scholarly journals AN OPTIMAL CONSUMPTION AND INVESTMENT PROBLEM WITH QUADRATIC UTILITY AND SUBSISTENCE CONSUMPTION CONSTRAINTS: A DYNAMIC PROGRAMMING APPROACH

2018 ◽  
Vol 23 (4) ◽  
pp. 627-628 ◽  
Author(s):  
Yong Hyun Shin ◽  
Jung Lim Koo ◽  
Kum Hwan Roh
Keyword(s):  
Dynamic Programming ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Dynamic Programming Method ◽  
Programming Approach ◽  
Optimal Consumption ◽  
Dynamic Programming Approach ◽  
Investment Problem ◽  
Optimal Consumption And Investment ◽  
Consumption Constraints

In this paper, we analyze the optimal consumption and investment problem of an agent who has a quadratic-type utility function and faces a subsistence consumption constraint. We use the dynamic programming method to solve the optimization problem in continuous-time. We further provide the sufficient conditions for the optimization problem to be well-defined.

scholarly journals Portfolio Selection with Subsistence Consumption Constraints and CARA Utility

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Gyoocheol Shim ◽  
Yong Hyun Shin
Keyword(s):  
Portfolio Choice ◽  
Optimization Problem ◽  
Absolute Risk ◽  
Programming Approach ◽  
Optimal Consumption ◽  
Choice Problem ◽  
Dynamic Programming Approach ◽  
Cara Utility ◽  
Constant Absolute Risk Aversion ◽  
Consumption Constraints

We consider the optimal consumption and portfolio choice problem with constant absolute risk aversion (CARA) utility and a subsistence consumption constraint. A subsistence consumption constraint means there exists a positive constant minimum level for the agent’s optimal consumption. We use the dynamic programming approach to solve the optimization problem and also give the verification theorem. We illustrate the effects of the subsistence consumption constraint on the optimal consumption and portfolio choice rules by the numerical results.

scholarly journals A Novel Dynamic Programming Approach for Optimizing Driving Strategy of Subway Trains

2020 ◽  
Vol 325 ◽  
pp. 01002
Author(s):  
Hao Gao ◽  
Yadong Zhang ◽  
Jin Guo
Keyword(s):  
Dynamic Programming ◽  
Optimization Problem ◽  
Cost Functions ◽  
Programming Approach ◽  
Safe Driving ◽  
Dynamic Programming Approach ◽  
Urban Rail ◽  
Rail Line ◽  
Optimal Driving

The reduction of operation energy consumption without decreasing service quality has become a great challenge in subways daily operation. A novel DP based approach is proposed for optimizing the train driving strategy. The optimal driving problem is first considered as a multi-objective problem with five optimal targets (i.e., energy saving, punctual arriving, less switching, safe driving and accurate stopping). The optimization problem is remodelled as a multistage decision problem by discretizing the continuous train movement in space. The process of dynamic programming is carried out in the velocity-space status space. Due to the discretizing rules of searching space, the optimal goals of safe driving and accurate stopping can be satisfied during the searching process. The rest of multiple goals are spilt into cost functions and constrains for each stage. Due to the multiple cost functions, a set of pareto optimal solutions can be achieved at each vertex during the process of dynamic programming. To further improve the efficiency of algorithm, two evaluation criterions are introduced to maintain the capacity of the pareto set at each vertex. A case study of Yizhuang urban rail line in Beijing is conducted to verify the effectiveness and the efficiency of DP based algorithms.

Shortest Route Application via Dynamic Programming in the Transportation Networks

2021 ◽  
pp. 362-371
Author(s):  
Arzu Eren Şenaras ◽  
Şahin İnanç ◽  
Hayrettin Kemal Sezen ◽  
Onur Mesut Şenaras
Keyword(s):  
Dynamic Programming ◽  
Shortest Path ◽  
Dynamic Programming Method ◽  
Programming Approach ◽  
Dynamic Programming Approach ◽  
Transportation Sector ◽  
Shortest Route ◽  
Starting Point ◽  
Visual Basic Application ◽  
Destination Point

The purpose of this study is to develop an application for finding the shortest path in the transportation sector. The application was developed using the dynamic programming method in MS Excel Visual Basic application. These types of problems are also called stagecoach problems. The purpose of the problem is finding the shortest path between the starting point (node) and the destination point. Values are related to the roads in the network to specify the distance between two nodes. In case of a small number of nodes (activities), a solution can be reached by evaluating all options. But the number of possible options to be scanned for real problems is quite large. In such cases, a suitable method is needed for the solution. It can produce effective solutions with the dynamic programming approach.

scholarly journals A Note on Multimachine Scheduling with Weighted Early/Late Work Criteria and Common Due Date

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Kerang Cao ◽  
Xin Chen ◽  
Kwang-nam Choi ◽  
Yage Liang ◽  
Qian Miao ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Flow Shop ◽  
Dynamic Programming Method ◽  
Programming Approach ◽  
Due Date ◽  
Enumeration Algorithm ◽  
Late Work ◽  
Common Due Date ◽  
Dynamic Programming Approach ◽  
Early Late

In this note, we revisit two types of scheduling problem with weighted early/late work criteria and a common due date. For parallel identical machines environment, we present a dynamic programming approach running in pseudopolynomial time, to classify the considered problem into the set of binary NP-hard. We also propose an enumeration algorithm for comparison. For two-machine flow shop systems, we focus on a previous dynamic programming method, but with a more precise analysis, to improve the practical performance during its execution. For each model, we verify our studies through computational experiments, in which we show the advantages of our techniques, respectively.

scholarly journals A Discrete-Binary Transformation of the Reliability Redundancy Allocation Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Marco Caserta ◽  
Stefan Voß
Keyword(s):  
Dynamic Programming ◽  
Optimization Problem ◽  
Allocation Problem ◽  
Programming Approach ◽  
Redundancy Allocation Problem ◽  
Redundancy Allocation ◽  
Dynamic Programming Approach ◽  
Integer Problem ◽  
Redundancy Optimization

Given a reliability redundancy optimization problem in itsdiscreteversion, it is possible to transform such integer problem into a correspondingbinaryproblem in log-time. A simple discrete-binary transformation is presented in this paper. The proposed transformation is illustrated using an example taken from the reliability literature. An immediate implication is that a standard exact dynamic programming approach may easily solve instances to optimality that were usually only solved heuristically.

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