Cost Tradeoff Problem with Multiple Assessments and Release Times on a Chain Precedence Graph

2021 ◽  
pp. 2150012
Author(s):  
Myoung-Ju Park ◽  
Byung-Cheon Choi ◽  
Jibok Chung
Keyword(s):  
Total Weighted Tardiness ◽  
Release Time ◽  
Time Cost ◽  
Penalty Cost ◽  
Processing Times ◽  
Release Times ◽  
Penalty Costs ◽  
Precedence Graph ◽  
A Chain ◽  
Tardy Jobs

We consider two variants of a time–cost tradeoff problem with multiple assessments on a chain precedence graph. Furthermore, each job can only be started after a release time, and a penalty cost is incurred when a job is not finished before its due date. The motivation is from the project such that a project owner can control the duration of each job and the support level of each project partner to avoid the penalty cost from the tardy jobs. We describe the penalty costs of the first and the second variants as the total weighted number of tardy jobs and the total weighted tardiness, respectively. These can be avoided by compressing the processing times or advancing the release times, which incurs a compression cost or release cost according to the linear and the piecewise constant functions, respectively. The objective is to minimize the total penalty, compression cost and release cost. In this paper, we propose the procedure based on the reduction to a shortest path problem, and show that the procedure can solve two variants in strongly polynomial time.

Optimal Consumption and Insurance: A Continuous-time Markov Chain Approach

2008 ◽  
Vol 38 (01) ◽  
pp. 231-257 ◽  
Author(s):  
Holger Kraft ◽  
Mogens Steffensen
Keyword(s):  
Continuous Time ◽  
Optimal Solution ◽  
Decision Problems ◽  
Optimal Consumption ◽  
Continuous Time Markov Chain ◽  
Financial Decision Making ◽  
Markov Chain Approach ◽  
Special Cases ◽  
Financial Decision ◽  
The Individual

Personal financial decision making plays an important role in modern finance. Decision problems about consumption and insurance are in this article modelled in a continuous-time multi-state Markovian framework. The optimal solution is derived and studied. The model, the problem, and its solution are exemplified by two special cases: In one model the individual takes optimal positions against the risk of dying; in another model the individual takes optimal positions against the risk of losing income as a consequence of disability or unemployment.

Finite-time control of uncertain time-varying systems in p-normal form

2020 ◽  
Author(s):  
Kanya Rattanamongkhonkun ◽  
Radom Pongvuthithum ◽  
Chulin Likasiri
Keyword(s):  
Normal Form ◽  
Finite Time ◽  
Control Law ◽  
Time Varying ◽  
Time Control ◽  
Special Cases ◽  
Time Varying Systems ◽  
A Chain ◽  
Uncertain Time ◽  
Power Integrator

Abstract This paper addresses a finite-time regulation problem for time-varying nonlinear systems in p-normal form. This class of time-varying systems includes a well-known lower-triangular system and a chain of power integrator systems as special cases. No growth condition on time-varying uncertainties is imposed. The control law can guarantee that all closed-loop trajectories are bounded and well defined. Furthermore, all states converge to zero in finite time.

On the GIX/G/∞ system

1990 ◽  
Vol 27 (3) ◽  
pp. 671-683 ◽  
Author(s):  
L. Liu ◽  
B. R. K. Kashyap ◽  
J. G. C. Templeton
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Continuous Time ◽  
Transient State ◽  
System Size ◽  
Noise Process ◽  
Shot Noise Process ◽  
Special Cases

By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases. System size before arrivals is also discussed.

scholarly journals Stackelberg equilibria in a continuous-time vertical contracting model with uncertain demand and delayed information

2014 ◽  
Vol 51 (A) ◽  
pp. 213-226 ◽  
Author(s):  
Bernt Øksendal ◽  
Leif Sandal ◽  
Jan Ubøe
Keyword(s):  
Continuous Time ◽  
Variable Coefficients ◽  
Uncertain Demand ◽  
Uhlenbeck Process ◽  
Delayed Information ◽  
Equilibrium Prices ◽  
Special Cases ◽  
Explicit Formulae ◽  
Contracting Model ◽  
Vertical Contracting

We consider explicit formulae for equilibrium prices in a continuous-time vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand is an Itô-Lévy process, and to increase realism, information is delayed. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time-variable coefficients. Moreover, explicit solution formulae are given, so these results are operational. An interesting finding is that information that is more precise may be a considerable disadvantage for the retailer.

scholarly journals Dynamic Programming and Hamilton–Jacobi–Bellman Equations on Time Scales

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yingjun Zhu ◽  
Guangyan Jia
Keyword(s):  
Dynamic Programming ◽  
Dynamic System ◽  
Time Scales ◽  
Discrete Time ◽  
Continuous Time ◽  
Stochastic Dynamic ◽  
Optimality Principle ◽  
Bellman Equations ◽  
Special Cases ◽  
Hamilton Jacobi Bellman

Bellman optimality principle for the stochastic dynamic system on time scales is derived, which includes the continuous time and discrete time as special cases. At the same time, the Hamilton–Jacobi–Bellman (HJB) equation on time scales is obtained. Finally, an example is employed to illustrate our main results.

Optimal estimation for semimartingales

1986 ◽  
Vol 23 (02) ◽  
pp. 409-417 ◽  
Author(s):  
A. Thavaneswaran ◽  
M. E. Thompson
Keyword(s):  
Continuous Time ◽  
Asymptotic Properties ◽  
Optimal Estimation ◽  
Parametric Estimation ◽  
Local Martingale ◽  
Regularity Conditions ◽  
Probability Measures ◽  
Simple Process ◽  
Special Cases ◽  
Least Squares Estimates

This paper extends a result of Godambe's theory of parametric estimation for discrete-time stochastic processes to the continuous-time case. LetP={P} be a family of probability measures such that (Ω,F, P) is complete, (Ft, t≧0) is a standard filtration, andX = (XtFt, t ≧ 0)is a semimartingale for everyP ∈ P. For a parameterθ(Ρ), supposeXt=Vt,θ+Ht,θwhere theVθprocess is predictable and locally of bounded variation and theHθprocess is a local martingale. Consider estimating equations forθof the formprocess is predictable. Under regularity conditions, an optimal form forαθin the sense of Godambe (1960) is determined. WhenVt,θis linear inθthe optimal, corresponds to certain maximum likelihood or least squares estimates derived previously in special cases. Asymptotic properties of, are discussed.

scholarly journals EXTRA DIMENSIONS AND POSSIBLE SPACE-TIME SIGNATURE CHANGES

1995 ◽  
Vol 04 (04) ◽  
pp. 491-516 ◽  
Author(s):  
K.A. BRONNIKOV
Keyword(s):  
Black Hole ◽  
Extra Dimensions ◽  
Field Potential ◽  
Space Time ◽  
Spherically Symmetric ◽  
Vector Coupling ◽  
Special Cases ◽  
Dimensional Gravity ◽  
Time Changes ◽  
A Chain

Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in D-dimensional gravity with a chain of n Ricci-flat internal spaces are considered, with the Maxwell field potential having two nonzero components: the temporal, Coulomb-like one and the one pointing to one of the extra dimensions. The properties and special cases of the solutions are discussed, in particular, those when there are horizons in the space-time. Two types of horizons are distinguished: the conventional black-hole (BH) ones and those at which the physical section of the space-time changes its signature (the latter are called T-horizons). Two theorems are proved, one fixing the BH- and T-horizon existence conditions, the other claiming that the system under study cannot have a regular center. The stability of a selected family of solutions under spherically symmetric perturbations is studied. It is shown that only black-hole solutions are stable, while all others, in particular, those with T-horizons are unstable.

Filters and parameter estimation for a partially observable system subject to random failure with continuous-range observations

2004 ◽  
Vol 36 (4) ◽  
pp. 1212-1230 ◽  
Author(s):  
Daming Lin ◽  
Viliam Makis
Keyword(s):  
Condition Monitoring ◽  
Continuous Time ◽  
The State ◽  
Parameter Estimates ◽  
State Process ◽  
Observation Process ◽  
Special Cases ◽  
Random Failure ◽  
Prediction Problems ◽  
Continuous Range

We consider a failure-prone system operating in continuous time. Condition monitoring is conducted at discrete time epochs. The state of the system is assumed to evolve as a continuous-time Markov process with a finite state space. The observation process with continuous-range values is stochastically related to the state process, which, except for the failure state, is unobservable. Combining the failure information and the condition monitoring information, we derive a general recursive filter, and, as special cases, we obtain recursive formulae for the state estimation and other quantities of interest. Updated parameter estimates are obtained using the expectation-maximization (EM) algorithm. Some practical prediction problems are discussed and finally an illustrative example is given using a real dataset.

On the GIX/G/∞ system

1990 ◽  
Vol 27 (03) ◽  
pp. 671-683 ◽  
Author(s):  
L. Liu ◽  
B. R. K. Kashyap ◽  
J. G. C. Templeton
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Continuous Time ◽  
Transient State ◽  
System Size ◽  
Noise Process ◽  
Shot Noise Process ◽  
Special Cases

By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases. System size before arrivals is also discussed.

Sign in / Sign up

Export Citation Format

Share Document