不确定运行时间环境下的车辆调度问题及启发式算法

考虑到物流公司或者配送中心车辆实际运行过程中时间的不确定性,提出了配送服务线路包含时间窗口、车辆容量约束的随机规划模型,以最小化车辆运行成本同时尽可能降低所服务顾客的不满意度.同时,又稍作改进给出了平均-风险模型,由于VRP问题是NP难的,给出了一种基于禁忌搜索的启发式算法,并以北京市13个点的为例,给出求解结果.     

A Lagrangean Heuristic for a Modular Capacitated Location Problem

This paper considers the Modular Capacitated Location Problem (MCLP) which consists of finding the location and capacity of the facilities, to serve a set of customers at a minimum total cost. Each customer has an associated demand and the capacity of each potential location must be chosen from a finite and discrete set of available capacities. Practical applications of this problem can be found in the location of warehouses, schools, health care services or other types of public services. For the MCLP different mixed integer linear programming models are proposed. The authors develop upper and lower bounds on the problem's optimal value and present computational results with randomly generated tests problems.     

同顺序流水作业排序问题的一个启发式算法

本文主要给出了同顺序m×n排序问题初始序的选取方法以及通过计算可避免出现高重循环的初始序的排序算法,然后又给出了利用矩阵可行线性质将初始序调试成较优序的可行方法.利用该文方法对n=15,m=3～14的144个例题计算,得出平均相对误差为3.145%的结果,对于m=3与m=4的128个例题计算,得出平均相对误差为0.6306%.统计结果表明该方法可在实际中进行应用.     

一种求解柔性资源约束前摄性项目调度问题的启发式算法

在不确定环境中,一个具有较高鲁棒性的进度计划可以保证项目的稳定实施。考虑到现实中资源可能具有多种技能,会对制定鲁棒性较高进度计划的过程产生影响,因此本文研究了柔性资源约束下前摄性项目调度优化问题。首先界定研究问题;然后从鲁棒性最大化的视角出发,构建了研究问题的优化模型,在对模型进行分析的基础上将其分解为经典鲁棒优化和资源技能分配两个子模型;随后设计了求解问题的基于削峰算法的启发式算法;最后用一个实际案例验证了算法有效性,并分析了关键参数对进度计划鲁棒性的影响,得到如下结论:项目进度计划鲁棒性随着项目工期的延长、资源可用量的增加或资源柔性的提高而增大。     

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.      

A Family of Stochastic Programming Test Problems Based on a Model for Tactical Manpower Planning

Ariyawansa and Felt (2001, 2004) have recently created a test problem collection for testing software for stochastic linear programs. This freely-available, web-based collection was originally created with 35 problem instances from 11 problem families representing a variety of application areas. The collection was created with plans for enriching it with problem instances based on different application areas from the research community. The work of Martel and Al-Nuaimi (1973) on manpower planning under uncertain demand represents an application area suitable for creating new problem instances to be added to the collection. The purpose of this paper is to describe the construction of a new family of stochastic programming test problems based on the work of Martel and Al-Nuaimi (1973). As part of our construction, we review the work of Martel and Al-Nuaimi (1973) leading to an extension of their models for which their solution procedure does not apply. The new test problems are based on this extension. We also present solutions to the test problems obtained using the software package CPA (2002) for stochastic programming developed by Ariyawansa, Felt and Sarich. Mathematics Subject Classifications (2000) 90C15, 90C90, 65K05. K. A. Ariyawansa: The work of this author was supported in part by the U.S. Army Research Office under Grant DAAD 19-00-1-0465.     

Asymptotic Analysis of a Greedy Heuristic for the Multi-Period Single-Sourcing Problem: The Acyclic Case

The multi-period single-sourcing problem that we address in this paper can be used as a tactical tool for evaluating logistics network designs in a dynamic environment. In particular, our objective is to find an assignment of customers to facilities, as well as the location, timing and size of production and inventory levels, that minimizes total assignment, production, and inventory costs. We propose a greedy heuristic, and prove that this greedy heuristic is asymptotically optimal in a probabilistic sense for the subclass of problems where the assignment of customers to facilities is allowed to vary over time. In addition, we prove a similar result for the subclass of problems where each customer needs to be assigned to the same facility over the planning horizon, and where the demand for each customer exhibits the same seasonality pattern. We illustrate the behavior of the greedy heuristic, as well as some improvements where the greedy heuristic is used as the starting point of a local interchange procedure, on a set of randomly generated test problems. These results suggest that the greedy heuristic may be asymptotically optimal even for the cases that we were unable to analyze theoretically.     

单机单转包商调度与外包联合优化问题的改进启发式算法

针对以总完工时间与总外包费用加权和为优化目标、总外包费用不超过给定上限的单机单转包商调度与外包联合优化问题,设计出一种改进的剔除型启发式算法。该算法通过运用动态规划技术求解新的辅助问题来获取初始外包工件集,并引入判定条件提前从初始外包工件集中剔除特定工件。为满足对总外包费用的上限约束,还利用新型的启发式筛选次序族逐一确定从当前外包工件集中剔除的工件。在仿真实验中,通过生成大量的测试算例,对比分析了改进算法与另2种已报道算法在求解质量、计算时间上的表现情况。实验结果表明所提出的改进算法在解的整体质量上具备显著的比较优势,并且能在5.6秒内完成对工件总数为1500的测试算例的求解。     

Heuristic Control of a Constraint-Based Algorithm for the Preemptive Job-Shop Scheduling Problem

In the recent years, constraint programming has been applied to a wide variety of academic and industrial non-preemptive scheduling problems, i.e., problems in which activities cannot be interrupted. In comparison, preemptive scheduling problems have received almost no attention from both the Operations Research and the Artificial Intelligence community. Motivated by the needs of a specific application, we engaged in a study of the applicability of constraint programming techniques to preemptive scheduling problems. This paper presents the algorithms we developed and the results we obtained on the preemptive variant of the famous job-shop scheduling problem. Ten heuristic search strategies, combined with two different constraint propagation techniques, are presented, and compared using two well-known series of job-shop scheduling instances from the literature. The best combination, which relies on limited discrepancy search and on edge-finding techniques, is shown to provide excellent solutions to the preemptive job-shop scheduling problem. A mean relative distance to the optimal solution of 0.32% is achieved in five minutes, on instances with 10 jobs and 10 machines (100 activities).     

呼叫中心坐席人员排班问题优化模型与算法研究

国内呼叫企业在保证每个坐席人员周内当值相同班次情况下,通过灵活安排周内当班日期与班次来制定排班方案。针对该实际排班场景,构建问题整数规划模型。通过对问题数据特征及优化性质分析,以及对班次人力有效满足区段电话服务需求的量化指标表征,分别提出两个构造性启发式算法。使用企业实例数据对模型算法进行计算实验。实验结果显示,整数规划模型适合于求解小规模排班问题最优解,而启发式算法能够以小计算成本获得大规模排班问题优化解。最后讨论保证员工上班规律性的同班次用工制度对企业人力成本控制的影响。     

同时加工排序问题的分支定界法和启发式算法

同时加工机器或者称为批加工机器是可以同时加工多个工件的机器．本文研究使带权总完工时间为最小的同时加工排序问题1|B|∑wjGj.这个问题的计算复杂性还没有解决．我们给出这个问题的精确解法——分支定界法和几个启发式算法，并且用较多实例对启发式算法的性能进行了比较．     

A Tabu Search Heuristic Procedure for Solving the Transportation Problem with Exclusionary Side Constraints

A new heuristic procedure for the transportation problem with exclusionary side constraints is developed and implemented. Tabu search, a meta-heuristic method, is used to guide the search to follow a path selectively to prevent from being trapped at local optimal solutions in order to find a global optimal or near global optimal solution. The simplex method on a graph is employed to lead the search from one solution to an adjacent solution in order to take advantage of the underlying network structure of the problem. In the procedure, net changes in cost and in infeasibility are used to measure the attractiveness of a move, and strategic oscillation is used to implement the intensification and diversification functions. A computational experiment was conducted to test the performance of the heuristic procedure and substantial computational results are reported. These results show that the new heuristic procedure finds very good quality solutions and outperforms an existing heuristic procedure in terms of both solution quality and CPU time.     

A Genetic Approach for Solving a Scheduling Problem in a Robotized Analytical System

We consider a robotized analytical system in which a chemical treatment has to be performed on a given set of identical samples. The objective is to carry out the chemical treatment on the whole set of samples in the shortest possible time. All constraints have to be satisfied since a modification of the chemical process could create unexpected reactions.We have developed a new robust method governed by a genetic algorithm to solve this scheduling problem. The crossover mechanism of this evolutionary method is based on an extension of the uniform crossover introduced by Syswerda (1989).The proposed approach can be adapted to other combinatorial problems where decisions, based on rules, have to be taken at each step of a constructive method.     

Maximum Principle for a Stochastic Optimal Control Problem and Application to Portfolio/Consumption Choice

We consider mainly an optimal control problem motivated by a portfolio and consumption choice problem in a financial market where the utility of the investor is assumed to have a given homogeneous form. A Pontryagin local maximum principle is obtained by using classical variational methods. We apply the result to make optimal portfolio and consumption decisions for the problem under consideration. The optimal selection coincides with the one obtained in Refs. 1 and 2, where the Bellman dynamic programming principle was used.     

Stochastic optimization of an urban rail timetable under time‐dependent and uncertain demand

Urban rail planning is extremely complex, mainly because it is a decision problem under different uncertainties. In practice, travel demand is generally uncertain, and therefore, the timetabling decisions must be based on accurate estimation. This research addresses the optimization of train timetable at public transit terminals of an urban rail in a stochastic setting. To cope with stochastic fluctuation of arrival rates, a two‐stage stochastic programming model is developed. The objective is to construct a daily train schedule that minimizes the expected waiting time of passengers. Due to the high computational cost of evaluating the expected value objective, the sample average approximation method is applied. The method provided statistical estimations of the optimality gap as well as lower and upper bounds and the associated confidence intervals. Numerical experiments are performed to evaluate the performance of the proposed model and the solution method.     

一类最小-最大车辆路线问题的启发式算法研究

针对个性化和多样性的需求,建立以缩短最长子线路为目标的最小-最大车辆路径问题模型, 并提出启发式算法求解。首先,采用自然数编码,使问题变得更简洁;用最佳保留选择法,以保证群体的多样性;引入爬山算法,加强局部搜索能力;其次,对遗传算法求得的精英种群再进行禁忌搜索,保证算法能够收敛到全局最优。最后,通过实例的计算,表明本算法均优于遗传算法和禁忌搜索算法,并为大规模解决实际问题提供思路。     

需要安装时间的平行多功能机排序问题的启发式算法

考虑需要安装时间的平行多功能机排序问题。在该模型中,每个工件对应机器集合的一个子集,其只能在这个子集中的任一台机器上加工,称这个子集为该工件的加工集合;工件分组,同组工件具有相同的加工时间和加工集合,不同组中的工件在同一台机器上连续加工需要安装时间,目标函数为极小化最大完工时间。对该问题NP-难的一般情况设计启发式算法:首先按照特定的规则将所有工件组都整组地安排到各台机器上,然后通过在各机器间转移工件不断改进当前最大完工时间。通过与下界的比较检验算法的性能,大量的计算实验表明,算法是实用而有效的。     

Shooting Methods for Numerical Solution of Stochastic Boundary-Value Problems

Abstract

In the present investigation, numerical methods are developed for approximate solution of stochastic boundary-value problems. In particular, shooting methods are examined for numerically solving systems of Stratonovich boundary-value problems. It is proved that these methods accurately approximate the solutions of stochastic boundary-value problems. An error analysis of these methods is performed. Computational simulations are given.     

Effective Heuristic Procedures for a Field Technician Scheduling Problem

This paper addresses a field technician scheduling problem faced by many service providers in telecommunication industry. The problem is to assign a set of jobs, at different locations with time windows, to a group of field technicians with different job skills. Such a problem can be viewed as a generalization of the well-known vehicle routing problem with time windows since technician skills need to be matched with job types. We designed and tested several heuristic procedures for solving the problem, namely a greedy heuristic, a local search algorithm, and a greedy randomized adaptive search procedure (GRASP). Our computational results indicate that GRASP is the most effective among them but requires more CPU time. However, the unique structure of GRASP allows us to exploit parallelism to achieve linear speed-up with respect to the number of machines used.     

Stochastic quasigradient methods for optimization of discrete event systems

In this paper, stochastic programming techniques are adapted and further developed for applications to discrete event systems. We consider cases where the sample path of the system depends discontinuously on control parameters (e.g. modeling of failures, several competing processes), which could make the computation of estimates of the gradient difficult. Methods which use only samples of the performance criterion are developed, in particular finite differences with reduced variance and concurrent approximation and optimization algorithms. Optimization of the stationary behavior is also considered. Results of numerical experiments and convergence results are reported.