Multi-mode Resource-constrained Project Scheduling Problem Research Articles

Multi-mode resource-constrained project scheduling using RCPSP and SAT solvers

This paper reports on a new solution approach for the well-known multi-mode resource-constrained project scheduling problem (MRCPSP). This problem type aims at the selection of a single activity mode from a set of available modes in order to construct a precedence and a (renewable and non-renewable) resource feasible project schedule with a minimal makespan. The problem type is known to be NP-hard and has been solved using various exact as well as (meta-)heuristic procedures. The new algorithm splits the problem type into a mode assignment and a single mode project scheduling step. The mode assignment step is solved by a satisfiability (SAT) problem solver and returns a feasible mode selection to the project scheduling step. The project scheduling step is solved using an efficient meta-heuristic procedure from literature to solve the resource-constrained project scheduling problem (RCPSP). However, unlike many traditional meta-heuristic methods in literature to solve the MRCPSP, the new approach executes these two steps in one run, relying on a single priority list. Straightforward adaptations to the pure SAT solver by using pseudo boolean non-renewable resource constraints has led to a high quality solution approach in a reasonable computational time. Computational results show that the procedure can report similar or sometimes even better solutions than found by other procedures in literature, although it often requires a higher CPU time.

A robust hybrid method for the multimode resource-constrained project scheduling problem

This paper presents the computational results of a robust hybrid algorithm for the multi-mode resource-constrained project scheduling problem (MRCPSP). In the presented approach a harmony search algorithm is combined with a new and effective ‘head-tail’ local search procedure based on a mixed integer linear programming (MILP) formulation. In order to illustrate the essence and viability of the proposed new approach, the computational results for the J30MM set from PSPLIB are reported. J30MM is the one of the ‘hardest’ multi-mode benchmark set of PSPLIB generated by Kolish and Sprecher.

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. In this paper, we propose and investigate two new ideas. On the one hand, we transform the problem of single objective MRCPSP to bi-objective one to cope with the potential violation of nonrenewable resource constraints. Relaxing the latter constraints allows to visit a larger solution set and thus to simplify the evolutionary operators. On the other hand, we build the fitness function not on a priori grid of the bi-objective space, but on an adaptive one relying on clustering techniques. This proposed idea aims at more relevant fitness values. We show that a clustering-based fitness function can be an appealing feature in multi-objective evolutionary algorithms since it may promote diversity and avoid premature convergence of the algorithms. Clustering heuristics require certainly computation time, but they are still competitive with respect to classical niche formation multi-objective genetic algorithm.

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.

Reactive scheduling in the multi-mode RCPSP

The multi-mode resource-constrained project scheduling problem (MRCPSP) involves the determination of a baseline schedule of the project activities, which can be executed in multiple modes, satisfying the precedence relations and resource constraints while minimizing the project duration. During the execution of the project, the baseline schedule may become infeasible due to activity duration and resource disruptions. We propose and evaluate a number of dedicated exact reactive scheduling procedures as well as a tabu search heuristic for repairing a disrupted schedule, under the assumption that no activity can be started before its baseline starting time. We report on promising computational results obtained on a set of benchmark problems.

An efficient algorithm for the multi-mode resource constrained project scheduling problem with resource flexibility

The scheduling problem under study may be viewed as an extension of the standard multi-mode resource-constrained project scheduling problem (MRCPSP) including multi-skilled labour and will be called as MRCPSP-MS. This problem requires an integration of resource limitation, labour skills and multiple possible execution modes for each task, and the objective is to minimise the overall project duration. This paper present a new tabu search (TS) algorithm using a powerful neighbourhood function based on a flow graph representation in order to implement various search strategies. The search of the solution space is carried out via two types of moves. Furthermore, the TS algorithm is embedded in a decomposition-based heuristic (DBH) which serve to reduce the solution space. The effectiveness of the new TS is demonstrated through extensive experimentation on different standard benchmark problem instances and proves that our results are competitive.

Optimizing Discounted Cash Flows in Project Scheduling—An Ant Colony Optimization Approach

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The multimode resource-constrained project-scheduling problem with discounted cash flows (MRCPSPDCF) is important and challenging for project management. As the problem is strongly nondeterministic polynomial-time hard, only a few algorithms exist and the performance is still not satisfying. To design an effective algorithm for the MRCPSPDCF, this paper proposes an ant colony optimization (ACO) approach. ACO is promising for the MRCPSPDCF due to the following three reasons. First, MRCPSPDCF can be formulated as a graph-based search problem, which ACO has been found to be good at solving. Second, the mechanism of ACO enables the use of domain-based heuristics to accelerate the search. Furthermore, ACO has found good results for the classical single-mode scheduling problems. But the utility of ACO for the much more difficult MRCPSPDCF is still unexplored. In this paper, we first convert the precedence network of the MRCPSPDCF into a mode-on-node (MoN) graph, which becomes the construction graph for ACO. Eight domain-based heuristics are designed to consider the factors of time, cost, resources, and precedence relations. Among these heuristics, the hybrid heuristic that combines different factors together performs well. The proposed algorithm is compared with two different genetic algorithms (GAs), a simulated annealing (SA) algorithm, and a tabu search (TS) algorithm on 55 random instances with at least 13 and up to 98 activities. Experimental results show that the proposed ACO algorithm outperforms the GA, SA, and TS approaches on most cases. </para>

Two-Phase Genetic Local Search Algorithm for the Multimode Resource-Constrained Project Scheduling Problem

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, the resource-constrained project scheduling problem with multiple execution modes for each activity is explored. This paper aims to find a schedule of activities such that the makespan of the schedule is minimized subject to the precedence and resource constraints. We present a two-phase genetic local search algorithm that combines the genetic algorithm and the local search method to solve this problem. The first phase aims to search globally for promising areas, and the second phase aims to search more thoroughly in these promising areas. A set of elite solutions is collected during the first phase, and this set, which acts as the indication of promising areas, is utilized to construct the initial population of the second phase. By suitable applications of the mutation with a large mutation rate, the restart of the genetic local search algorithm, and the collection of good solutions in the elite set, the strength of intensification and diversification can be properly adapted and the search ability retained in a long term. Computational experiments were conducted on the standard sets of project instances, and the experimental results revealed that the proposed algorithm was effective for both the short-term (with 5000 schedules being evaluated) and the long-term (with 50000 schedules being evaluated) search in solving this problem. </para>

Scheduling projects with heterogeneous resources to meet time and quality objectives

In service organizations, heterogeneity in workforce skills can lead to variation in end-product/service quality. The multi-mode, resource-constrained, project scheduling problem (MRCPSP), which assumes similar skills among resources in a given resource pool, accounts for differences in quality levels of individuals by assigning different activity durations depending on the skill level used. This approach is often inadequate to model the problem type investigated here. Using typical projects from the customer training division of a large telecommunications company (which motivated this research), a labor assignment problem using a successive work–time concept is formulated and solved using integer programming optimization procedures. The setting represents a multiple-project environment where projects are separate and independent, but require the same renewable resource mix for their completion. The paper demonstrates how the output of the model can be used to identify bottlenecks (or critical resource skills), and also demonstrates how cross-training the appropriately skilled groups or individuals can increase throughput. The approach guides decision-making concerning which workers to cross-train in order to extract the greatest benefits from worker-flexibility.

A multi-mode resource-constrained discrete time–cost tradeoff problem and its genetic algorithm based solution

The discrete time–cost tradeoff problem (DTCTP) is an important subject in the project scheduling theory and applications. Due to the fact that the resources used in projects in modern enterprises mainly belong to renewable resources, e.g. manpower resources, the general DTCTP is extended to a new multi-mode resource-constrained DTCTP model (MRC-DTCTP). The multi-mode resource-constrained project scheduling problem (MRCPSP) was referred and the renewable resource constraints were added to the general DTCTP. By predefining the resource price, the renewable resources are related to the project costs, including direct cost and indirect cost. Every activity can be executed in the crashing way in which the project direct costs are used to shorten the activity duration. According to the characteristics of the MRC-DTCTP, an improved genetic algorithm for solving it was developed and its effectiveness was verified by compared with the exact algorithm. Finally an entire time–cost tradeoff curve for a project network was drawn through computing project deadline problem, and the advantages of the MRC-DTCTP were investigated based on computation results.

Ant colony optimization with parameter adaptation for multi-mode resource-constrained project scheduling

An effective algorithm capable of solving the multi-mode resource-constrained project scheduling problem (MRCPSP) is an essential component for project planning and control since it can fully explo...

An efficient hybrid genetic algorithm for scheduling projects with resource constraints and multiple execution modes

Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) aims at finding the start times and execution modes for the activities of a project that optimize a given objective function while verifying a set of precedence and resource constraints. In this paper, we focus on this problem and develop a hybrid Genetic Algorithm (MM-HGA) to solve it. Its main contributions are the mode assignment procedure, the fitness function and the use of a very efficient improving method. Its performance is demonstrated by extensive computational results obtained on a set of standard instances and against the best currently available algorithms.

Exact and Heuristic Reactive Planning Procedures for Multimode Resource-Constrained Projects

The multi-mode resource-constrained project scheduling problem (MRCPSP) involves the determination of a baseline schedule of the project activities, which can be executed in multiple modes, satisfying the precedence relations and resource constraints while minimizing the project duration. During the execution of the project, the baseline schedule may become infeasible due to activity duration and resource disruptions. We propose and evaluate a number of dedicated exact reactive scheduling procedures as well as a tabusearch heuristic for repairing a disrupted schedule. We report on promising computational results obtained on a set of benchmark problems.

Modelling and solving a multimode and multisite industrial problem: Lagrangean relaxation and heuristic approaches

In this paper, we tackle the problem of scheduling multisite and multimode activities in order to minimise the project duration that meets the constraints imposed by limited resources. The industrial system is composed of many production sites, and each site has its own resources called local resources, and every site can receive resources called global resources. The objective is to support the repartition of all the lots of pieces on different sites in a cooperative way, and to assign resources. The system reduced to only one site highlights the well-known problem of the Multimode Resource-Constrained Project Scheduling Problem (MRCPSP). We propose a mathematical programming approach based on competitive feasible solutions and strong lower bounds, within quite reasonable computation times. The basic ingredients of this approach are the Lagrangean relaxation. We also propose a method based on stochastic descent with restart to compute large-sized industrial instances. The experiments show that this technique gives solutions close to the optimum. This seems to indicate that these resolution methods are good candidates for real industrial problems.

Energy-oriented deconstruction and recovery planning

The reduction of waste through the establishment of closed-loop material flows has an important role in creating a more sustainable built environment. Especially in deconstruction projects, participants could take advantage of the application of waste management and recovery strategies while adhering to the principle of ‘sustainable construction’. The opportunity for materials recovery depends on the type of deconstruction technique applied at a building's end-of-life. An integrated deconstruction–recovery planning approach for deconstruction projects is developed to include ecological as well as economic benefits. This planning approach is an extension of the multi-mode resource-constrained project-scheduling problem (MMRCPSP) from operations research. Although the general MMRCPSP considers time– and resource–resource trade-offs, the proposed extension incorporates energy–time–resource trade-offs. The energy–time–resource trade-offs reflect the realization of energy savings or costs over the life cycle of a building. Based on a life cycle energy analysis, recovery options can be selected for deconstructed components and materials dependent on the chosen deconstruction techniques (e.g. demolition, selective deconstruction, manual deconstruction, and deconstruction using various resources). La réduction des déchets par l'établissement de flux de matériaux en boucles fermées a un rôle important dans la création d'un milieu bâti plus durable. Dans les projets de démolition, en particulier, les participants pourraient tirer parti de l'application de stratégies de gestion des déchets et de récupération tout en respectant les principes de la construction durable. L'opportunité de la récupération de matériaux dépend du type de technique de démolition utilisée à la fin de la vie utile d'un bâtiment. Une méthode de planification intégrée de la démolition-récupération pour les projets de démolition est développée pour inclure des avantages écologiques et économiques. Cette méthode de planning est une prolongation du problème d'ordonnancement de projet à réaliser à l'aide de ressources en nombre limité à plusieurs modes (MMRCPSP) inspiré de la recherche opérationnelle. Bien que le MMRCPSP général considère les arbitrages concernant le temps et les ressources, l'extension proposée inclut des arbitrages portant sur l'énergie, le temps et les ressources. De tels arbitrages traduisent la réalisation d'économies d'énergie ou de coût sur le cycle de vie d'un bâtiment. En se basant sur l'analyse énergétique du cycle de vie, on peut choisir des options de récupération portant sur des éléments démolis et des matériaux en fonction de la technique de démolition choisie (par exemple, démolition, démolition sélective, démolition manuelle et démolition utilisant diverses ressources). déchets de la construction et de la démolition; démolition; cycle de vie; récupération de matériaux; planning de projet; recyclage

A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems

The particle swarm optimization (PSO) has been widely used to solve continuous problems. The discrete problems have just begun to be also solved by the discrete PSO. However, the combinatorial problems remain a prohibitive area to the PSO mainly in case of integer values. In this paper, we propose a combinatorial PSO (CPSO) algorithm that we take up challenge to use in order to solve a multi-mode resource-constrained project scheduling problem (MRCPSP). The results that have been obtained using a standard set of instances, after extensive experiments, prove to be very competitive in terms of number of problems solved to optimality. By comparing average deviations and percentages of optima found, our CPSO algorithm outperforms the simulated annealing algorithm and it is close to the PSO algorithm.

A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem

This paper considers the multimode resource-constrained project-scheduling problem (MRCPSP) with a minimum-makespan objective. An exact branch and cut algorithm is presented based on the integer linear programming (ILP) formulation of the problem. In the preprocessing stage, lower bounds on the distance between each pair of precedence-constrained activities are derived. These bounds are used to reduce the number of variables in the model and to generate cuts that tighten the linear programming relaxation. The solution process is accelerated by an adaptive branching scheme in conjunction with a bound-tightening scheme that is called iteratively after branching. To find good feasible solutions in the early stages of the computations, a high-level neighborhood search strategy known as local branching is included. Here, a neighborhood of a feasible solution is defined by the linear inequalities in the ILP model and is searched first. As implemented, the full algorithm is exact rather than heuristic in nature. Numerical results are reported for 20- and 30-activity benchmark problems. These are the largest instances available and are generally viewed to be notoriously difficult. Up until now, there were no confirmed optimal solutions for any of the 552 30-activity instances. We were able to find several better solutions and to show that at least 506 are optimal.

Fuzzy approach for production planning and detailed scheduling in paints manufacturing

Due to growing competition, small- and medium-sized companies face within supply chains the challenge of providing short and reliable throughput times while coping with uncertainties, especially concerning time parameters, in production planning and detailed scheduling. The application of fuzzy scheduling is an adequate way to model these uncertainties in a supply chain. The paper presents an approach for the fuzzy scheduling of hybrid flow shops based on the general multi-mode resource-constrained project-scheduling problem. The approach is validated in a case study of a small- and medium-sized enterprise producing paints in a batch production process.

Multimode Project Scheduling Based on Particle Swarm Optimization

Abstract: The multimode resource-constrained project scheduling problem (MRCPSP) considers both renewable and nonrenewable resources that have not been addressed efficiently in the construction field. This article introduces a methodology for solving the MRCPSP based on particle swarm optimization (PSO) that has not been utilized for this and other construction-related problems. The framework of the PSO-based methodology is developed. A particle representation formulation is proposed to represent the potential solution to the MRCPSP in terms of priority combination and mode combination for activities. Each particle-represented solution should be checked against the nonrenewable resource infeasibility and will be handled by adjusting the mode combination. The feasible particle-represented solution is transformed to a schedule through a serial generation scheme. Experimental analyses are presented to investigate the performance of the proposed methodology.

Solving the Multi-Mode Resource-Constrained Project Scheduling Problem with genetic algorithms

In this paper we consider the Multi-Mode Resource-Constrained Project Scheduling Problem with makespan minimisation as the objective. We have developed new genetic algorithms, extending the representation and operators previously designed for the single-mode version of the problem. Moreover, we have defined a new fitness function for the individuals who are infeasible. We have tested different variants of the algorithm and chosen the best to be compared to different heuristics previously published, using standard sets of instances included in PSPLIB. Results illustrate the good performance of our algorithm.