Multi-objective multi-mode resource-constrained project scheduling with fuzzy activity durations in prefabricated building construction

Highlights

• We formulate a multiobjective MRCPSP with fuzzy activities in PB construction.

• We construct the interval value of the execution time to express it by fuzzy theory.

• We propose a hybrid CCEA to obtain the highly robust project scheduling.

• We improve CCEA with a self-adaptive mechanism and a self-adaptive selection process.

Abstract

Different from traditional project management, the prefabricated building (PB) construction project has a complex distributed supply chain model, and the overall project is completed by multi-stage cooperation. Therefore, the implementation process will be restricted by many constraints, and various uncertain factors will also interfere with the smooth implementation of the project. In order to improve the stability and reliability of the PB construction project implementation process, it is very important to study an effective robust project scheduling method considering resource constraints in an uncertain environment. In this paper, we formulate a PB construction resource-constrained project scheduling with multi-objective multi-mode, focus on the uncertainty of the execution time of the execution activity, and constructs the interval value of the execution time to express it through fuzzy theory; also considers the multiple objectives of PB construction project, including time-based profit, and cost-based profit. Secondly, we propose a hybrid cooperative co-evolution algorithm (HCOEA) to obtain the highly robust project scheduling, reduce the impact of the uncertainty of the execution time of the activity on the overall project. Resource-constrained project scheduling problem (RCPSP) is an NP-hard combinatorial optimization problem. This paper also needs to consider the complex combination of time-resource and/or time–cost constraints. At the same time, it is necessary to consider the impact of time changes in different mode combinations. Therefore, how to design an effective multi-objective optimization algorithm is very difficult. This paper design a Hybrid Cooperative Co-evolution Algorithm (HCOEA) with multi-stage representation for the activity sequencing and the resource allocation, further improve the search efficiency. We improve the cooperative co-evolution framework with a self-adaptive mechanism and a self-adaptive selection process. Finally, benchmarks and extended datasets with fuzzy processing time are adopted to test our HCOEA. Computational results show that the HCOEA performs better than the existing state-of-the-art methods.

Introduction

Project scheduling is a core technology which could ensure efficient implementation of projects. Considering how to allocate resources effectively, arrange project execution process reasonably, and realize the optimization of project scheduling efficiency in the actual complex environment, is the key to the application and promotion of project scheduling. Resource-constrained Project Scheduling Problem (RCPSP) widely exists in practice projects with various theoretical models. Most of them belong to NP hard problems, which attract the attention of lots of domestic and overseas scholars (Habibi et al., 2018, Issa and Tu, 2020, Pellerin et al., 2020).

Prefabricated building (PB) construction, which is different from the traditional buildings built on site, refers to a new type of buildings in which the (concrete, steel, and wood) components are produced in the prefabrication factory using industrial production, and assembled on site. Compared with traditional cast-in-place integral building, PB construction projects has lots of advantages, such as improving engineering quality, shortening construction period, saving labor force, and being environment friendly. However, the advantages mentioned before are hard to guarantee in the actual implementation process of PB construction projects. As shown in Table 1, the implementation process is affected by different resource constraints and uncertainties in multiple stages:

• Components’ quality assurance problem, such as component size, positioning deviation, grouting hole blockage in the production stage, finished product protection in transportation stage, insufficient bond strength in the assembly stage, etc.

• Project cost problems, such as high production cost, high transportation cost, low assembly rate and unreasonable combination of prefabricated components, all of which will lead to cost increase.

• Project implementation progress problem, such as the component production capacity of manufacturer, inventory backlog, low efficiency in on-site assembly, long time in precision correction and unreasonable construction organization.

PB construction projects management is faced with (1) more complex constraints; (2) the impact of various uncertainties on the project implementation process. Therefore, the scheduling research of PB construction projects could ensure the effective and reasonable activity arrangement under the complex resource constraints. What’ s more, it could ensure the project implementation progress, construction quality, construction cost optimization and construction period in a complex and variable project.

The scheduling problems of PB construction projects is more complicated than the traditional RCPSP model, which means that a PB construction project must suffers from design, manufacturing, logistics, on-site assembly, and post-service, and then completed by multi-party cooperation. In details, complex resource types and diverse resource attributes may be involved in the implementation process; The activities in manufacturing process and on-site assembly process can be completed in distributed and parallel manner; In executing process, the activity scheduling is flexible, and the execution time under different resource combination modes maybe uncertainty; Compared with the traditional RCPSP model, which has a single goal with the shortest project completion time, the scheduling of prefabricated construction projects requires comprehensive consideration of multiple goals. In this paper, the multi-mode RCPSP model with multiple resource combinations is considered in the modeling of assembly construction project scheduling problem.

This paper also considers the uncertainty in PB construction project scheduling. Currently, uncertainty project scheduling researches mainly include stochastic scheduling, robust scheduling and fuzzy scheduling. Stochastic scheduling uses the discrete (or continuous) probability distributions to express the uncertainty. Robust scheduling is a measure of the resilience target of the scheduling in the face of uncertain parameters and unexpected events. Some researchers argue that many uncertainties in scheduling problems are related to subjective human perceptions, such as delivery time, delay time, and processing time estimates. Fuzzy scheduling is the use of fuzzy set theory to describe these uncertainties and define the satisfaction of constraints. In the PB construction projects, the uncertainty of activity execution time is more appropriately set to be a fuzzy set. Therefore, we expressing it by constructing execution time interval by fuzzy theory. What’s more, we considered multiple benefit composition of the prefabricated construction project scheduling, including Time-based benefit, and Cost-based benefit in order to build a multi-objective optimization model.

Traditional RCPSP is a classic NP-hard combinatorial optimization problem. In recent years, many scholars have proposed heuristic algorithms, Evolutionary Algorithms (EA), or hybrid algorithms which incorporate multiple evolutionary algorithms to solve it (Pellerin et al., 2020, Lin et al., 2020, Servranckx and Vanhoucke, 2019). Based on the above-mentioned algorithms, we consider the complex combination of activity modes, as well as the combination of time-resource and/or time–cost constraints, and try to reduce the impact of the uncertainty with activity execution time in the overall project, in order to achieve the multi-objective optimization. Therefore, the design of algorithm is challenging. In this paper, based on cooperative co-evolution algorithm, we improve the search efficiency of activity pattern combination by designing a multi-stage activity sorting-resource allocation method. A self-adaptive mechanism and a self-adaptive selection process can improve the robustness of project scheduling.

The rest of this paper is organized as follows: ‘Literature review’ section presents the research results of project scheduling and optimization algorithms in recent years; The mathematical modeling of multi-objective multi-mode PCPSP with fuzzy activity durations in PB construction is shown in ‘Problem description’ section; The implementation processes of the proposed a hybrid cooperative co-evolution algorithm (HCOEA) are presented in ‘Hybrid COEA’ section; The numerical experiments are designed and the numerical results compared with the existing state-of-the-art methods are discussed to demonstrate the effectiveness and efficiency of the proposed algorithm in ‘Numerical experiments’ section. The conclusion of this paper and future researches is presented in ‘Conclusion’ section.