Resource Planning and Allocation Problem Under Uncertain Environment

This paper generalizes the classic resource allocation problem to the resource planning and allocation problem, in which the resource itself is a decision variable and the cost of each activity is uncertain when the resource is determined. The authors formulate this problem as a two-stage stochastic programming. The authors first propose an efficient algorithm for the case with finite states. Then, a sudgradient method is proposed for the general case and it is shown that the simple algorithm for the unique state case can be used to compute the subgradient of the objective function. Numerical experiments are conducted to show the effectiveness of the model.

Approximate Dynamic Programming for Stochastic Resource Allocation Problems

A stochastic resource allocation model, based on the principles of Markov decision processes(MDPs), is proposed in this paper. In particular, a general-purpose framework is developed, which takes into account resource requests for both instant and future needs. The considered framework can handle two types of reservations(i.e., specified and unspecified time interval reservation requests), and implement an overbooking business strategy to further increase business revenues. The resulting dynamic pricing problems can be regarded as sequential decision-making problems under uncertainty, which is solved by means of stochastic dynamic programming(DP) based algorithms. In this regard, Bellman’s backward principle of optimality is exploited in order to provide all the implementation mechanisms for the proposed reservation pricing algorithm. The curse of dimensionality, as the inevitable issue of the DP both for instant resource requests and future resource reservations,occurs. In particular, an approximate dynamic programming(ADP) technique based on linear function approximations is applied to solve such scalability issues. Several examples are provided to show the effectiveness of the proposed approach.

Egalitarian Allocations and the Inverse Problem for the Shapley Value

In a cooperative transferable utilities game, the allocation of the win of the grand coalition is an Egalitarian Allocation, if this win is divided into equal parts among all players. The Inverse Set relative to the Shapley Value of a game is a set of games in which the Shapley Value is the same as the initial one. In the Inverse Set, we determined a family of games for which the Shapley Value is also a coalitional rational value. The Egalitarian Allocation of the game is efficient, so that in the set called the Inverse Set relative to the Shapley Value, the allocation is the same as the initial one, but may not be coalitional rational. In this paper, we shall find out in the same family of the Inverse Set, a subfamily of games with the Egalitarian Allocation is also a coalitional rational value. We show some relationship between the two sets of games, where our values are coalitional rational. Finally, we shall discuss the possibility that our procedure may be used for solving a very similar problem for other efficient values. Numerical examples show the procedure to get solutions for the efficient values.

Using the Simplex Method for a Type of Allocation Problems

In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0 - 1 integer programming method, H. W. Kuhn [1] suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the existence theorem of the solution along with partially total unimodularity and nonnegativeness of the incidence matrix to prove that the simplex method facilitates solving these problems. We also provide insights as to how a partition including a particular unit may be obtained.

Mathematical Model and Algorithm for the Task Allocation Problem of Robots in the Smart Warehouse

In the smart warehousing system adopting cargo-to-person mode, all the items are stored in the movable shelves. There are some warehouse robots transporting the shelves to the working platforms for completing order picking or items replenishment tasks. When the number of robots is insufficient, the task allocation problem of robots is an important issue in designing the warehousing system. In this paper, the task allocation problem of insufficient warehouse robots (TAPIR) is investigated. Firstly, the TAPIR problem is decomposed into three sub-problems: task grouping problem, task scheduling problem and task balanced allocation problem. Then three sub-problems are respectively formulated into integer programming models, and the corresponding heuristic algorithms for solving three sub-problems are designed. Finally, the simulation and analysis are done on the real data of online bookstore. Simulation results show that the mathematical models and algorithms of this paper can provide a theoretical basis for solving the TAPIR problem.

An Intelligent System for a Resource Allocation Problem Based on Fuzzy Reasoning

The development of the assistive abilities regarding the decision-making process o fan Intelligent Control System （ICS） like a fuzzy expert system implies the development of its functionality and its ability of specification. Fuzzy expert systems can model fuzzy controllers, i.e., the knowledge representation and the abilities of making decisions corresponding to fuzzy expert systems are much more complicated that in the case of standard fuzzy controllers. The expert system acts also as a supervisor, creating meta-level reasoning on a set of fuzzy controllers, in order to choose the best one for the management of the process. Knowledge Management Systems （KMSs） is a new development paradigm of Intelligent Systems which has resulted from a synergy between fuzzy sets, artificial neural networks, evolutionary computation, machine learning, etc., broadening computer science, physics, economics, engineering, mathematics. This paper presents, after a synergic new paradigm of intelligent systems, as a practical case study the fuzzy and temporal properties of knowledge formalism embedded in an ICS. We are not dealing high with level reasoning methods, because we think that real-time problems can only be solved by rather low-level reasoning. Solving the match-time predictability problem would allow us to build much more powerful reasoning techniques.

The Capacitated Location-Allocation Problem in the Presence of <i>k</i>Connections

We consider a capacitated location-allocation problem in the presence of k connections on the horizontal line barrier. The objective is to locate a set of new facilities among a set of existing facilities and to allocate an optimal number of existing facilities to each new facility in order to satisfy their demands such that the summation of the weighted rectilinear barrier distances from new facilities to existing facilities is minimized. The proposed problem is designed as a mixed-integer nonlinear programming model. To show the efficiency of the model, a numerical example is provided. It is worth noting that the global optimal solution is obtained.

Energy efficient resource allocation for D2D multicast communications

The resource allocation for device-to-device(D2D)multicast communications is investigated.To achieve fair energy efficiency(EE)among different multicast groups,the max-min fairness criterion is used as the optimization criterion and the EE of D2D multicast groups are taken as the optimization objective function.The aim is to maximize the minimum EE for different D2D multicast groups under the constraints of the maximum transmit power and minimum transmit rate,which is modeled as a non-convex and mixed-integer fractional programming problem.Here,suboptimal resource allocation algorithms are proposed to solve this problem.First,channel assignment scheme is performed to assign channel to D2D multicast groups.Second,for a given channel assignment,iterative power allocation schemes with and without loss of cellular users’rate are completed,respectively.Simulation results corroborate the convergence performance of the proposed algorithms.In addition,compared with the traditional throughput maximization algorithm,the proposed algorithms can improve the energy efficiency of the system and the fairness achieved among different multicast groups.

Dynamic Promotional Resource Allocation for Segment Specific and Spectrum Effect of Promotion for a Product Line Incorporating Repeat Purchase Behavior

Promotion is an essential element in the marketing mix. It is used by businesses to inform, influence and persuade customers to adopt the products and services they offer. Without promotion, business would be stagnant and lack substantial growth because the brands would have low visibility in the market. Moreover, today’s vast and assorted markets comprise of customers with different needs and varied behavior. So it is rarely possible for companies to satisfy all customers by treating them alike. Thus there arises a need to divide the market into segments having customers with similar traits/characteristics. After identifying appropriate market segments, firms can design differentiated promotional campaigns for each segment. At the same time there can be a mass market promotional campaign that reaches different segments with a fixed spectrum. Also since promotional effort resources are limited, one must use them judiciously. In this paper, we formulate mathematical programming problem under repeat purchase scenario, which optimally allocates mass promotional effort resources and differentiated promotional effort resources across the segments dynamically in order to maximize the overall sales obtained from multiple products of a product line under budgetary and minimum sales aspiration level constraint on each product under consideration in each segment. The planning horizon is divided into multi periods, the adoption pattern of each product in each segment is observed in every subinterval and accordingly promotional effort allocations are determined for the next period till we reach the end of planning period. The optimization model has been further extended to incorporate minimum aspiration level constraints on total sales for each product under consideration from all the segments taken together. The non linear programming problem so formulated is solved using differential evolution approach. A numerical example has been discussed to illustrate applicability of the model.

SOME EXTENDED KNAPSACK PROBLEMS INVOLVING JOB PARTITION BETWEEN TWO PARTIES

Some novel applications and pragmatic variations of knapsack problem （KP） are presented and constructed, which are formulated and developed from a model initiated in this paper on profit allocation from partition of jobs in terms of two-person discrete cooperation game.

Generative Neural Network Based Spectrum Sharing Using Linear Sum Assignment Problems

Spectrum management and resource allocation(RA)problems are challenging and critical in a vast number of research areas such as wireless communications and computer networks.The traditional approaches for solving such problems usually consume time and memory,especially for large-size problems.Recently different machine learning approaches have been considered as potential promising techniques for combinatorial optimization problems,especially the generative model of the deep neural networks.In this work,we propose a resource allocation deep autoencoder network,as one of the promising generative models,for enabling spectrum sharing in underlay device-to-device(D2D)communication by solving linear sum assignment problems(LSAPs).Specifically,we investigate the performance of three different architectures for the conditional variational autoencoders(CVAE).The three proposed architecture are the convolutional neural network(CVAECNN)autoencoder,the feed-forward neural network(CVAE-FNN)autoencoder,and the hybrid(H-CVAE)autoencoder.The simulation results show that the proposed approach could be used as a replacement of the conventional RA techniques,such as the Hungarian algorithm,due to its ability to find solutions of LASPs of different sizes with high accuracy and very fast execution time.Moreover,the simulation results reveal that the accuracy of the proposed hybrid autoencoder architecture outperforms the other proposed architectures and the state-of-the-art DNN techniques.

Strict greedy design paradigm applied to the stochastic multi-armed bandit problem

The process of making decisions is something humans do inherently and routinely,to the extent that it appears commonplace. However,in order to achieve good overall performance,decisions must take into account both the outcomes of past decisions and opportunities of future ones. Reinforcement learning,which is fundamental to sequential decision-making,consists of the following components: 1 A set of decisions epochs; 2 A set of environment states; 3 A set of available actions to transition states; 4 State-action dependent immediate rewards for each action.At each decision,the environment state provides the decision maker with a set of available actions from which to choose. As a result of selecting a particular action in the state,the environment generates an immediate reward for the decision maker and shifts to a different state and decision. The ultimate goal for the decision maker is to maximize the total reward after a sequence of time steps.This paper will focus on an archetypal example of reinforcement learning,the stochastic multi-armed bandit problem. After introducing the dilemma,I will briefly cover the most common methods used to solve it,namely the UCB and εn- greedy algorithms. I will also introduce my own greedy implementation,the strict-greedy algorithm,which more tightly follows the greedy pattern in algorithm design,and show that it runs comparably to the two accepted algorithms.

生存进化阶段性搜索微粒群算法及其可靠性冗余分配优化应用

为高效解决含有异质冗余的多态系统(MSS)可靠性优化问题,并弥补微粒群优化(PSO)算法易早熟收敛的不足,从作用力方式和种群拓扑结构两方面对算法进行改进。改进PSO算法中单一的作用力方式,设置前后两个搜索阶段,对应两个搜索阶段分别构造平衡引斥力方式和双层引力(个体和全局最优解引力、中间适应度微粒引力)方式,提出阶段性搜索微粒群(SPSO)算法;利用生物个体“择友而交”和优胜劣汰的生存体系构建生存进化(SE)拓扑结构,以结构演化和算法进化并行方式将该拓扑结构融入SPSO算法,提出生存进化阶段性搜索微粒群(SPSO-SE)算法,进一步提升算法的优化性能;利用Benchmark函数对所提算法与PSO的改进算法进行测试对比,结果表明,所提SPSO-SE算法具有更好的寻优能力。采用SPSO-SE算法对串-并联和桥式结构的多态系统的可靠性冗余分配问题进行优化,得到的系统结构费用更低、可靠度更高。

叠合板钢筋网片柔性生产线控制系统研究

针对当前叠合板钢筋网片生产过程中调试效率低的问题,提出了一套适用于装配式建筑领域的叠合板钢筋网片柔性生产线,通过灵活调整网片间距,实现网片柔性化生产。为解决叠合板钢筋网片柔性生产线中的控制器分配问题,建立了安装空间、网络传输距离与制造成本相结合的多目标优化模型,运用增强精英保留的多目标遗传算法对模型进行求解。计算结果表明:优化后的方案可以有效降低成本,保证网络传输,为设计一套安装便利、传输稳定及低成本的生产线控制系统提供了理论依据。

Lingo软件求解医院排班问题案例研究

排班问题是运筹学领域经典的问题,在医疗资源优化配置中有着广泛应用。医院排班问题是指合理安排医生、护士和其他医务人员的工作时间表和班次的问题。本文针对三个典型的医院排班问题,基于排班理论分别构建0-1规划模型,利用Lingo语言的特点对目标函数和约束条件进行巧妙处理,进而实现模型求解,获得最优排班方案,从而实现医疗资源的优化配置。

基于国贸货物需求的国际港口布局及港口分工研究——以海南岛为例

科学规划国际港口分布和分工对促进国际贸易、发展经济有着重要意义。以包含港口建设及运营成本、航运成本、港口作业成本和港口其他服务费用在内的物流总成本最小为目标,构建了一种特殊选址-分配模型,应用趋势增长法和弹性系数法分析了货物进出口贸易量,并以海南岛为例进行了实证研究,同时进行了模型的情形对比和敏感性分析,验证了模型的有效性和结果的合理性。研究结果表明:模型能够有效确定基于国际货物贸易需求的物流总成本最小的国际港口布局及港口间的协作分工方案,且求解效率较高;相对于仅将海南洋浦港和海口港作为国际港口的情形,将其与海南三亚港、八所港和清澜港一共5个港口均作为国际港口可使物流总成本降低;货物进出口贸易量和各港口外贸吞吐能力均对国际港口布局及港口间的协作分工有影响,增大其他港口外贸吞吐能力可降低物流总成本。

基于质量问题统计数据的某型车辆备件配置研究

基于交付用户使用后的某型特种车辆质量问题统计数据,对发生的质量问题进行了分类和分析,梳理出车辆易损件备件清单。最后对该产品备件配置存在的问题进行了探讨并提出了建议,以期对其他产品备件配置提供一定的借鉴。

基于两阶段搜索与动态资源分配的约束多目标进化算法

解决约束多目标优化问题(CMOP)的难点在于平衡目标优化和约束满足的同时兼顾解集的收敛性和多样性。为解决具有大型不可行区域和较小可行区域的复杂约束多目标优化问题,提出一种基于两阶段搜索与动态资源分配的约束多目标进化算法(TSDRA)。该算法在第一阶段通过忽略约束跨越不可行区域;然后在第二阶段通过动态分配两种计算资源协调局部开发和全局探索,兼顾算法的收敛性和多样性。在LIRCMOP和MW系列测试问题上进行的仿真实验结果表明,与四个代表性的算法CMOEA-MS(Constrained Multi-Objective Evolutionary Algorithm with Multiple Stages)、ToP(Two-phase)、PPS(Push and Pull Search)和MSCMO(Multi Stage Constrained Multi-Objective evolutionary algorithm)相比,所提算法在反转世代距离(IGD)和超体积(HV)上得到了更优异的结果。在LIRCMOP系列测试问题上,TSDRA获得了10个最佳的IGD值和9个最佳的HV值;在MW系列测试问题上,TSDRA获得了9个最佳的IGD值和10个最佳的HV值,表明所提算法可以更有效地解决具有大型不可行区域和较小可行区域的问题。

基于最小权覆盖的医药电商配送中心选址及区域覆盖优化研究

配送中心选址及区域划分是物流配送过程中的关键环节,直接决定了配送时效及配送成本,在当今电子商务领域显得尤为重要。本文针对国内医药电商企业,提出了一种考虑药品配送时效的配送中心选址策略;随后建立该问题的整数规划模型,采用最小权顶点覆盖方法描述问题,并通过优先队列分支限界算法对此模型进行求解,得出最优选址结果;最后按最小运费原则将被重复覆盖区域进行再划分,得到配送中心选址及区域划分最终方案。本文基于上述策略为国内某头部医药电商企业提供了两种选址方案:保留企业原有配送中心并确定新配送中心选址点(改进选址方案)和从企业所有需求节点中重新为配送中心选址(重选址方案),并使用企业真实销量和物流数据进行算例分析。

基于改进黑猩猩算法的异构多无人机协同任务分配

针对异构多无人机对地面多类型固定目标的任务分配问题,提出一种基于协同多任务分配模型和改进黑猩猩算法的任务分配方法。通过对四元组内元素的设定完成模型构建,建立总收益最高、威胁代价最低、总航程最短的多目标评价函数。使用改进黑猩猩算法完成模型求解,引入混沌反向学习策略提升初始种群分布的多样性,在迭代阶段使用抢食行为动态调整策略,提升了跳出局部最优解的能力。实验表明:相比原算法,改进黑猩猩算法所得任务分配方案在保持较高任务收益和较低威胁代价的同时,在两种规模场景下的平均总航程分别降低了22.6%和21.1%。