共查询到20条相似文献,搜索用时 10 毫秒
1.
R. F. Hartl 《Journal of Optimization Theory and Applications》1984,43(1):51-72
In this paper, the Nerlove-Arrow model of optimal dynamic advertising policies is generalized by assuming a general probability distribution of the forgetting time, rather than the exponential one. A control problem with integrodifferential equations of motion is defined for which the transitory and steady-state properties of the optimal advertising policy are examined. The effects of assumptions like IHR-distributions and DHR-distributions, the existence of an upper bound for the forgetting time, etc., are explained. It is shown that there are two (in the case of an exponential distribution even three) different current-value adjoint functions associated with the problem, and relations between the two (three) are established. Also provided is a sensitivity analysis.Thanks are due to G. Feichtinger and S. Jorgensen for useful discussions. 相似文献
2.
Roy Cerqueti 《Journal of Global Optimization》2012,53(3):539-561
This paper deals with a theoretical stochastic dynamic optimization model for the external financing of firms. We aim at searching for the best intensity of payment that a financier has to apply to a company in order to have a loan repaid. The techniques involved are related to the optimal control theory with exit time. We follow a dynamic programming approach. Our model also presents a distinction between the legal and the illegal financier, and a theoretical comparison analysis of the results is presented. Some numerical examples provide further validation of the theoretical results. 相似文献
3.
I. Chryssochoos 《Journal of Mathematical Analysis and Applications》2003,287(1):118-140
Dynamic programming identifies the value function of continuous time optimal control with a solution to the Hamilton-Jacobi equation, appropriately defined. This relationship in turn leads to sufficient conditions of global optimality, which have been widely used to confirm the optimality of putative minimisers. In continuous time optimal control, the dynamic programming methodology has been used for problems with state space a vector space. However there are many problems of interest in which it is necessary to regard the state space as a manifold. This paper extends dynamic programming to cover problems in which the state space is a general finite-dimensional C∞ manifold. It shows that, also in a manifold setting, we can characterise the value function of a free time optimal control problem as a unique lower semicontinuous, lower bounded, generalised solution of the Hamilton-Jacobi equation. The application of these results is illustrated by the investigation of minimum time controllers for a rigid pendulum. 相似文献
4.
W. Pauwels 《Journal of Optimization Theory and Applications》1977,22(1):79-89
The Nerlove-Arrow model of optimal dynamic advertising policies is generalized by incorporating a continuously distributed lag between advertising expenditures and increases in the stock of goodwill. This leads to a control problem where the equation of motion is given by an integro-differential equation. The transitory and steady-state properties of the optimal policies are examined, both for a general lag function and for a gamma distributed lag. The dependence of the steady-state solution on the parameters of the gamma distribution is also investigated. An example is given using specific demand and cost functions. 相似文献
5.
H I Mesak 《The Journal of the Operational Research Society》2002,53(11):1247-1255
Using a modified version of a Vidale–Wolfe model, proposed by Little, this paper examines the impact of initial sales rate on the performance of a variety of discrete, piecewise-continuous advertising policies for a finite planning horizon. The deployment of a non-discounted measure of performance reveals, irrespective of the shape of the advertising response function, that when the initial sales rate is different from zero at the beginning of the planning period: (1) a firm would be better off concentrating its advertising effort at the end rather than at the beginning of the planning period for a Blitz Policy (BP), (2) for an Advertising Pulsing/Maintenance Policy (APMP), it is more lucrative for a firm to alternate between a lower level of advertising followed by higher level (low–high) in a cyclic manner rather than to cycle the opposite way (high–low), and (3) in the presence of an initial sales rate, the pattern of the optimal advertising policy determined by dynamic programming can be significantly different from its alternative counterpart in its absence. In addition, it has been demonstrated, among other theoretical findings, that, for any given mean rate of advertising, the mean sales is bounded from below and is a decreasing function of the length of the planning horizon. Numerical examples are introduced to illustrate and reinforce the above research findings. 相似文献
6.
Summary The question of the existence of good Markov [good stationary] policies is studied for a general class of Borel [stationary] dynamic programming models. It is shown, for example, that Markov [stationary] policies are uniformly adequate if every transition law is absolutely continuous with respect to a fixed measure [and the reward function is positive or the model satisfies certain compactness and continuity conditions].Research supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 72Research supported by National Science Foundation Grant MCS 8100789 相似文献
7.
Insurance companies sell contracts of various types each of them having a specific probability of return. Insurers may also own, at the same time, several insurance contracts which evolve through time. In this context, expectation and variance of the free reserves appear as functions of the number of customers in different classes as well as their evolution. Assuming that the customer system can be formulated as an open Markov one characterized by free entry, it is interesting to seek the optimal new customer distribution over the different customer classes j, which permits the minimization of the variance of free reserves for a desired average level of free reserves at a given time horizon. It is shown that, under some conditions, the customer system converges to an optimal growth steady state. 相似文献
8.
Manfred Schäl 《Stochastic Processes and their Applications》1975,3(4):345-364
The compactness of the set of policies in a dynamic programming decision model, which guarantees the existence of an optimal policy, is proven by reducing the problem to the compactness of the set of probability measures which are induced by the policies. When studying the set of probability measures, use is made of the weak topology and the so-called ws∞-topology. A definition and a discussion of the latter topology is given in this paper, where we pay attention to criteria for relative compactness. 相似文献
9.
Michael Kolonko 《Mathematical Methods of Operations Research》1993,37(1):75-95
We examine an algorithm for the compactification of an arrangement of rectangles in the plane as it is used for floorplans in the automated design of electronic circuits (also called sizing of floorplans). We reformulate this problem as a multistage decision problem and show that the algorithm is in fact the optimal solution obtained by the backward induction procedure of dynamic programing. The model allows generalisations to non-geometrical applications in scheduling and reliability. 相似文献
10.
We consider the general continuous time finite-dimensional deterministic system under a finite horizon cost functional. Our
aim is to calculate approximate solutions to the optimal feedback control. First we apply the dynamic programming principle
to obtain the evolutive Hamilton–Jacobi–Bellman (HJB) equation satisfied by the value function of the optimal control problem.
We then propose two schemes to solve the equation numerically. One is in terms of the time difference approximation and the
other the time-space approximation. For each scheme, we prove that (a) the algorithm is convergent, that is, the solution
of the discrete scheme converges to the viscosity solution of the HJB equation, and (b) the optimal control of the discrete
system determined by the corresponding dynamic programming is a minimizing sequence of the optimal feedback control of the
continuous counterpart. An example is presented for the time-space algorithm; the results illustrate that the scheme is effective. 相似文献
11.
《European Journal of Operational Research》2005,166(1):266-277
When should one refinance a mortgage loan? It is one of the most common finance questions in today's world. There have been surprisingly few attempts to answer this question in a structured manner, however. Moreover, the existing guidelines for refinancing consist of a short list of very simple rules that have a limited application. This article addresses the question through a dynamic programming model coupled with an analysis of historical interest rates. The analysis reveals a more complex set of rules for an optional refinance decision––oftentimes conflicting with the conventionally accepted idea that rate differences must be greater than two percent. 相似文献
12.
13.
This paper deals with a continuous-time Markov decision process in Borel state and action spaces and with unbounded transition rates. Under history-dependent policies, the controlled process may not be Markov. The main contribution is that for such non-Markov processes we establish the Dynkin formula, which plays important roles in establishing optimality results for continuous-time Markov decision processes. We further illustrate this by showing, for a discounted continuous-time Markov decision process, the existence of a deterministic stationary optimal policy (out of the class of history-dependent policies) and characterizing the value function through the Bellman equation. 相似文献
14.
Reshma Khemchandani Nishil Gupta Arpit Chaudhary Suresh Chandra 《Optimization Letters》2013,7(3):575-592
In this paper, we develop optimal trading strategies for a risk averse investor by minimizing the expected cost and the risk of execution. Here we consider a law of motion for price which uses a convex combination of temporary and permanent market impact. In the special case of unconstrained problem for a risk neutral investor, we obtain a closed form solution for optimal trading strategies by using dynamic programming. For a general problem, we use a quadratic programming approach to get approximate dynamic optimal trading strategies. Further, numerical examples of optimal execution strategies are provided for illustration purposes. 相似文献
15.
Ching Wai-Ki; Yuen Wai-On; Ng Michael K.; Zhang Shu-Qin 《IMA Journal of Management Mathematics》2006,17(1):83-96
** Email: wkc{at}maths.hku.hk In this paper, we propose a new advertising model which cancapture the advertising wear out phenomenon. The objective hereis to maximize overall sales. We show how to derive the optimalpulsation advertising strategy. The optimization problem canbe formulated as a linear programming problem. Closed-form optimalsolution can also be obtained under some conditions. We presentnumerical examples to illustrate the proposed model and applythe model to practical sales data. 相似文献
16.
This paper investigates the computation of transient-optimal policies in discrete dynamic programming. The model, is quite
general: it may contain transient as well as nontransient policies. and the transition matrices are not necessarily substochastic.
A functional equation for the so-called transient-value-vector is derived and the concept of superharmonicity is introduced.
This concept provides the linear program to compute the transientvalue-vector and a transient-optimal policy.
We also discuss the elimination of suboptimal actions, the solution of problems with additional constraints, and the computation
of an efficient policy for a multiple objective dynamic programming problem. 相似文献
17.
Israel Brosh 《European Journal of Operational Research》1981,8(1):40-46
We examine a case study of an airline company whose problem is to plan cargo allocations on board a plane. Given the volume, weight, and structural constraints, the problem of finding the optimal load layout is formulated as a fractional programming problem. An algorithm is suggested to solve the linearized problem as a sequence of linear programming problems whose optimal solutions converge to the optimum (with a predetermined level of tolerance). 相似文献
18.
Bernardo Villarreal Mark H Karwan 《Journal of Mathematical Analysis and Applications》1981,81(2):524-544
Several interactive schemes for solving multicriteria discrete programming problems are developed under a dynamic programming framework. It is assumed that the decision maker's preference structure satisfies the conditions of transitivity, monotonicity, and nonsatiation. Hybrid procedures are also structured by including branch and bound ideas into the recursions. Initial computational results are offered. 相似文献
19.
Nuno P. Faísca Konstantinos I. Kouramas Pedro M. Saraiva Berç Rustem Efstratios N. Pistikopoulos 《Optimization Letters》2008,2(2):267-280
In this work, we present a new algorithm for solving complex multi-stage optimization problems involving hard constraints
and uncertainties, based on dynamic and multi-parametric programming techniques. Each echelon of the dynamic programming procedure,
typically employed in the context of multi-stage optimization models, is interpreted as a multi-parametric optimization problem,
with the present states and future decision variables being the parameters, while the present decisions the corresponding
optimization variables. This reformulation significantly reduces the dimension of the original problem, essentially to a set
of lower dimensional multi-parametric programs, which are sequentially solved. Furthermore, the use of sensitivity analysis
circumvents non-convexities that naturally arise in constrained dynamic programming problems. The potential application of
the proposed novel framework to robust constrained optimal control is highlighted. 相似文献
20.
Multicriteria integer programming: A (hybrid) dynamic programming recursive approach 总被引:1,自引:0,他引:1
Dynamic programming recursive equations are used to develop a procedure to obtain the set of efficient solutions to the multicriteria integer linear programming problem. An alternate method is produced by combining this procedure with branch and bound rules. Computational results are reported. 相似文献