A genetic algorithm for multi-mode resource constrained project scheduling problem

This article considers a general class of nonpreemptive multi-mode resource-constrained project scheduling problems in which activity durations depend on committed renewable resources (multi-mode time resource tradeoff). We propose a genetic algorithm for these problems and compare it with a stochastic scheduling method proposed by Drexl and Gruenewald. Computational results show that the proposed genetic algorithm is superior to the stochastic scheduling method.     

An automatic algorithm selection approach for the multi-mode resource-constrained project scheduling problem

This paper investigates the construction of an automatic algorithm selection tool for the multi-mode resource-constrained project scheduling problem (MRCPSP). The research described relies on the notion of empirical hardness models. These models map problem instance features onto the performance of an algorithm. Using such models, the performance of a set of algorithms can be predicted. Based on these predictions, one can automatically select the algorithm that is expected to perform best given the available computing resources. The idea is to combine different algorithms in a super-algorithm that performs better than any of the components individually. We apply this strategy to the classic problem of project scheduling with multiple execution modes. We show that we can indeed significantly improve on the performance of state-of-the-art algorithms when evaluated on a set of unseen instances. This becomes important when lots of instances have to be solved consecutively. Many state-of-the-art algorithms perform very well on a majority of benchmark instances, while performing worse on a smaller set of instances. The performance of one algorithm can be very different on a set of instances while another algorithm sees no difference in performance at all. Knowing in advance, without using scarce computational resources, which algorithm to run on a certain problem instance, can significantly improve the total overall performance.     

A faster exact method for solving the robust multi-mode resource-constrained project scheduling problem

This paper presents a mixed-integer linear programming formulation for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. We consider a two-stage robust optimisation approach and find solutions that minimise the worst-case project makespan, whilst assuming that activity durations lie in a budgeted uncertainty set. Computational experiments show that this easy-to-implement formulation is many times faster than the current state-of-the-art solution approach for this problem, whilst solving over 40% more instances to optimality over the same benchmarking set.     

A genetic algorithm for the preemptive and non-preemptive multi-mode resource-constrained project scheduling problem

In this paper we present a genetic algorithm for the multi-mode resource-constrained project scheduling problem (MRCPSP), in which multiple execution modes are available for each of the activities of the project. We also introduce the preemptive extension of the problem which allows activity splitting (P-MRCPSP). To solve the problem, we apply a bi-population genetic algorithm, which makes use of two separate populations and extend the serial schedule generation scheme by introducing a mode improvement procedure. We evaluate the impact of preemption on the quality of the schedule and present detailed comparative computational results for the MRCPSP, which reveal that our procedure is amongst the most competitive algorithms.     

The multi-mode resource-constrained project scheduling problem with generalized precedence relations

In this paper, we tackle the challenging problem of scheduling activities to minimize the project duration, in which the activities (a) are subject to generalized precedence relations, (b) require units of multiple renewable, non-renewable and doubly constrained resources for which a limited availability is imposed, and (c) can be performed in one of several different ways, reflected in multiple activity scenarios or modes. These multiple modes give rise to several kinds of trade-offs (time/resource, time/cost and resource/resource trade-offs) which allow for a more efficient allocation and use of resources. We present a local search-based solution methodology which is able to handle many real-life project scheduling characteristics such as time-varying resource requirements and availabilities, activity ready times, due dates and deadlines, activity overlaps, activity start time constraints and other types of temporal constraints.     

Metaheuristics for multi-mode capital-constrained project payment scheduling

This paper involves the multi-mode capital-constrained project payment scheduling problem, where the objective is to assign activity modes and payments so as to maximize the net present value (NPV) of the contractor under the constraint of capital availability. In the light of different payment patterns adopted, four optimization models are constructed using the event-based method. For the NP-hardness of the problem, metaheuristics, including tabu search and simulated annealing, are developed and compared with multi-start iterative improvement and random sampling based on a computational experiment performed on a data set generated randomly. The results indicate that the loop nested tabu search is the most promising procedure for the problem studied. Moreover, the effects of several key parameters on the contractor’s NPV are investigated and the following conclusions are drawn: The contractor’s NPV rises with the increase of the contractor’s initial capital availability, the payment number, the payment proportion, or the project deadline; the contractor has a decreasing marginal return as the contractor’s initial capital availability goes up; the contractor’s NPVs under the milestone event based payment pattern are not less than those under the other three payment patterns.     

Adaptive policies for multi-mode project scheduling under uncertainty

In this paper we propose an adaptive model for multi-mode project scheduling under uncertainty. We assume that there is a due date for concluding the project and a tardiness penalty for failing to meet this due date, and that several distinct modes may be used to undertake each activity. We define scheduling policies based on a set of thresholds. The starting time of the activity is compared with those thresholds in order to define the execution mode.We propose a procedure, based on the electromagnetism heuristic, for choosing a scheduling policy. In computational tests, we conclude that the adaptive scheduling policy found by using the model and the heuristic solution procedure is consistently better than the optimal non-adaptive policy. When the different modes have very different characteristics and there is a reasonable difference between the average duration of the project and the due date, the cost advantage of the adaptive policy becomes very significant.     

A hybrid rank-based evolutionary algorithm applied to multi-mode resource-constrained project scheduling problem

We consider the multi-mode resource-constrained project scheduling problem (MRCPSP), where a task has different execution modes characterized by different resource requirements. Due to the nonrenewable resources and the multiple modes, this problem is NP-hard; therefore, we implement an evolutionary algorithm looking for a feasible solution minimizing the makespan.     

A branch-and-bound procedure for the multi-mode resource-constrained project scheduling problem with minimum and maximum time lags

The paper presents an exact procedure for a general resource-constrained project scheduling problem where multiple modes are available for the performance of the individual activities and minimum as well as maximum time lags between the different activities may be given. The objective is to determine a mode and a start time for each activity such that all constraints are observed and the project duration is minimized. Project scheduling problems of this type occur, e.g. in process industries. The solution method is a depth-first search based branch-and-bound procedure. It makes use of a branching strategy where the branching rule is selected dynamically. The solution approach is an integration approach where the modes and start times are determined simultaneously. Within an experimental performance analysis this procedure is compared with existing solution procedures.     

An experimental investigation of metaheuristics for the multi-mode resource-constrained project scheduling problem on new dataset instances

In this paper, an overview is presented of the existing metaheuristic solution procedures to solve the multi-mode resource-constrained-project scheduling problem, in which multiple execution modes are available for each of the activities of the project. A fair comparison is made between the different metaheuristic algorithms on the existing benchmark datasets and on a newly generated dataset. Computational results are provided and recommendations for future research are formulated.     

Railway scheduling reduces the expected project makespan over roadrunner scheduling in a multi-mode project scheduling environment

The Critical Chain Scheduling and Buffer Management (CC/BM) methodology, proposed by Goldratt (Critical chain, 1997), introduced the concepts of feeding buffers, project buffers and resource buffers as well as the roadrunner mentality. This last concept, in which activities are started as soon as possible, was introduced in order to speed up projects by taking advantage of predecessors finishing early. Later on, the railway scheduling concept of never starting activities earlier than planned was introduced as a way to increase the stability of the project, typically at the cost of an increase in the expected project makespan. In this paper, we will indicate a realistic situation in which railway scheduling improves both the stability and the expected project makespan over roadrunner scheduling.     

Simulated annealing and tabu search for multi-mode project payment scheduling

This paper involves the multi-mode project payment scheduling problem where the activities can be performed with one of several discrete modes and the objective is to assign activities’ modes and progress payments so as to maximize the net present value of the contractor under the constraint of project deadline. Using the event-based method the basic model of the problem is constructed and in terms of the different payment rules it is extended as the progress based, expense based, and time based models further. For the strong NP-hardness of the problem which is proven by simplifying it to the deadline subproblem of the discrete time–cost tradeoff problem, we develop two heuristic algorithms, namely simulated annealing and tabu search, to solve the problem. The two heuristic algorithms are compared with the multi-start iterative improvement method as well as random sampling on the basis of a computational experiment performed on a data set constructed by ProGen project generator. The results show that the proposed simulated annealing heuristic algorithm seems to be the most promising algorithm for solving the defined problem especially when the instances become larger. In addition, the effects of several key parameters on the net present value of the contractor are analyzed and some conclusions are given based on the results of the computational experiment.     

Tabu search for multi-mode resource-constrained project scheduling with schedule-dependent setup times

In this paper, a multi-mode resource-constrained project scheduling problem with schedule-dependent setup times is considered. A schedule-dependent setup time is defined as a setup time dependent on the assignment of resources to activities over time, when resources are, e.g., placed in different locations. In such a case, the time necessary to prepare the required resource for processing an activity depends not only on the sequence of activities but, more generally, on the locations in which successive activities are executed. Activities are non-preemptable, resources are renewable, and the objective is to minimize the project duration. A local search metaheuristic—tabu search is proposed to solve this strongly NP-hard problem, and it is compared with the multi-start iterative improvement method as well as with random sampling. A computational experiment is described, performed on a set of instances based on standard test problems constructed by the ProGen project generator. The algorithms are computationally compared, the results are analyzed and discussed, and some conclusions are given.     

Branch-and-price approach for the multi-skill project scheduling problem

This work introduces a procedure to solve the multi-skill project scheduling problem (MSPSP) (Néron and Baptista, International symposium on combinatorial, optimization (CO’2002), 2002). The MSPSP mixes both the classical resource constrained project scheduling problem and the multi-purpose machine model. The aim is to find a schedule that minimizes the completion time (makespan) of a project, composed of a set of activities. In addition, precedence relations and resources constraints are considered. In this problem, resources are staff members that master several skills. Thus, a given number of workers must be assigned to perform each skill required by an activity. Practical applications include the construction of buildings, as well as production and software development planning. We present a column generation approach embedded within a branch-and-price (B&P) procedure that considers a given activity and time-based decomposition approach. Obtained results show that the proposed B&P procedure is able to reach optimal solutions for several small and medium sized instances in an acceptable computational time. Furthermore, some previously open instances were optimally solved.     

A branch-and-bound algorithm for the resource-constrained project scheduling problem

We describe a time-oriented branch-and-bound algorithm for the resource-constrained project scheduling problem which explores the set of active schedules by enumerating possible activity start times. The algorithm uses constraint-propagation techniques that exploit the temporal and resource constraints of the problem in order to reduce the search space. Computational experiments with large, systematically generated benchmark test sets, ranging in size from thirty to one hundred and twenty activities per problem instance, show that the algorithm scales well and is competitive with other exact solution approaches. The computational results show that the most difficult problems occur when scarce resource supply and the structure of the resource demand cause a problem to be highly disjunctive.     

Proactive policies for the stochastic resource-constrained project scheduling problem

The resource-constrained project scheduling problem involves the determination of a schedule of the project activities, satisfying the precedence and resource constraints while minimizing the project duration. In practice, activity durations may be subject to variability. We propose a stochastic methodology for the determination of a project execution policy and a vector of predictive activity starting times with the objective of minimizing a cost function that consists of the weighted expected activity starting time deviations and the penalties or bonuses associated with late or early project completion. In a computational experiment, we show that our procedure greatly outperforms existing algorithms described in the literature.     

A hybrid metaheuristic for the resource-constrained project scheduling problem

This study presents a hybrid metaheuristic ANGEL for the resource-constrained project scheduling problem (RCPSP). ANGEL combines ant colony optimization (ACO), genetic algorithm (GA) and local search strategy. The procedures of ANGEL are as follows. First, ACO searches the solution space and generates activity lists to provide the initial population for GA. Next, GA is executed and the pheromone set in ACO is updated when GA obtains a better solution. When GA terminates, ACO searches again by using a new pheromone set. ACO and GA search alternately and cooperatively in the solution space. This study also proposes an efficient local search procedure which is applied to yield a better solution when ACO or GA obtains a solution. A final search is applied upon the termination of ACO and GA. The experimental results of ANGEL on the standard sets of the project instances show that ANGEL is an effective method for solving the RCPSP.     

Two empirical uncertain models for project scheduling problem

The project scheduling problem with uncertain activity durations is considered, and two types of models for uncertain project scheduling problems are established according to different management requirements. These models are transformed to their crisp forms, which may be solved by classical optimization methods. For the models that could not be transformed to their crisp forms, an uncertain simulation is employed to approximate uncertain functions. Finally, two numerical examples are given to illustrate the usefulness of proposed models.