A Stochastic Stefan Problem

We consider a stochastic perturbation of the Stefan problem. The noise is Brownian in time and smoothly correlated in space. We prove existence and uniqueness and characterize the domain of existence.     

A Stochastic Bottleneck Transportation Problem

In this paper, a stochastic bottleneck transportation problem, which aims at minimizing the transportation time target subject to a chance constraint, is formulated and an algorithm based on a parametric programming approach is developed to solve it. Further, assuming the transportation costs to be deterministic, a trade-off analysis between the transportation time target and the total cost is given. In addition, methods are developed which give the whole spectrum of optimal solutions to the problems mentioned above. The algorithms are illustrated by numerical examples. The computational complexity of the algorithms is also discussed.     

风险的动态定量和一个相关的随机对策问题

本文讨论不完全市场中股票收益率不确定时的动态风险度量问题和一个相关的随机对策问题。该动态风险度量可表示为一个随机最优控制问题的值函数,以倒向随机微分方程为工具我们给出了最优目标具有的形式,并给出随机对策问题上值与下值相等的充分条件和鞍点的存在性。     

Numerical Analysis of the Stochastic Moving Boundary Problem

We extend and generalize some recent results on complete convergence (cf. Hu, Moricz, and Taylor [14], Gut [11], Wang, Bhaskara Rao, and Yang [26], Kuczmaszewska and Szynal [17], and Sung [23]) for arrays of rowwise independent Banach space valued random elements. In the main result, no assumptions are made concerning the existence of expected values or absolute moments of the random elements and no assumptions are made concerning the geometry of the underlying Banach space. Some well-known results from the literature are obtained easily as corollaries. The corresponding convergence rates are also established     

A Smoothing SAA Method for a Stochastic Linear Complementarity Problem

Utilizing the well-known aggregation technique, we propose a smoothing sample average approximation (SAA) method for a stochastic linear complementarity problem, where the underlying functions are represented by expectations of stochastic functions. The method is proved to be convergent and the preliminary numerical results are reported.     

Stochastic Analysis of the Weber Problem on the Sphere

In this paper we deal with the location of one facility on the surface of the sphere (globe) that minimizes the weighted sum of distances to a given set of demand points on the surface of the sphere. We assume that demand points are randomly generated on the sphere, and so are the weights. We prove that when the number of demand points increases to infinity, then the ratio between the maximum possible value of the objective function and the minimum possible value of the objective function converges to one. We also show that the expected number of demand points that are a local minimum is approximately one when there are a large number of demand points. Some computational experiments are presented.     

A Solution Method for a Two-dispatch Delivery Problem with Stochastic Customers

We study a vehicle routing problem in which vehicles are dispatched multiple times a day for product delivery. In this problem, some customer orders are known in advance while others are uncertain but are progressively realized during the day. The key decisions include determining which known orders should be delivered in the first dispatch and which should be delivered in a later dispatch, and finding the routes and schedules for customer orders. This problem is formulated as a two-stage stochastic programming problem with the objective of minimizing the expected total cost. A worst-case analysis is performed to evaluate the potential benefit of the stochastic approach against a deterministic approach. Furthermore, a sample-based heuristic is proposed. Computational experiments are conducted to assess the effectiveness of the model and the heuristic.      

The Stochastic Location-Assignment Problem on a Tree

In the assignment problem units of supply are assigned on a one-to-one basis to units of demand so as to minimize the sum of the cost associated with each supply-to-demand matched pair. Defined on a network, the supplies and demands are located at vertices and the cost of a supply-to-demand matched pair is the distance between them. This paper considers a two-stage stochastic program for locating the units of supply based upon only a probabilistic characterization of demand. The objective of the first-stage location problem is to minimize the expected cost of the second-stage assignment problem. Principal results include showing that the problem is NP-hard on a general network, has a simple solution procedure on a line network, and is solvable by a low order polynomial greedy procedure on a tree network. Potential applications are discussed.     

Existence Theory for a Stochastic Bolza Problem

The direct method is used to prove the existence of optimalopen-loop controls for stochastic optimal control problems inBolza form. Instead of requiring the control set to be compact,as previous authors have done, we impose a superquadratic growthcondition on the running cost. Degeneracy of the diffusion coefficientis allowed by this approach—in fact, the main result reducesto a well known deterministic theorem when the diffusion coefficientis zero.     

Stochastic Optimization over a Pareto Set Associated with a Stochastic Multi-Objective Optimization Problem

We deal with the problem of minimizing the expectation of a real valued random function over the weakly Pareto or Pareto set associated with a Stochastic Multi-objective Optimization Problem, whose objectives are expectations of random functions. Assuming that the closed form of these expectations is difficult to obtain, we apply the Sample Average Approximation method in order to approach this problem. We prove that the Hausdorff–Pompeiu distance between the weakly Pareto sets associated with the Sample Average Approximation problem and the true weakly Pareto set converges to zero almost surely as the sample size goes to infinity, assuming that our Stochastic Multi-objective Optimization Problem is strictly convex. Then we show that every cluster point of any sequence of optimal solutions of the Sample Average Approximation problems is almost surely a true optimal solution. To handle also the non-convex case, we assume that the real objective to be minimized over the Pareto set depends on the expectations of the objectives of the Stochastic Optimization Problem, i.e. we optimize over the image space of the Stochastic Optimization Problem. Then, without any convexity hypothesis, we obtain the same type of results for the Pareto sets in the image spaces. Thus we show that the sequence of optimal values of the Sample Average Approximation problems converges almost surely to the true optimal value as the sample size goes to infinity.     

A Preference Order Dynamic Program for a Knapsack Problem with Stochastic Rewards

In this paper, we extend the knapsack problem to include more realistic situations by treating the rewards (or values) associated with each item included in the solution as random variables with distributions that are known (or may be estimated) rather than known integers, as in the usual formulation. We propose a dynamic programming solution methodology where the usual real-valued return function is replaced by a preference ordering on the distributions of returns from the items selected. In addition to extending previous solutions to the knapsack problem, we demonstrate the selection of a preference ordering criterion and illustrate the conditions required of the ordering to guarantee optimality of the procedure. A sample problem is shown to demonstrate the algorithm, and results of computational experience with 459 problems of varying sizes and parameters are presented.     

A Stochastic (Adaptive) Problem of Optimal Harvesting

We study a population-growth parametric model described by a Cauchy problem for an ordinary differential equation with the right-hand side depending on the population size, time, and a stochastic parameter. For this problem, we consider an adaptive optimal control problem, the problem of optimal harvesting. For the case where the stochastic parameter is piecewise constant and changes at fixed moments, we construct a synthesis of the adaptive trajectory and the optimal control strategy. The results are illustrated with five simple population-growth models.     

Error Estimates for a Stochastic Impulse Control Problem

We obtain error bounds for monotone approximation schemes of a stochastic impulse control problem. This is an extension of the theory for error estimates for the Hamilton-Jacobi-Bellman equation. We obtain almost the same estimate on the rate of convergence as in the equation without impulsions [2], [3].     

Applying Stochastic Algorithms to a Locomotive Scheduling Problem

This paper addresses a problem common to all railway networks. Given a fixed train timetable and locomotives (or other forms of traction) of various types, each train must be allocated a locomotive. This paper examines the use of stochastic algorithms for such a problem. Two types of algorithm are used—a simple ‘local improvement’ method, performed successively from randomly chosen starting points, and a ‘simulated annealing’ approach. Both are found to give considerably better results than a deterministic method in current use, and the annealing approach is probably the better stochastic method.     

单时期需求为"离散随机型存储问题"的研究

作者通过举例以及理论证明指出目前单时期需求为"离散随机型存储问题"的处理方法所存在的错误,在此基础上引入排队论,并在对单时期需求为"离散随机型存储问题"的盈利数学期望进行研究后,根据盈利期望最大化原则,推导并建立了最佳订购量公式.     

A Stochastic Nash Equilibrium Problem for Medical Supply Competition

Journal of Optimization Theory and Applications - In this paper, we study the competition of healthcare institutions for medical supplies in emergencies caused by natural disasters. In particular,...     

随机需求收益最大化分销网络设计问题

研究随机需求的供应链分销网络设计问题。考虑供应商可以选择所服务的零售商,且供应商通过定价决策确定所服务的零售商。针对此问题,建立了一个非线性整数规划模型和一个等价的集合包裹模型,并利用列生成算法求解集合包裹模型,同时提出一种O（ n3 logn）时间的算法求解列生成算法中产生的子问题。数值计算表明,本文所提出的算法具有很好的最优性和可行性。     

Fix and Relax Heuristic for a Stochastic Lot-Sizing Problem

This paper addresses a particular stochastic lot-sizing and scheduling problem. The evolution of the uncertain parameters is modelled by means of a scenario tree and the resulting model is a multistage stochastic mixed-integer program. We develop a heuristic approach that exploits the specific structure of the problem. The computational experiments carried out on a large set of instances have shown that the approach provides good quality solutions in a reasonable amount of time.