A note on the paper “Resource-constrained project scheduling: Notation,classification, models and methods” by Brucker et al.

The great variety of project scheduling problems studied in the ever growing literature motivated the recent development of classification schemes. In a recent paper (European Journal of Operational Research 112 (1999) 3–41), Brucker et al. make the claim that, so far, no classification scheme exists which is compatible with what is commonly accepted in machine scheduling and introduce a new classification. In this note, we critically review major shortcomings of the suggested scheme which place heavy limitations on its potential use.     

A heuristic solution framework for the resource constrained (multi-)project scheduling problem with sequence-dependent transfer times

We consider the problem of scheduling multiple projects subject to joint resource constraints. Most approaches proposed in the literature so far are based on the unrealistic assumption that resources can be transferred from one project to the other without any expense in time or cost. In order to contribute to closing this gap to reality, we generalise the multi-project scheduling problem by additionally including sequence- and resource-dependent transfer times, which represent setup activities necessary when a resource is removed from one project and reassigned to another (or from one job to another within the same project). In this paper, we define the modified resource constrained multi-project scheduling problem with transfer times (called RCMPSPTT), which aims at minimising the multi-project duration for the single-project approach or the mean project duration for the multi-project approach. We formulate both perspectives as an integer linear program, propose priority rule based solution procedures and present results of comprehensive computational experiments. Provided that the combination of scheduling scheme and priority rules is chosen appropriately, the procedures obtain good results. In particular, resource oriented priority rules are identified to be successful.     

Packing problems and project scheduling models: an integrating perspective

This paper considers two problem classes, namely packing and project scheduling problems that are important to researchers as well as practitioners. The two problem categories are described, and a classification is given for the different kinds of packing problems and project scheduling concepts. While both problem classes are different with respect to their fields of application, similarities of their mathematical structures are examined. It is shown that all packing problems considered here are special cases of models for project scheduling. The aim is to indicate which project scheduling models can be used to capture the different types of packing problems. Finally, some implications for research on optimisation algorithms for these two problem classes are discussed, and the applicability of the results of this work in practice are pointed out.     

Time and work generalised precedence relationships in project scheduling with pre-emption: An application to the management of Service Centres

In this paper we present an application of project scheduling concepts and solution procedures for the solution of a complex problem that comes up in the daily management of many company Service Centres. The real problem has been modelled as a multi-mode resource-constrained project scheduling problem with pre-emption, time and work generalised precedence relationships with minimal and maximal time lags between the tasks and due dates. We present a complete study of work GPRs which includes proper definitions, a new notation and all possible conversions amongst them. Computational results that show the efficiency of the proposed hybrid genetic algorithm and the advantages of allowing pre-emption are also presented.     

Crossdocking— Just in Time scheduling: an alternative solution approach

In this paper, a scheduling problem which allows a warehouse to function as a crossdock where transit storage time for cargo is minimized according to Just in Time scheduling is studied. A model that uses the machine scheduling notation to describe the problem is written. As the problem is NP-hard, a solution approach based on a combination of two metaheuristics, Reactive GRASP and Tabu Search (RGTS), is provided. Experiments are carried out to determine the usefulness of this approach. The results obtained from the exact method that uses the ILOG CPLEX 9.1 solver for 16 problem instances and the results obtained from the RGTS metaheuristic scheduling algorithm and two other algorithms proposed by other authors for the same problem instances are discussed. Analysis and comparisons are made.     

On scheduling an unbounded batch machine

A batch machine is a machine that can process up to c jobs simultaneously as a batch, and the processing time of the batch is equal to the longest processing time of the jobs assigned to it. In this paper, we deal with the complexity of scheduling an unbounded batch machine, i.e., c=+∞. We prove that minimizing total tardiness is binary NP-hard, which has been an open problem in the literature. Also, we establish the pseudopolynomial solvability of the unbounded batch machine scheduling problem with job release dates and any regular objective. This is distinct from the bounded batch machine and the classical single machine scheduling problems, most of which with different release dates are unary NP-hard. Combined with the existing results, this paper provides a nearly complete mapping of the complexity of scheduling an unbounded batch machine.     

问题Pm|rj,B|∑Cj的多项式时间近似算法

本文针对同型机分批排序问题Pm|rj,B|∑Cj进行了研究,给出了该问题在批容量B及机器台数m为常数情况下的多项式时间近似算法(以下简称PTAS);在B为常数时设计出了问题1|rj,B|∑WjCj的计算时间更少的PTAS．     

A new probabilistic approach to the path criticality in stochastic PERT

The notion of critical path is a key issue in the temporal analysis of project scheduling in deterministic setting. The very essence of the CPM consists in identifying the critical path, i.e., the longest path in a project network, because this path conveys information on how long it should take to complete the project to the project manager. The problem how can a stochastic counterpart of the deterministic critical path be defined is an important question in stochastic PERT. However, in the literature of stochastic PERT this question has so far almost been ignored, and the research into the random nature of a project duration has mainly been concentrated on the completion time in stochastic PERT in which any concrete special path is not specified. In the present paper we attempt to take first steps to fill this gap. We first developed a probabilistic background theory for univariate and bivariate marginal distributions of path durations of stochastic PERT whose joint path durations are modelled by multivariate normal distribution. Then, a new probabilistic approach to the comparison of path durations is introduced, and based on this comparison we define the concept of probabilistically critical path as a stochastic counterpart of the deterministic critical path. Also, an illustrative simple example of PCP and numerical results on the established probability bounds are presented.     

Approximability of two-machine no-wait flowshop scheduling with availability constraints

We consider in this paper the two-machine no-wait flowshop scheduling problem in which each machine may have an unavailable interval. We present a polynomial time approximation scheme for the problem when the unavailable interval is imposed on only one machine, or the unavailable intervals on the two machines overlap.     

加工时间可控单机加权总完工时间Pareto优化研究

针对单机环境最优化加权总完工时间问题,当工件加工时间可通过分配资源进行压缩时,研究对工件的加工次序和时间压缩量的优化,从而权衡调度性能目标和资源成本目标。调度性能目标为压缩后工件的加权总完工时间,资源成本目标为工件压缩量的线性函数。此问题复杂性已被证明为NP-hard,为弥补较少有研究从Pareto优化角度求解该问题有效前沿的不足,针对经典NSGA-II求解时易早熟收敛的特点,采用算法混合方式进行优化方法研究。融合归档式多目标模拟退火算法跳出局部极值的优势,启用外部存档策略提升种群的多样性,采用主从模式的并行结构提升求解效率。最后为检验优化方法的有效性,一方面通过对Benchmark测试函数ZDT1-6的求解,表明混合算法对不同结构和形状目标函数兼具普适性和有效性;另一方面结合问题特点设计有效编码方式,针对随机生成算例进行求解。通过分析有效前沿收敛性和多样性,验证了所提方法对于优化加工时间可控单机加权总完工时间问题的有效性。     

带机器准备时间的平行机排序问题

研究了带机器准备时间的m台平行机排序问题,设计出了一个多项式时间近似方案(PTAS),并给出了一个机器数m为固定常数的情形下的全多项式时间近似方案(FPTAS).     

Scheduling parallel machines with inclusive processing set restrictions and job release times

We consider the problem of scheduling a set of jobs with different release times on parallel machines so as to minimize the makespan of the schedule. The machines have the same processing speed, but each job is compatible with only a subset of those machines. The machines can be linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process. We present an efficient algorithm for this problem with a worst-case performance ratio of 2. We also develop a polynomial time approximation scheme (PTAS) for the problem, as well as a fully polynomial time approximation scheme (FPTAS) for the case in which the number of machines is fixed.     

Deteriorating jobs scheduling on a single machine with release dates,rejection and a fixed non-availability interval

This paper studies single machine scheduling with a fixed non-availability interval. The processing time of a job is a linear increasing function of its starting time, and each job has a release date. A job is either rejected by paying a penalty cost or accepted and processed on the machine. The objective is to minimize the makespan of the accepted jobs and the total rejection penalties of the rejected jobs. We present a fully polynomial-time approximation scheme for the problem. We also show that the special case without non-availability interval can be solved using the same method with a lower order.     

Some no-wait shops scheduling problems: Complexity aspect

We investigate the computational complexity of no-wait shops scheduling problems. The problem of finding optimal finish time schedules is shown to be NP-hard for flowshops with two machine centres where each machine centre has one or more parallel machines for processing tasks. The complexity results are also reported for no-wait shops scheduling when all nonzero tasks have unit or identical processing time requirement. A polynomial time algorithm for 3-machine flowshops is proposed for optimal finish time schedules. Finding optimal finish time schedules in 2-machine jobshops in NP-hard. Also we establish NP-hard results for 3-machine jobshops for both optimal finish time and mean flow time schedules. Some results are deduced with the present work and with those reported earlier.     

The wafer probing scheduling problem (WPSP)

The wafer probing scheduling problem (WPSP) is a variation of the parallel-machine scheduling problem, which has many real-world applications, particularly, in the integrated circuit (IC) manufacturing industry. In the wafer probing factories, the jobs are clustered by their product types, which must be processed on groups of identical parallel machines and be completed before the due dates. Further, the job processing time depends on the product type, and the machine setup time is sequence dependent on the orders of jobs processed. Since the wafer probing scheduling problem involves constraints on job clusters, job-cluster dependent processing time, due dates, machine capacity, and sequence dependent setup time, it is more difficult to solve than the classical parallel-machine scheduling problem. In this paper, we formulate the WPSP as an integer programming problem. We also transform the WPSP into the vehicle routing problem with time windows (VRPTW), a well-known network routing problem which has been investigated extensively. An illustrative example is given to demonstrate the proposed transformation. Based on the provided transformation, we present three efficient algorithms to solve the WPSP near-optimally.     

Disruption management for resource-constrained project scheduling

In this paper, we study the problem of how to react when an ongoing project is disrupted. The focus is on the resource-constrained project scheduling problem with finish–start precedence constraints. We begin by proposing a classification scheme for the different types of disruptions and then define the constraints and objectives that comprise what we call the recovery problem. The goal is to get back on track as soon as possible at minimum cost, where cost is now a function of the deviation from the original schedule. The problem is formulated as an integer linear program and solved with a hybrid mixed-inter programming/constraint programming procedure that exploits a number of special features in the constraints. The new model is significantly different from the original one due to the fact that a different set of feasibility conditions and performance requirements must be considered during the recovery process. The complexity of several special cases is analysed. To test the hybrid procedure, 554 20-activity instances were solved and the results compared with those obtained with CPLEX. Computational experiments were also conducted to determine the effects of different factors related to the recovery process.     

A review and classification on distributed permutation flowshop scheduling problems

The Distributed Permutation Flowshop Scheduling (DPFS) problem is one of the fastest-growing topics in the scheduling literature, which in turn is among the most prolific fields in Operational Research (OR). Although the problem has been formally stated only twelve years ago, the number of papers on the topic is growing at a rapid pace, and the rising interest –both from academics and practitioners– on distributed manufacturing paradigms seems to indicate that this trend will continue to increase. Possibly as a side effect of this steady growth, the state-of-the-art on many decision problems within the field is far from being clear, with substantial overlaps in the solution procedures, lack of (fair) comparisons against existing methods, or the use of different denominations for the same problem, among other issues. In this paper, we carry out a review of the DPFS literature aimed at providing a classification and notation for DPFS problems under a common framework. Within this framework, contributions are exhaustively presented and discussed, together with the state-of-the-art of the problems and lines for future research.     

Exploiting process plan flexibility in production scheduling: A multi-objective approach

When solving a product/process design problem, we must exploit the available degrees of freedom to cope with a variety of issues. Alternative process plans can be generated for a given product, and choosing one of them has implications on manufacturing functions downstream, including planning/scheduling. Flexible process plans can be exploited in real time to react to machine failures, but they are also relevant for off-line scheduling. On the one hand, we should select a process plan in order to avoid creating bottleneck machines, which would deteriorate the schedule quality; on the other one we should aim at minimizing costs. Assessing the tradeoff between these possibly conflicting objectives is difficult; actually, it is a multi-objective problem, for which available scheduling packages offer little support. Since coping with a multi-objective scheduling problem with flexible process plans by an exact optimization algorithm is out of the question, we propose a hierarchical approach, based on a decomposition into a machine loading and a scheduling sub-problem. The aim of machine loading is to generate a set of efficient (non-dominated) solutions with respect to the load balancing and cost objectives, leaving to the user the task of selecting a compromise solution. Solving the machine loading sub-problem essentially amounts to selecting a process plan for each job and to routing jobs to the machines; then a schedule must be determined. In this paper we deal only with the machine loading sub-problem, as many scheduling methods are already available for the problem with fixed process plans. The machine loading problem is formulated as a bicriterion integer programming model, and two different heuristics are proposed, one based on surrogate duality theory and one based on a genetic descent algorithm. The heuristics are tested on a set of benchmark problems.     

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts.     

Joint production and preventive maintenance scheduling for a single degraded machine by considering machine failures

Production scheduling and maintenance planning are two interdependent issues that most often have been investigated independently. Although both preventive maintenance (PM) and minimal repair affect availability and failure rate of a machine, only a few researchers have considered this interdependency in the literature. Furthermore, most of the existing joint production and preventive maintenance scheduling methods assume that machine is available during the planning horizon and consider only a possible level for PM. In this research, an integrated model is proposed that coordinates preventive maintenance planning with single-machine scheduling to minimize the weighted completion time of jobs and maintenance cost, simultaneously. This paper not only considers multiple PM levels with different costs, times and reductions in the hazard rate of the machine, but also assumes that a machine failure may occur at any time. To illustrate the effectiveness of the suggested method, it is compared to two situations of no PM and a single PM level. Eventually, to tackle the suggested problem, multi-objective particle swarm optimization and non-dominated sorting genetic algorithm (NSGA-II) are employed and their parameters are tuned Furthermore, their performances are compared in terms of three metrics criteria.