Decision support for unrelated parallel machine scheduling with discrete controllable processing times

In a manufacturing or service system, the actual processing time of a job can be controlled by the amount of an indivisible resource allocated, such as workers or auxiliary facilities. In this paper, we consider unrelated parallel-machine scheduling problems with discrete controllable processing times. The processing time of a job is discretely controllable by the allocation of indivisible resources. The planner must make decisions on whether or how to allocate resources to jobs during the scheduling horizon to optimize the performance measures. The objective is to minimize the total cost including the cost measured by a standard criterion and the total processing cost. We first consider three scheduling criterions: the total completion time, the total machine load, and the total earliness and tardiness penalties. If the number of machines and the number of possible processing times are fixed, we develop polynomial time algorithms for the considered problems. We then consider the minimization problem of the makespan cost plus the total processing cost and present an integer programming method and a heuristic method to solve the studied problem.     

A coordinated scheduling of production-and-delivery under dynamic delivery cost environments

This paper considers a coordination scheduling of production and delivery, where delivery cost depends on time period for delivery, but not dependent on individual jobs. The objective is to find a coordinated production-and-delivery schedule to minimize sum of the scheduling cost (either one of makespan, sum of completion times, or maximum lateness) and delivery cost. The problem is proved to be strongly NP-hard for all the objective measures tested. Some restricted cases of the problem are also characterized for their complexities, for which the associated dynamic programming algorithms are derived.     

基于联姻遗传算法的混合FloWshop提前/拖期调度问题

混合流水车间(Flowshop)提前／拖期调度问题的目标是4~_r-件的提前／拖期惩罚成本最小，这是一个NP完全问题，很难用一般的方法解决。文中首先给出了问题的数学模型，然后采用联姻遗传算法求解该问题。仿真结果表明此算法能有效地解决该类复杂调度问题。     

项目调度与物料订购集成优化研究综述

在项目管理实践中,活动安排与物料供应相互影响、相互制约,需要对这两个决策事项进行协同管理和规划.项目调度与物料订购集成优化问题(project scheduling and material ordering problem, PSMOP)研究的是如何合理制定项目调度和物料采购协同计划,以实现项目总成本最低、净现值最大、总工期最短等目标. PSMOP因其重要的理论价值和应用前景,近年来受到学术界和产业界的广泛关注.鉴于此,对国内外项目调度与物料订购集成优化的相关研究成果进行系统性总结与梳理:首先,介绍PSMOP问题及其常见的目标函数;其次,针对确定和不确定环境,分别总结了考虑不同特征的集成优化问题研究进展;然后,归纳了PSMOP常用求解算法及其在实践领域的应用情况;最后,指出未来进一步的研究方向.     

A decomposition-based stochastic programming approach for the project scheduling problem under time/cost trade-off settings and uncertain durations

Resource allocation in project networks allows for the control of the processing time of an activity under time–cost tradeoff settings. In practice, project decisions are made in advance when activity durations are still highly uncertain. Given an activity-on-node project network and a set of execution modes for each activity, we consider the problem of deciding how and when to execute each activity to minimize project completion time or total cost with respect to captured activity durations. The inherent stochasticity is represented using a set of discrete scenarios in which each scenario is associated with a probability of occurrence and a realization of activity durations. In this paper, we propose a path-based two-stage stochastic integer programming approach in which the execution modes are determined in the first stage while the second stage performs activity scheduling according to the realizations of activity durations, hence, providing flexibility in the scheduling process at subsequent stages. The solution methodology is based on a decomposition algorithm which has been implemented and widely tested using a large number of test instances of varying size and uncertainty. The reported computational results demonstrate that the proposed algorithm converges fast to the optimal solution and present the benefits of using the stochastic model as opposed to the traditional deterministic model that considers only expected values of activity durations.     

基于前摄策略的项目调度优化方法研究*

为了解决不确定性因素对项目调度造成的扰动,在综合考虑项目资源紧张度、网络图结构复杂度等因素影响的前提下,对关键链和非关键链分别添加适当时间缓冲,减小了不确定性因素带来的扰动,提高了项目调度的健壮性。在此基础上提出以在制品水平和净成本最低为目标的项目调度优化方法;最后通过大量仿真验证,结果表明该方法优于文献中的项目调度方法。     

Scheduling jobs with simultaneous considerations of controllable processing times and learning effect

This paper considers a scheduling problem with general job-dependent learning curves and controllable processing times on a single machine. The objective is to determine the optimal compressions of the processing times and the optimal sequence of jobs so as to minimize some total cost functions, which consist of regular and non-regular functions and the processing time compressions. It shows that the problem can be solved by an assignment problem and thus can be solved in polynomial time. Some extensions of the problem are also given.

     

Robust scheduling on a single machine to minimize total flow time

In a real-world manufacturing environment featuring a variety of uncertainties, production schedules for manufacturing systems often cannot be executed exactly as they are developed. In these environments, schedule robustness that guarantees the best worst-case performance is a more appropriate criterion in developing schedules, although most existing studies have developed optimal schedules with respect to a deterministic or stochastic scheduling model. This study concerns robust single machine scheduling with uncertain job processing times and sequence-dependent family setup times explicitly represented by interval data. The objective is to obtain robust sequences of job families and jobs within each family that minimize the absolute deviation of total flow time from the optimal solution under the worst-case scenario. We prove that the robust single machine scheduling problem of interest is NP-hard. This problem is reformulated as a robust constrained shortest path problem and solved by a simulated annealing-based algorithmic framework that embeds a generalized label correcting method. The results of numerical experiments demonstrate that the proposed heuristic is effective and efficient for determining robust schedules. In addition, we explore the impact of degree of uncertainty on the performance measures and examine the tradeoff between robustness and optimality.     

Hybrid genetic algorithms with dispatching rules for unrelated parallel machine scheduling with setup time and production availability

This article considers the unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times and machine-dependent processing times. Furthermore, the machine has a production availability constraint to each job. The objective of this problem is to determine the allocation policy of jobs and the scheduling policy of machines to minimize the total completion time. To solve the problem, a mathematical model for the optimal solution is derived, and hybrid genetic algorithms with three dispatching rules are proposed for large-sized problems. To assess the performance of the algorithms, computational experiments are conducted and evaluated using several randomly generated examples.     

Single machine scheduling problems with resource dependent release times

We consider two single machine scheduling problems with resource dependent release times that can be controlled by a non-increasing convex resource consumption function. In the first problem, the objective is to minimize the total resource consumption with a constraint on the sum of job completion times. We show that a recognition version of the problem is NP-complete. In the second problem, the objective is to minimize the weighted total resource consumption and sum of job completion times with an initial release time greater than the total processing times. We provide some optimality conditions and show that the problem is polynomially solvable.     

Logistical support scheduling under stochastic travel times given an emergency repair work schedule

Stochastic factors during the operational stage could have a significant influence on the planning results of logistical support scheduling for emergency roadway repair work. An optimal plan might therefore lose its optimality when applied in real world operations where stochastic disturbances occur. In this study we employ network flow techniques to construct a logistical support scheduling model under stochastic travel times. The concept of time inconsistency is also proposed for precisely estimating the impact of stochastic disturbances arising from variations in vehicle trip travel times during the planning stage. The objective of the model is to minimize the total operating cost with an unanticipated penalty cost for logistical support under stochastic traveling times in short term operations, based on an emergency repair work schedule, subject to related operating constraints. This model is formulated as a mixed-integer multiple-commodity network flow problem and is characterized as NP-hard. To solve the problem efficiently, a heuristic algorithm, based on problem decomposition and variable fixing techniques, is proposed. A simulation-based evaluation method is also presented to evaluate the schedules obtained using the manual method, the deterministic model and the stochastic model in the operation stage. Computational tests are performed using data from Taiwan’s 1999 Chi-Chi earthquake. The preliminary test results demonstrate the potential usefulness of the proposed stochastic model and solution algorithm in actual practice.     

A bicriteria approach to minimize the total weighted number of tardy jobs with convex controllable processing times and assignable due dates

We study a single-machine scheduling problem in a flexible framework where both job processing times and due dates are decision variables to be determined by the scheduler. The model can also be applied for quoting delivery times when some parts of the jobs may be outsourced. We analyze the problem for two due date assignment methods and a convex resource consumption function. For each due date assignment method, we provide a bicriteria analysis where the first criterion is to minimize the total weighted number of tardy jobs plus due date assignment cost, and the second criterion is to minimize total weighted resource consumption. We consider four different models for treating the two criteria. Although the problem of minimizing a single integrated objective function can be solved in polynomial time, we prove that the three bicriteria models are NP\mathcal{NP}-hard for both due date assignment methods. We also present special cases, which frequently occur in practice, and in which all four models are polynomially solvable.     

单台批处理机生产运输协调合作博弈调度问题

研究单台批处理机生产与生产前运输的协调调度问题,目标函数为最小化与完成时间相关的生产总成本.以工件为博弈方,以联盟的最大成本节省为特征函数,将调度问题转换为合作博弈模型.针对相同运输时间与加工时间的情形,证明该合作博弈具有非空核,beta规则可得一个核分配.针对一般问题,设计Q-learning算法求解联盟最优调度,并利用beta规则对节省的成本进行分配.数值算例验证了合作博弈模型的可行性以及Q-learning算法与beta规则对节省成本分配的有效性.     

A fuzzy random resource-constrained scheduling model with?multiple projects and its application to a working procedure in?a?large-scale water conservancy and hydropower construction project

The aim of this paper is to deal with resource-constrained multiple project scheduling problems (rc-mPSP) under a fuzzy random environment by a hybrid genetic algorithm with fuzzy logic controller (flc-hGA), to a large-scale water conservancy and hydropower construction project in the southwest region of China, whose main project is a dam embankment. The objective functions in this paper are to minimize the total project time (that is the sum of the completion time for all projects) and to minimize the total tardiness penalty of multiple projects, which is the sum of penalty costs for all the projects. After describing the problem of the working procedure in the project and presenting the mathematical formulation model of a resource-constrained project scheduling problem under a fuzzy random environment, we give some definitions and discuss some properties of fuzzy random variables. Then, a method of solving solution sets of fuzzy random multiple objective programming problems is proposed. Because traditional optimization techniques could not cope with the rc-mPSP under a fuzzy random environment effectively, we present a new approach based on the hybrid genetic algorithm (hGA). In order to improve its efficiency, the proposed method hybridized with the fuzzy logic controller (flc) concept for auto-tuning the GA parameters is presented. For the practical problems in this paper, flc-hGA is proved the most effective and most appropriate compared with other approaches. The computer generated results validate the effectiveness of the proposed model and algorithm in solving large-scale practical problems.     

Theoretical aspects of multicriteria flight gate scheduling: deterministic and fuzzy models

This paper addresses the airport flight gate scheduling problem with multiple objectives. The objectives are to maximize the total flight gate preferences, to minimize the number of towing activities, and to minimize the absolute deviation of the new gate assignment from a so-called reference schedule. The problem examined is a multicriteria multi-mode resource-constrained project scheduling problem with generalized precedence constraints or time windows. While in previous approaches the problem has been simplified to a single objective counterpart, we tackle it directly by a multicriteria metaheuristic, namely Pareto Simulated Annealing, in order to get a representative approximation of the Pareto front. Possible uncertainty of input data is treated by means of fuzzy numbers.     

Valiant load-balanced robust routing algorithm for multi-granularity connection requests in traffic-grooming WDM mesh networks

The paper considers the problem of establishing robust routes for multi-granularity connection requests in traffic-grooming WDM mesh networks and proposes a novel Valiant load-balanced robust routing scheme for the hose uncertain model. Our objective is to minimize the total network cost when construct the stable virtual topology that assure robust routing for all possible multi-granularity connection requests under the hose model. Since the optimization problem is shown to be NP-complete, two heuristic algorithms are proposed and evaluated. Finally we compare the traffic throughput of the virtual topology by Valiant load-balanced robust routing scheme with that of the traditional traffic-grooming algorithm under the same total network cost by computer simulation.     

考虑“时间-资源”的大型客机协同研制GERT网络优化

研究大型客机协同研制过程中项目活动时间和投入资源具有不确定性的图示评审技术(GERT)网络优化问题.采用GERT网络表征复杂项目研制过程,给出基于GERT的项目完成费用计算方法,提出项目时间与资源投入数量影响下的完工实现概率表征方式;为实现对复杂产品研制项目中时间-费用-资源优化调整,针对项目各活动和整体完工时间的不确定性,建立总完工时间、资源、实现概率受限情况下的时间规划与资源调度优化模型,并给出问题求解的差分进化启发式算法;考虑到大型客机全面试制过程是衡量能否按期完工的关键,以此过程为例进行案例分析,从而表明所提出方法的可行性和有效性.     

Multi-mode resource constrained project scheduling and contractor selection: Mathematical formulation and metaheuristic algorithms

Contractor selection is a matter of particular attraction for project managers whose aim is to complete projects considering time, cost and quality issues. Traditionally, project scheduling and contractor selection decisions are made separately and sequentially. However, it is usually necessary to satisfy some principles and obligations that impose hard constraints to the problem under consideration. Ignoring this important issue and making project scheduling and contractor selection decisions consecutively may be suboptimal to a holistic view that makes all interrelated decisions in an integrated manner. In this paper, an integrated bi-objective optimization model is proposed to deal with Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) and Contractor Selection (CS) problem, simultaneously. The objective of the proposed model is to minimize the total costs of the project, and minimize the makespan of the project, simultaneously. To solve the integrated MRCPSP-CS, two multi-objective meta-heuristic algorithms, Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization algorithm (MOPSO), are adopted, and 30 test problems of different sizes are solved. The parameter tuning is performed using the Taguchi method. Then, diversification metric (DM), mean ideal distance (MID), quality metric (QM) and number of Pareto solutions (NPS) are used to quantify the performance of meta-heuristic algorithms. Analytic Hierarchy Process (AHP), as a prominent multi-attribute decision-making method, is used to determine the relative importance of performance metrics. Computational results show the superior performance of MOPSO compared to NSGA-II for small-, medium- and large-sized test problems. Moreover, a sensitivity analysis shows that by increasing the number of available contractors, not only the makespan of the project is shortened, but also, the value of NPS in the Pareto front increases, which means that the decision maker(s) can make a wider variety of decisions in a more flexible manner.     

Using meta-heuristics for project scheduling under mode identity constraints

Mode identity and resource constrained project scheduling problem (MIRCPSP) is a substantial generalization of the well-known multi-mode problem. It arises when certain activities in the project are interdependent. That is, the set of all activities in the project are partitioned into disjoint subsets where all activities forming one subset have to be processed in the same mode. This paper addresses project scheduling problem with resource and mode identity constraints to minimize the project makespan. This problem is strongly NP-hard and three meta-heuristic algorithms namely imperialist competitive algorithm, simulated annealing and differential evolution are proposed to solve it. In order to improve the quality of the employed algorithms a local search and learning module is combined with the meta-heuristic algorithms. The performance of the algorithms is evaluated on 180 test problems by statistically comparing their solution in term of the objective function and computational times. The obtained computational results indicate that the integration of the learning module and the proposed algorithm is efficient and effective.     

Procurement scheduling for complex projects with fuzzy activity durations and lead times

Material procurement is a vital activity for manufacturing complex products like ships and aircrafts with long manufacturing cycle times. The project activities are interlinked through numerous precedence and succession rules. Given these interdependencies, it is difficult to ascertain the durations of the activities precisely at planning stage and creates uncertainty in the requirement dates of the items. The lead times of items are also not known accurately and result in uncertainty in the availability dates. Consequently, inventory holding and shortage costs incurred cannot be crisply defined. The objective of this paper is to develop a procurement scheduling model considering the above uncertainties.We have developed a method to calculate fuzzy holding and shortage costs and used those as fuzzy cost coefficients in the procurement scheduling model. It minimizes the sum of the above costs under budget constraints and generates optimal ordering schedule. It is applied for procurement scheduling of a real ship building project. Two types of sensitivity analyses were performed: first to understand the effect of variation of degree of uncertainty on total cost and on stage budget requirements and second to study the effect of changes in allocated stage budget parameters on total cost. The results indicate that total cost can be reduced significantly if stage wise budgets are determined considering the uncertainties rather than allocating budget upfront and treating them as constraints. The sensitivity analyses performed, helps in identifying the most sensitive stage of the project and determine the ranges in which stage-wise budgets can be varied.