线性分式规划优化分析的元模型方法

1引言线性分式规划(LFP): min f(x)=(p~Tx α)/(q~Tx β) s.t. Ax=b (1) x≥0有着重要的应用背景,特别在经济管理中受到广泛关注．例如,以净收益率为优化目标函数的海洋运输问题;当价格系数为随机变量时,优化目标为获得满意的收益水平概率最大的资源分配问题等[11]．线性分式规划是一类特殊的非线性规划,除一般的非线性规划求解方法外,它还有一些特殊的专用算法．这里,我们要考虑的问题是;当右端资源约束向量在一定范围内(即L≤b≤U,L,U分别为b的下界和上界)变化时,目标函数的最优值如何变化?我们把这一问题称之为线性分式规划的优化分析．     

Efficiency,effectiveness and productivity of marketing in services

In this paper we consider complex deterministic problems, where there are two models that can be used to predict the performance for a given design. One of the models can give a precise estimation, but is complex and time consuming. The other model is simple and fast, but can only give a very crude estimation. We have proposed a learning-based ordinal optimization approach to tackle this problem. In this approach, we first run a simple model for all the designs and a complex model for a few designs, and then, through regression analysis, we estimate the noise trend, and this noise trend together with the crude estimates from the simple model will be used to screen the designs. The proposed approach is applied to solve an integrally bladed rotor (IBR) manufacturing problem where the production sequence and the production parameters need to be determined in order to minimize the overall manufacturing cost while satisfying the manufacturing constraints. The results indicate that, by using a very crude and simple model, we are able to identify good designs with a high degree of confidence.     

Modelling recruitment training in mathematical human resource planning

This paper deals with mathematical human resource planning; more specifically, it suggests a new model for a manpower‐planning system. In general, we study a k‐classed hierarchical system where the workforce demand at each time period is satisfied through internal mobility and recruitment. The motivation for this work is based on various European Union incentives, which promote regional or local government assistance programs that could be exploited by firms not only for hiring and training newcomers, but also to improve the skills and knowledge of their existing personnel. In this respect, in our augmented mobility model we establish a new ‘training/standby’ class, which serves as a manpower inventory position for potential recruits. This class, which may very well be internal or external to the system, is incorporated into the framework of a non‐homogeneous Markov chain model. Furthermore, cost objectives are employed using the goal‐programming approach, under different operating assumptions, in order to minimize the operational cost in the presence of system's constraints and regulations. Copyright © 2002 John Wiley & Sons, Ltd.     

Single-machine scheduling with convex resource dependent processing times and deteriorating jobs

In this study, we consider scheduling problems with convex resource dependent processing times and deteriorating jobs, in which the processing time of a job is a function of its starting time and its convex resource allocation. The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately. This paper focus on the single-machine problems with objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost, and a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. It shows that the problems remain polynomially solvable under the proposed model.     

The multivariate non-homogeneous Markov manpower system in a departmental mobility framework

The present paper proposes a non-homogeneous multivariate Markov manpower system in the general category of mathematical human resource planning. More specifically, we suggest a model, which takes into account the divisions existing in an organization categorizing its employees into several groups (departments). In this context, it considers not only possible transitions within the departments (intra-department transitions), but also, transfers of personnel between departments (inter-department transitions). Additionally, the proposed modeling structure is accompanied by cost and stocks (personnel) objectives which are set and in the sequel could be achieved by controlling either the recruitment policy or the allocation policy of employees transferred to other departments (or both). We use a minmax fuzzy goal-programming approach, under different operating assumptions, in order to keep the operational cost below desired aspiration levels and reach desirable stock structures in the presence of system’s constraints and regulations. The paper concludes with a numerical illustration.     

Unrelated parallel machines scheduling with deteriorating jobs and resource dependent processing times

We consider unrelated parallel machines scheduling problems involving resource dependent (controllable) processing times and deteriorating jobs simultaneously, i.e., the actual processing time of a job is a function of its starting time and its resource allocation. Two generally resource consumption functions, the linear and convex resource, were investigated. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. This paper focus on the objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost, and a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. If the number of unrelated parallel machines is a given constant, we show that the problems remain polynomially solvable under the proposed model.     

Excess of locally D-optimal designs and homothetic transformations

The paper is devoted to the study of homothety’s influence on the number of optimal design support points under fixed values of a regression model’s parameters. The Ayen–Peters two-dimensional nonlinear in parameters model used in analytical chemistry is considered. It is shown that the number of optimal design support points must be greater than or equal to the number of parameters depending on certain conditions. The optimal designs with the minimal number of support points are constructed explicitly. Some numerical methods for constructing designs with greater number of points (we suggest to call them excess designs) are used.     

A mixed integer program for partitioning graphs with supply and demand emphasizing sparse graphs

The focus of this paper is on finding optimal solutions for the problem of maximal partitioning of graphs with supply and demand (MPGSD) for arbitrary graphs. A mixed integer programming (MIP) model is developed for the problem of interest. We also present some specific constraints that can be used in the case of tree graphs. With the goal of lowering the computational cost for solving the underlying model, a preprocessing stage is included. It is used to produce additional constraints based on shortest paths in the graph. With the aim of exploring the effectiveness of the proposed MIP formulation we have performed computational experiments for general graphs and trees. The main objective of the tests is to observe the properties and sizes of supply/demand graphs that can be solved to optimality using the proposed approach in reasonable time. The conducted computational experiments have shown that the proposed method is especially suitable for sparse graphs.     

Optimal harvesting policy of an inland fishery resource under incomplete information

A new mathematical model for finding the optimal harvesting policy of an inland fishery resource under incomplete information is proposed in this paper. The model is based on a stochastic control formalism in a regime‐switching environment. The incompleteness of information is due to uncertainties involved in the body growth rate of the fishery resource: a key biological parameter. Finding the most cost‐effective harvesting policy of the fishery resource ultimately reduces to solving a terminal and boundary value problem of a Hamilton‐Jacobi‐Bellman equation: a nonlinear and degenerate parabolic partial differential equation. A simple finite difference scheme for solving the equation is then presented, which turns out to be convergent and generates numerical solutions that comply with certain theoretical upper and lower bounds. The model is finally applied to the management of Plecoglossus altivelis, a major inland fishery resource in Japan. The regime switching in this case is due to the temporal dynamics of benthic algae, the main food of the fish. Model parameter values are identified from field measurement results in 2017. Our computational results clearly show the dependence of the optimal harvesting policy on the river environmental and biological conditions. The proposed model would serve as a mathematical tool for fishery resource management under uncertainties.     

On various aspects of evolutionary structural optimization for problems with stiffness constraints

An evolutionary structural optimization (ESO) method for problems with stiffness constraints which is capable of performing simultaneous shape and topology optimization has been recently presented. This paper discusses various aspects of this method such as influences of the element removal ratio, the mesh size and the element type on optimal designs.     

Robust designs for Haar wavelet approximation models

In this paper, we discuss the construction of robust designs for heteroscedastic wavelet regression models when the assumed models are possibly contaminated over two different neighbourhoods: G ₁ and G ₂ . Our main findings are: (1) A recursive formula for constructing D‐optimal designs under G ₁ ; (2) Equivalency of Q‐optimal and A‐optimal designs under both G ₁ and G ₂ ; (3) D‐optimal robust designs under G ₂ ; and (4) Analytic forms for A‐ and Q‐optimal robust design densities under G ₂ . Several examples are given for the comparison, and the results demonstrate that our designs are efficient. Copyright © 2010 John Wiley & Sons, Ltd.     

First and Second Order Necessary Conditions for Stochastic Optimal Control Problems

In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.     

Optimal Control Problems for Elliptic–Parabolic Variational Inequalities with Time-Dependent Constraints

In this paper, we study optimal control problems for quasi-linear elliptic–parabolic variational inequalities with time-dependent constraints. We prove the existence of an optimal control that minimizes the nonlinear cost functional. Moreover, we apply our general results to some model problems. In particular, we show the necessary condition of optimal pair for a problem of partial differential equation (PDE) with a non-homogeneous Dirichlet boundary condition.     

Efficient Computation of Bayesian Optimal Discriminating Designs

An efficient algorithm for the determination of Bayesian optimal discriminating designs for competing regression models is developed, where the main focus is on models with general distributional assumptions beyond the “classical” case of normally distributed homoscedastic errors. For this purpose, we consider a Bayesian version of the Kullback–Leibler (KL). Discretizing the prior distribution leads to local KL-optimal discriminating design problems for a large number of competing models. All currently available methods either require a large amount of computation time or fail to calculate the optimal discriminating design, because they can only deal efficiently with a few model comparisons. In this article, we develop a new algorithm for the determination of Bayesian optimal discriminating designs with respect to the Kullback–Leibler criterion. It is demonstrated that the new algorithm is able to calculate the optimal discriminating designs with reasonable accuracy and computational time in situations where all currently available procedures are either slow or fail.     

Time substitution with application to data envelopment analysis

In this paper we analyze resource allocation distinguishing between the decision of when to begin allocation and over how many periods to apply the resources. We present analytical results for specific production technologies under different returns to scale assumptions, under capacity constraints and for production with technical change. Using a dynamic activity analysis framework we show how to compute in general optimal solutions for resource intensity use.     

The vehicle routing problem with flexible time windows and traveling times

We generalize the standard vehicle routing problem by allowing soft time window and soft traveling time constraints, where both constraints are treated as cost functions. With the proposed generalization, the problem becomes very general. In our algorithm, we use local search to determine the routes of vehicles. After fixing the route of each vehicle, we must determine the optimal start times of services at visited customers. We show that this subproblem is NP-hard when cost functions are general, but can be efficiently solved with dynamic programming when traveling time cost functions are convex even if time window cost functions are non-convex. We deal with the latter situation in the developed iterated local search algorithm. Finally we report computational results on benchmark instances, and confirm the benefits of the proposed generalization.     

An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static-dynamic uncertainty strategy. The effectiveness of the proposed method hinges on three novelties: (i) the proposed relaxation is computationally efficient and provides an optimal solution most of the time, (ii) if the relaxation produces an infeasible solution, then this solution yields a tight lower bound for the optimal cost, and (iii) it can be modified easily to obtain a feasible solution, which yields an upper bound. In case of infeasibility, the relaxation approach is implemented at each node of the search tree in a branch-and-bound procedure to efficiently search for an optimal solution. Extensive numerical tests show that our method dominates the MIP solution approach and can handle real-life size problems in trivial time.     

Improved load balancing and resource utilization for the Skill Vehicle Routing Problem

The Skill Vehicle Routing Problem (Skill VRP) considers vehicle routing under the assumption of skill requirements given on demand nodes. These requirements have to be met by the serving vehicles. No further constraints, like capacity or cost restrictions, are imposed. Skill VRP solutions may show a tendency to have a bad load balancing and resource utilization. In a majority of solutions only a subset of vehicles is active. Moreover, a considerable share of demand nodes is served by vehicles that have a skill higher than necessary. A reason for that solution behavior lies in the model itself. As no resource restrictions are imposed, the Skill VRP tends to produce TSP-like solutions. To obtain better balanced solutions, we introduce two new approaches. First we propose a minmax model that aims at minimizing the maximal vehicle tour length. Second we suggest a two-step method combining the minmax approach with a distance constrained model. Our experiments illustrate that these approaches lead to improvements in load balancing and resource utilization, but, with different impact on routing costs.     

一种构造E(s~2)最优超饱和设计的方法

本文中我们基于E(s2)最优超饱和设计和区组设计之间存在的对等关系,利用构造区组设计的方法之一－循环设计法,通过最小化ｆｒｍａｘ的进一步区分,对试验次数２４的情形,构造了相应的一系列超饱和设计．同时与现有的一些结果作了比较,验证了我们构造的设计的优良性。     

Single-machine scheduling with time-and-resource-dependent processing times

We consider single-machine scheduling problems in which the processing time of a job is a function of its starting time and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. We show that the problems remain polynomially solvable under the proposed model.