动态需求下车辆路径问题的周期性优化模型及求解

针对客户点不断更新的动态需求车辆路径问题,依据滚动时域对配送中心工作时间进行划分,提出基于延迟服务的周期性客户点实时重置策略,策略中延迟服务机制能结合车辆启动延迟系数对照当前时域的时间进行检验,满足所有客户点的服务需求,保证车辆满足中心时间窗约束。设计多阶段求解的混合变邻域人工蜂群算法对各时间片内子问题进行连续迭代优化,算法中子路径动态转变的设计能较好平衡原有客户点和新客户点对路径更新和车辆实时信息匹配的要求。算例验证及对比分析表明本文策略和算法在求解动态问题时的有效性和可行性。     

带工期指派的产品服务系统订单随机调度问题研究

针对由一个制造工厂和多个区域服务中心组成的服务型制造企业，研究了考虑生产时间和服务时间均具有随机性且工期可指派的产品服务系统（PSS）订单调度问题。首先以最小化订单提前、误工和工期指派费用的期望总额为目标构建问题的优化模型，然后分析目标函数近似值的最优性条件，据此提出加权最短平均生产时间排序规则，并结合该规则与插入邻域局部搜索设计了启发式算法对问题进行求解，最后通过数值仿真验证算法的可行性和有效性。研究表明，提前费用偏差对PSS订单调度与工期指派决策的影响很小，因此企业管理者无需准确估计库存费用也能制定出比较有效的PSS订单调度策略；而工期指派费用偏差对决策结果的影响非常大，因此企业管理者在决策时必须谨慎估计该项费用。     

A Dynamic Disaggregation Approach to Approximate Linear Programs for Network Revenue Management

The linear programming approach to approximate dynamic programming has received considerable attention in the recent network revenue management (RM) literature. A major challenge of the approach lies in solving the resulting approximate linear programs (ALPs), which often have a huge number of constraints and/or variables. Starting from a recently developed compact affine ALP for network RM, we develop a novel dynamic disaggregation algorithm to solve the problem, which combines column and constraint generation and exploits the structure of the underlying problem. We show that the formulation can be further tightened by considering structural properties satisfied by an optimal solution. We prove that the sum of dynamic bid‐prices across resources is concave over time. We also give a counterexample to demonstrate that the dynamic bid‐prices of individual resources are not concave in general. Numerical experiments demonstrate that dynamic disaggregation is often orders of magnitude faster than existing algorithms in the literature for problem instances with and without choice. In addition, adding the concavity constraints can further speed up the algorithm, often by an order of magnitude, for problem instances with choice.     

Control of interrelated research and development projects

The purpose of this paper is to examine a type of resource allocation problem arising in the context of research and development activities. The particular problem analyzed involves scheduling a group of projects in such a way that total cost is minimized while several precedence relations are satisfied and specific completion times are maintained. The primary difficulty results from the existence of commonalities that allow the successful completion of a particular project to be applied to several different purposes. A solution approach is developed which combines a one-pass network algorithm to deal with the precedence and time restrictions and a dynamic programming procedure to allocate the resources to each project.     

Surgical scheduling under uncertainty by approximate dynamic programming

Surgical scheduling consists of selecting surgeries to be performed within a day, while jointly assigning operating rooms, starting times and the required resources. Patients can be elective or emergency/urgent. The scheduling of surgeries in an operating theatre with common resources to emergency or urgent and elective cases is highly subject to uncertainties not only on the duration of an intervention but mainly on the arrival of emergency or urgent cases. At the beginning of the day we are given a candidate set of elective surgeries with and an expected duration and a time window the surgery must start, but the expected duration and the time window of an emergency or urgent case become known when the surgery arrives. The day is divided into decision stages. Due to the dynamic nature of the problem, at the beginning of each stage the planner can make decisions taking into account the new information available. Decisions can be to schedule arriving surgeries, and to reschedule or cancel surgeries not started yet. The objective is to minimize the total expected cost composed of terms related to refusing arriving surgeries, to canceling scheduled surgeries, and to starting surgeries out of their time window. We address the problem with an approximate dynamic programming approach embedding an integer programming formulation to support decision making. We propose a dynamic model and an approximate policy iteration algorithm making use of basis functions to capture the impact of decisions to the future stages. Computational experiments have shown with statistical significance that the proposed algorithm outperforms a lookahead reoptimization approach.     

Ant Colony System for a Dynamic Vehicle Routing Problem

An aboundant literature on vehicle routing problems is available. However, most of the work deals with static problems, where all data are known in advance, i.e. before the optimization has started. The technological advances of the last few years give rise to a new class of problems, namely the dynamic vehicle routing problems, where new orders are received as time progresses and must be dynamically incorporated into an evolving schedule. In this paper a dynamic vehicle routing problem is examined and a solving strategy, based on the Ant Colony System paradigm, is proposed. Some new public domain benchmark problems are defined, and the algorithm we propose is tested on them. Finally, the method we present is applied to a realistic case study, set up in the city of Lugano (Switzerland).     

Dynamic Programming and Hill-Climbing Techniques for Constrained Two-Dimensional Cutting Stock Problems

In this paper we propose an algorithm for the constrained two-dimensional cutting stock problem (TDC) in which a single stock sheet has to be cut into a set of small pieces, while maximizing the value of the pieces cut. The TDC problem is NP-hard in the strong sense and finds many practical applications in the cutting and packing area. The proposed algorithm is a hybrid approach in which a depth-first search using hill-climbing strategies and dynamic programming techniques are combined. The algorithm starts with an initial (feasible) lower bound computed by solving a series of single bounded knapsack problems. In order to enhance the first-level lower bound, we introduce an incremental procedure which is used within a top-down branch-and-bound procedure. We also propose some hill-climbing strategies in order to produce a good trade-off between the computational time and the solution quality. Extensive computational testing on problem instances from the literature shows the effectiveness of the proposed approach. The obtained results are compared to the results published by Alvarez-Valdés et al. (2002).     

Improved approximation algorithms for non-preemptive multiprocessor scheduling with testing

Multiprocessor scheduling, also called scheduling on parallel identical machines to minimize the makespan, is a classic optimization problem which has been extensively studied. Scheduling with testing is an online variant, where the processing time of a job is revealed by an extra test operation, otherwise the job has to be executed for a given upper bound on the processing time. Albers and Eckl recently studied the multiprocessor scheduling with testing; among others, for the non-preemptive setting they presented an approximation algorithm with competitive ratio approaching 3.1016 when the number of machines tends to infinity and an improved approximation algorithm with competitive ratio approaching 3 when all test operations take one unit of time each. We propose to first sort the jobs into non-increasing order of the minimum value between the upper bound and the testing time, then partition the jobs into three groups and process them group by group according to the sorted job order. We show that our algorithm achieves better competitive ratios, which approach 2.9513 when the number of machines tends to infinity in the general case; when all test operations each takes one time unit, our algorithm achieves even better competitive ratios approaching 2.8081.

     

An Arborescent Network Formulation and Dual Ascent Based Procedure for the Two-Stage Multi-Item Dynamic Demand Lotsize Problem

Traditional approaches for modeling and solving dynamic demand lotsize problems are based on Zangwill's single-source network and dynamic programming algorithms. In this paper, we propose an arborescent fixed-charge network (ARBNET) programming model and dual ascent based branch-and-bound procedure for the two-stage multi-item dynamic demand lotsize problem. Computational results show that the new approach is significantly more efficient than earlier solution strategies. The largest set of problems that could be solved using dynamic programming contained 4 end items and 12 time periods, and required 475.38 CPU seconds per problem. The dual ascent algorithms averaged .06 CPU seconds for this problem set, and problems with 30 end items and 24 time periods were solved in 85.65 CPU seconds. Similar results verify the superiority of the new approach for handling backlogged demand. An additional advantage of the algorithm is the availability of a feasible solution, with a known worst-case optimality gap, throughout the problem-solving process.     

The Ordered Cutting Stock Problem

The one‐dimensional cutting stock problem (CSP) is a classic combinatorial optimization problem in which a number of parts of various lengths must be cut from an inventory of standard‐size material. The classic CSP ensures that the total demand for a given part size is met but ignores the fact that parts produced by a given cutting pattern may be destined for different jobs. As a result, applying the classic CSP in a dynamic production environment may result in many jobs being open (or partially complete) at any point in time—requiring significant material handling or sorting operations. This paper identifies and discusses a new type of one‐dimensional CSP, called the ordered CSP, which explicitly restricts to one the number of jobs in a production process that can be open, or in process, at any given point in time. Given the growing emphasis on mass customization in the manufacturing industry, this restriction can help lead to a reduction in both in‐process inventory levels and material handling activities. A formal mathematical formulation is provided for the new CSP model, and its applicability is discussed with respect to a production problem in the custom door and window manufacturing industry. A genetic algorithm (GA) solution approach is then presented, which incorporates a customized heuristic for reducing scrap levels. Several different production scenarios are considered, and computational results are provided that illustrate the ability of the GA‐based approach to significantly decrease the amount of scrap generated in the production process.     

Approximate and Exact Algorithms for Constrained (Un) Weighted Two-dimensional Two-staged Cutting Stock Problems

In this paper we propose two algorithms for solving both unweighted and weighted constrained two-dimensional two-staged cutting stock problems. The problem is called two-staged cutting problem because each produced (sub)optimal cutting pattern is realized by using two cut-phases. In the first cut-phase, the current stock rectangle is slit down its width (resp. length) into a set of vertical (resp. horizontal) strips and, in the second cut-phase, each of these strips is taken individually and chopped across its length (resp. width).First, we develop an approximate algorithm for the problem. The original problem is reduced to a series of single bounded knapsack problems and solved by applying a dynamic programming procedure. Second, we propose an exact algorithm tailored especially for the constrained two-staged cutting problem. The algorithm starts with an initial (feasible) lower bound computed by applying the proposed approximate algorithm. Then, by exploiting dynamic programming properties, we obtain good lower and upper bounds which lead to significant branching cuts. Extensive computational testing on problem instances from the literature shows the effectiveness of the proposed approximate and exact approaches.     

下料问题与运输问题联合优化建模

本文研究了考虑子材运输的标准一维下料问题。建立了由生产商负责运输时,标准一维下料与运输协调优化整数规划模型,最小化母材使用成本,子材库存成本及子材运输成本。采用拉格朗日松弛技术对有关约束进行松弛和模型分解,设计基于序列规则和FFD规则的混合启发式算法求解模型。该算法由两部分组成,分别用于求解标准一维下料子问题和卖方运输子问题。通过随机产生的1800个算例,验证模型合理性与算法的有效性。与基于列生成法的两阶段算法解进行比较,平均总成本降低了17.57%,表明集成算法优于两阶段算法。     

The optimum traversal of a graph

For a given graph (network) having costs [c_ij] associated with its links, the present paper examines the problem of finding a cycle which traverses every link of the graph at least once, and which incurs the minimum cost of traversal. This problem (called thegraph traversal problem, or theChinese postman problem [9]) can be formulated in ways analogous to those used for the well-known travelling salesman problem, and using this apparent similarity, Bellman and Cooke [1] have produced a dynamic programming formulation. This method of solution of the graph traversal problem requires computational times which increase exponentially with the number of links in the graph. Approximately the same rate of increase of computational effort with problem size would result by any other method adapting a travelling salesman algorithm to the present problem.This paper describes an efficient algorithm for the optimal solution of the graph traversal problem based on the matching method of Edmonds [5, 6]. The computational time requirements of this algorithm increase as a low order (2 or 3) power of the number of links in the graph. Computational results are given for graphs of up to 50 vertices and 125 links.The paper then discusses a generalised version of the graph traversal problem, where not one but a number of cycles are required to traverse the graph. In this case each link has (in addition to its cost) a quantity q_ij associated with it, and the sum of the quantities of the links in any one cycle must be less than a given amount representing the cycle capacity. A heuristic algorithm for the solution of this problem is given. The algorithm is based on the optimal algorithm for the single-cycle graph traversal problem and is shown to produce near-optimal results.There is a large number of possible applications where graph traversal problems arise. These applications include: the spraying of roads with salt-grit to prevent ice formation, the inspection of electric power lines, gas, or oil pipelines for faults, the delivery of letter post, etc.     

On the Robust Single Machine Scheduling Problem

The single machine scheduling problem with sum of completion times criterion (SS) can be solved easily by the Shortest Processing Time (SPT) rule. In the case of significant uncertainty of the processing times, a robustness approach is appropriate. In this paper, we show that the robust version of the (SS) problem is NP-complete even for very restricted cases. We present an algorithm for finding optimal solutions for the robust (SS) problem using dynamic programming. We also provide two polynomial time heuristics and demonstrate their effectiveness.     

A New Dynamic Programming Decomposition Method for the Network Revenue Management Problem with Customer Choice Behavior

In this paper, we propose a new dynamic programming decomposition method for the network revenue management problem with customer choice behavior. The fundamental idea behind our dynamic programming decomposition method is to allocate the revenue associated with an itinerary among the different flight legs and to solve a single‐leg revenue management problem for each flight leg in the airline network. The novel aspect of our approach is that it chooses the revenue allocations by solving an auxiliary optimization problem that takes the probabilistic nature of the customer choices into consideration. We compare our approach with two standard benchmark methods. The first benchmark method uses a deterministic linear programming formulation. The second benchmark method is a dynamic programming decomposition idea that is similar to our approach, but it chooses the revenue allocations in an ad hoc manner. We establish that our approach provides an upper bound on the optimal total expected revenue, and this upper bound is tighter than the ones obtained by the two benchmark methods. Computational experiments indicate that our approach provides significant improvements over the performances of the benchmark methods.     

超高频数据的日内效应调整方法研究

日内效应在金融高频数据研究中已被广泛证实,是一种日内周期性运动的动态效应,它影响了以微观金融指标为参数的计量模型的准确估计。基于金融超高频持续期数据,本文首先论述了日内效应调整的重要性,然后引入自适应映射(SOM)的方法对日内效应进行调整。SOM是一种基于神经网络学习的特征提取方法,能够动态识别高维数据中的结构特征,克服了静态调整方法的不足。最后通过建立基于自回归条件持续期模型(ACD)的蒙特卡罗模拟实验,比较了三种日内效应调整方法的效果。模拟结果表明SOM方法在日内效应调整中更为有效和稳定,特别适合大数据条件下的周期性结构分析。     

面向动态评价的长效机制及其构建研究

事物的动态发展变化催生了对动态评价方法的需求。为解决动态评价中跨阶段动态可比性和对新增阶段的适应性等动态评价长效性需求问题，提出动态评价长效机制的构建原理。通过对数据标准化方式和多种评价方法的特征分析，在分析动态评价过程各环节技术的动态有效性基础上，从数据采集、数据标准化、评价方法的选择与使用等方面，基于线性加权模式下的竞优评析方法，构建了一种面向动态评价的“客观民主式”动态评价长效机制。最后，通过一个实例说明本研究在实际应用上的有效性。面向动态评价的长效评价机制为解决动态评价有效性问题提供了思路，可作为综合评价理论方法的一种有益补充。     

Clustering Binary Oligonucleotide Fingerprint Vectors for DNA Clone Classification Analysis

We considered the problem of clustering binarized oligonucleotide fingerprints that attempts to identify clusters. Oligonucleotide fingerprinting is a powerful DNA array based method to characterize cDNA and rRNA libraries and has many applications including gene expression profiling and DNA clone classification. DNA clone classification is the main application for the problem considered in this paper. Most of the existing approaches for clustering use normalized real intensity values and thus do not treat positive and negative hybridization signals equally. This is demonstrated in a series of recent publications where a discrete approach typically useful in the classification of microbial rRNA clones has been proposed. In the discrete approach, hybridization intensities are normalized and thresholds are set such that a value of 1 represents hybridization, a value of 0 represents no hybridization, and an N represents unknown, which is also called a missing value. A combinatorial optimization problem is then formulated attempting to cluster the fingerprints and resolve the missing values simultaneously. It has been examined that missing values cause much difficulty in clustering analysis and most clustering methods are very sensitive to them. In this paper, we turned a little back to the traditional clustering problem, which takes in no missing values but with the revised goal to stabilize the number of clusters and maintain the clustering quality. We adopted the binarizing scheme used in the discrete approach as it is shown to be typically useful for the clone classifications. We formulated such a problem into another combinatorial optimization problem. The computational complexity of this new clustering problem and its relationships to the discrete approach and the traditional clustering problem were studied. We have designed an exact algorithm for the new clustering problem, which is an A* search algorithm for finding a minimum number of clusters. The experimental results on two commonly tested real datasets demonstrated that the A* search algorithm runs fast and performs better than some popular hierarchical clustering methods, in terms of separating clones that have different characteristics with respect to the given oligonucleotide probes.Supported by NSERC and CFI.Supported by NSERC.Supported partially by NSERC, CFI, and NNSF Grant 60373012.     

复杂系统ANP-BOCR立体网络结构建构新方法

表达复杂决策问题的传统ANP-BOCR网络结构(即综合考虑收益(B)、机会(O)、成本(C)、风险(R)四类ANP(网络分析法)子网络结构所形成的新型网络结构)不仅忽视了隶属于不同B,O,C,R子网络中的准则集和准则之间所存在的依赖关系,而且没有科学反映O,R子网络内部因素随预期时刻不同所呈现出的动态变化性。此外,传统ANP-BOCR网络结构针对系统内部准则(集)的确定方法也缺乏科学严密性。为克服上述缺陷,基于DEMATEL(决策试行和评价实验室)和动态决策思维,提出一种全新的ANP-BOCR立体网络结构建构方法。相对于现有ANP-BOCR网络结构,新方法突破了传统ANP-BOCR固定不变的准则、方案结构体系,构建出立体维度框架下的动态决策网络结构,并且在确定系统内部准则(集)时运用DEMATEL体现出更强的科学性。实例对比验证结果表明新方法是科学合理的,能够为进一步完善ANP-BOCR方案优选方法提供前期理论基础。     

The permutation flow shop problem with blocking. A tabu search approach

This paper develops a fast tabu search algorithm to minimize makespan in a flow shop problem with blocking. Some properties of the problem associated with the blocks of jobs have been presented and discussed. These properties allow us to propose a specific neighbourhood of algorithms. Also, the multimoves are used that consist in performing several moves simultaneously in a single iteration and guide the search process to more promising areas of the solutions space, where good solutions can be found. It allow us to accelerate the convergence of the algorithm. Besides, a dynamic tabu list is proposed that assists additionally to avoid being trapped at a local optimum. The proposed algorithms are empirically evaluated and found to be relatively more effective in finding better solutions than attained by the leading approaches in a much shorter time. The presented ideas can be applied in many local search procedures.