Inventory control problem with freight cost and stochastic demand

This paper generalizes the standard newsboy model to the case including freight cost, in which the capacity of one container is the limit and the freight cost is proportional to the number of the containers used. We show that the optimal ordering quantity is either the newsboy solution or some multiple of the container’s capacity. We also propose an algorithm to compute the optimal policy. Furthermore, we generalize these results to the case in which the inventory and the price are determined jointly with emergency purchase.     

A remark on two solutions to the rational Nehari interpolation problem

This paper shows that the formulas developed in [9], from the Schur representation for the Commutant Lifting Theorem, readily yield the usual state space solutions to the rational Nehari interpolation problem.     

A stochastic inventory problem with fuzzy shortage cost

Up to now, many inventory models have been considered in the literature. Some assume stochastic demands and others consider the deterministic case. Though they include a shortage cost due to lost sales, it is usually assumed to be known concretely and a priori. This paper introduces fuzziness of shortage cost explicitly into the classical newsboy problem. That is, we investigate the so-called fuzzy newsboy problem where its shortage cost is vague and given by an L shape fuzzy number. Then the total expected profit function also becomes a fuzzy number. Finally, we find an optimal ordering quantity realizing the fuzzy max order of the profit function (fuzzy min order considering the profit function) and compare it with the optimal ordering quantity of the non-fuzzy newsboy problem.     

A stochastic approach to the flood control problem

We propose a stochastic model in conjunction with reliability analysis concepts to improve estimates for the protection volume that should be allocated in a reservoir to control a flood wave. In this approach, the inflow that reaches the reservoir during a flood is considered to be a load, and the reservoir capacity to control this flood is considered to be the resistance that the reservoir offers against the propagation of the flood. Here, the load and the resistance are modeled as a diffusion stochastic process, and the protection volume is determined via Itô's formula. In this scenario, an explicit formula for the failure risk is derived. The parameter inference is carried out by a Bayesian approach for a time discrete version of the load, and the estimates are obtained by using Monte Carlo Markov Chain Algorithms (MCMC). The maximum likelihood estimators are used in the comparison. The record utilized comprises nine years of daily inflow rates during flood periods that come to the Chavantes hydroelectric power plant (CHPP) in Southeast Brazil. The protection volumes estimated through the proposed model are compared to the volumes obtained by other existing methods.     

On a stochastic control problem with exit constraints

In this paper the logarithmic transformation of Fleming [1] is used to discuss a specific problem of controlled diffusions. The problem is to minimize a certain quadratic functional of the applied drift while satisfying the requirement that the place where the process exits a domain is not in a specified subset of its boundary. The main result is that the solution of this problem is given by the logarithm of a related exit probability.This research was supported in part by the Air Force Office of Scientific Research under AF-AFOSR 76-3063.     

A remark on max-cut problem with an application to digital-analogue convertors

We introduce notions of a distance-decreasing weight function and of an alternating cut. For a class of distance-decreasing weights we solve the max-cut problem. In general, we prove that alternating cuts are near optimal. This has application to digital-analogue convertors.     

关于二维光滑线性方程无解的注记

Abstract. A smooth linear complex partial differential equation in two variables which is without solutions is found.     

Explicit solution to a linear-quadratic optimal control problem with an arbitrary terminal

An optimal control problem of minimization of the sum of a linear-quadratic integral functional and a terminal of arbitrary form is considered. It is proved that in this case a control can be also constructed in an explicit analytic form.     

A remark on the maximum principle and stochastic completeness

We prove that the stochastic completeness of a Riemannian manifold is equivalent to the validity of a weak form of the Omori-Yau maximum principle. Some geometric applications of this result are also presented.

     

Optimal investment problem with stochastic interest rate and stochastic volatility: Maximizing a power utility

In this paper, we assume that an investor can invest his/her wealth in a bond and a stock. In our wealth model, the stochastic interest rate is described by a Cox–Ingersoll–Ross (CIR) model, and the volatility of the stock is proportional to another CIR process. We obtain a closed‐form expression of the optimal policy that maximizes a power utility. Moreover, a verification theorem without the usual Lipschitz assumptions is proved, and the relationships between the optimal policy and various parameters are given. Copyright © 2009 John Wiley & Sons, Ltd.     

Lipschitz continuity and semiconcavity properties of the value function of a stochastic control problem

We investigate the Cauchy problem for a nonlinear parabolic partial differential equation of Hamilton–Jacobi–Bellman type and prove some regularity results, such as Lipschitz continuity and semiconcavity, for its unique viscosity solution. Our method is based on the possibility of representing such a solution as the value function of the associated stochastic optimal control problem. The main feature of our result is the fact that the solution is shown to be jointly regular in space and time without any strong ellipticity assumption on the Hamilton–Jacobi–Bellman equation.     

A remark on linearly unstable standing wave solutions to NLS

We obtain an optimal growth estimate of a semigroup generated by a linearized operator around a standing wave solution nonlinear Schrödinger equations in two-dimension. Using the growth estimate of the semigroup, we prove that a linearly unstable standing wave solution is orbitally unstable and that instability of the standing wave solution is mainly caused by a mode of an eigenfunction associated with the rightmost (or the leftmost) eigenvalues of the linearized operator. Our result is obtained by using the method of Yajima and Cuccagna that proved L^p$L^p$-boundedness of the wave operator.     

A necessary extremality condition for a set-valued stochastic control problem

For a controlled stochastic dynamic system with set-valued drift coefficient and a terminal cost functional we derive a necessary extremality condition in form of a minimum principle.     

A remark on a standard and linear vector network equilibrium problem with capacity constraints

In this paper, (weak) vector equilibrium principle with capacity constraints is introduced. A necessary condition that a vector minimum cost flow is a vector equilibrium flow with capacity constraints is obtained. When the number of paths connecting with each pair of source and sink is less than or equal to 2, a sufficient condition for a vector minimum cost flow to be a vector equilibrium flow is also obtained. A generalized (weak) vector equilibrium principle is also introduced. Without any additional assumption, a necessary and sufficient condition for a (weak) vector minimum cost flow to be a generalized (weak) vector equilibrium flow is obtained.     

A remark on the thermistor problem with rapidly growing conductivity

A comparison is made between existing results for the stationary thermistor problem. A theorem of existence is given even when the electrical conductivity is a superlinear function of the temperature.     

A remark on a boundary value problem for force-free fields

Summary For the equation rotv–v=0 with not necessarily constant a boundary value problem of Neumann's type is solved by reducing it to an equivalent integral equation.

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Zusammenfassung Für die Gleichung rotv–v=0 mit nicht notwendig konstantem wird ein Neumannsches Randwertproblem durch Zuruckführung auf eine äquivalente Integralgleichung gelöst.