A multi-objective GA-based optimisation for holistic Manufacturing , transportation and Assembly of precast construction

Resource scheduling of construction proposals allows project managers to assess resource requirements, provide costs and analyse potential delays. The Manufacturing, transportation and Assembly (MtA) sectors of precast construction projects are strongly linked, but considered separately during the scheduling phase. However, it is important to evaluate the cost and time impacts of consequential decisions from manufacturing up to assembly. In this paper, a multi-objective Genetic Algorithm-based (GA-based) searching technique is proposed to solve unified MtA resource scheduling problems (which are equivalent to extended Flexible Job Shop Scheduling Problems). To the best of the authors’ knowledge, this is the first time that a GA-based optimisation approach is applied to a holistic MtA problem with the aim of minimising time and cost while maximising safety. The model is evaluated and compared to other exact and non-exact models using instances from the literature and scenarios inspired from real precast constructions. Crown Copyright © 2016 Published by B.V. All rights reserved.


Introduction
Prefabrication has been around for many decades, even centuries in the US and many European countries. However, its concept and construction practices are evolving. The Renaissance architecture and master builder Andrea Palladio standardised and prefabricated columns and stairs because of the growing demand for palaces and villas of the same style [1]. Prefabrication was 5 then used in Europe for replacing houses that were destroyed in World War I. After World War II, there was a need for rapid and low-cost prefabricated housing for military personnel in the US [2]. Thus, there has been a continual need for prefabrication around the world for centuries, but the need is ever changing with the time and new technologies.
Design for Manufacturing and Assembly (DfMA) is a simultaneous design and engineer- 10 ing approach where construction components are manufactured and (sub-)assembled in a factory or warehouse, before being delivered to a construction site for installation. DfMA makes use of prefabrication techniques in order to utilise construction schedule, cost, workforce, safety and quality.
When optimising prefabrication, it is crucial how a project is divided into smaller parts such as a manufacturing line or an assembly line. By then combining smaller parts, larger elements can be 15 incorporated into the building system. Haas [3] identified the driving factors being cost and schedule for adopting prefabrication in industrial projects as the most critical factors (see FIGURE 1a).
The results also show that DfMA techniques have a significant positive impact on safety, quality and efficiency at every stage of the project. The time and cost savings due to prefabrication is reported as 66% and 65% in American projects as shown in FIGUREs 1b and 1c. 20 (a) (b) (c) DfMA might not always be a better choice than conventional construction, i.e., transporting structural materials to the building site and assembling on-site [5]. For instance, considerable cost overruns and project management issues have been associated with prefabrication from manufacturing up to assembly. The decision on whether prefabricating components of a building or 25 even an entire building is often based on subjective judgement rather than a thorough analysis of consequential decisions in the MtA sectors [6,7].
Scheduling in a precast construction project is a temporary execution plan of a DfMA proposal. A project schedule reports on the time and order, in which tasks need to take place, and their allocated resources. It reflects required costs and resources to deliver the project; it can provide 30 delay analysis to avoid exceeding the scope of the project or budgetary constraints. The schedule might highlight potential problems before they arise. Resource scheduling is an assignment problem and describes in detail when to accomplish tasks and how to utilise resources assuring the project's objectives. Scheduling requires selecting resource types (such as machineries, cranes, and workforce), determining the required number of each resource, and allocating them to simultane- 35 ously executed jobs (e.g., manufacturing a number of different components) over time to maximise productivity subject to the constraints (e.g., limited number of workforce, early start dates, late finish date). A sufficient number and type of resources is crucial for managing demand fluctuation, procurement processes and machine failures. Each sector can process a limited number of tasks at a time; each resource can execute at most one task at a time. Resource scheduling affects and is 40 affected by the manufacturing factory, transportation options and the construction site.
Nowadays, resource scheduling of a DfMA plan is not performed comprehensively: On the one hand, the available decision-making support tools do not cover the combined performance attributes of MtA sectors while evaluating prefabricated construction methods. On the other hand, they do not consider an optimal schedule for the combined MtA sectors before comparing conven-45 tional construction plan to prefabricated construction one. It is therefore essential to implement a decision support tool which considers all three MtA sectors as a unified system and acknowledges multiple objectives of the construction project. Hence, this paper proposes a Genetic Algorithmbased (GA-based) technique for solving a unified MtA construction system. The contributions are: 50 • The prefabrication scheduling problem has been considered as a holistic/unified MtA problem which needs to be solved.
• Due to the complexity of this unified MtA construction scheduling problem (which is equivalent to a complex extended Flexible Job Shop Scheduling Problem), a GA-based optimisation algorithm is applied for the first time. This non-exact model will return a 55 good sub-optimal result in less time than exact methods.
• The presented GA-based technique is multi-objective with one dominant objective function.
To evaluate the quality of the proposed GA for solving flexible job shop problems, the model is compared with other exact and non-exact models using instances from the literature and scenarios 60 inspired by real data from precast construction projects. Section 2 provides a summary of the available prefabrication decision-making tools and construction scheduling models and identifies the issues of excising algorithms. The detailed description of the problem in the prefabricated construction, input/output decision variables, resource constrains, the optimisation objectives and the framework for resource scheduling a unified MtA system are described in Section 3. This leads to defining the MtA system in terms of a Resourceconstrained Extended Flexible Job Shop Scheduling (REFJSS) problem with the aim of minimising the total completion time and cost. These types of problems are NP-complete problems and computationally demanding to solve [8]. Section 4 presents the MILP formulation for the REFJSS and the assumptions. Evolutionary algorithms such as the GA are suitable in finding a solution 70 that is close to the optimal and satisfies the constraints of complex problems. In order to solve the REFJSS problem, a GA-based approach is presented in Section 5, along with a custom tool developed in C# that allows evaluating different prefabrication scenarios. The numerical results of the presented algorithm for different instances from real world scenarios and the literature are presented in Section 6. The general conclusions and future work are summarised in Section 7. 75

Background
Having presented the practical advantages of developing a decision support tool and optimising the schedule for a unified MtA system, Section 2.1 summarises the available decisionmaking tools for choosing a construction method. In Section 2.2, an overview of the current construction scheduling models is provided. 80

Decision-making Tools for Construction Techniques
With regards to construction prefabrication, Murtaza et al. [9] developed the MOdulariz Decision EXpert (MODEX) system to help judging the feasibility and financial benefits of modular prefabrication for a power plant project. MODEX is based on a hybrid expert system, combining an Expert Decision System and a Decision Support System. It follows decision rules set by experts 85 in its feasibility analysis and reports the cost of different degrees of prefabrication in the financial 3 analysis. In the feasibility analysis, MODEX asks a user a series of qualitative questions regarding different factors that influence the prefabrication process. It then computes the total weighted feasibility value, applying preset relative weights, and compares this feasibility score to a pre-set threshold before making a recommendation. In the financial stage of the analysis, MODEX asks 90 for the estimated project cost and schedule, and uses an analytical method to evaluate the cost and time savings associated with different levels of prefabrication. MODEX's recommendation making process is not transparent, however, and it is not clear how the total cost is distributed. In addition, MODEX's decision rules needs to be kept updated as relevant expertise evolves.
Murtaza and Fisher [10] developed a further model, called Neuromodex, for construction 95 method decision-making processes. Neuromodex is based on a neural network system and uses different decision factors relating to a specific project (e.g. location, labor and environmental) as input values, forms a pattern, and then relate this input pattern with one of the output patterns (conventional, semi-prefabrication or prefabrication). In order to recognize the input patterns and produce rational and effective decisions, the neural network needs to be trained based on past mod-100 ularization decisions. Neuromodex uses MODEX for this training process, with the assumption that past principles using prefabrication were correct. Song et al. [5] also presented a decision-making framework and a computerized tool to validate the applicability of prefabrication methods in industrial projects. Their decision framework has three levels (strategic level 1, strategic 2 and tactical level). The first two levels are considered 105 to evaluate the feasibility of Prefabrication, Preassembly, Modularization and Off-site Fabrication (PPMOF) based on primary drivers and impediments (such as schedule, site attributes, availability of local labour and suppliers). The third level is designed to determine the cost benefits and the practicality of PPMOF. This tool provides a tactical analysis of the alternatives, and the weight given to each set is subjective. 110 Regarding prefabrication, the Interactive Method for Measuring PRE-assembly and Standardisation (IMMPREST) toolkit was developed by Loughborough University (UK) to compare the traditional construction with the prefabricated construction [6]. This decision-making tool in fact consists of three parts (A, B and C). Part 'A' is designed to make the toolkit user friendly; part 'B' is focused on project goals and constraints in order to guide a strategic argument on prefabri-115 cation; and tool 'C' is considered to evaluate the relevant factors for prefabrication in more depth. Although IMMPREST contains an inclusive comparison between traditional and prefabrication methods, the major challenge is not having sufficient information available at the start of a project to use the toolkit.
[11] implemented a framework for selecting the structural frame of build-120 ings. This framework requires the project members to determine evaluate seven criteria in relation to client and project objectives (e.g. physical form and space, construction process, long-term sustainability). The performance of various structural frame options in respect to the defined criteria needs to be stated, regardless of their importance. This framework is used to calculate a Performance Weighted Score (PWS) which presents the likelihood of achieving client objectives. Then, 125 an overall PWS is stated for each structural frame option based on the seven criteria. Luo [12] summarised a list of general prefabrication strategies, and developed a decisionmaking tool based on dynamic programming analysis. He evaluated prefabrication strategies based on the initial costs, schedule, quality and sustainability.
Chen et al. [13] developed a two-level Construction Method Selection Model (CMSM) 130 to evaluate different construction methods under risk and uncertainty considerations. The Sim-ple Multi-Attribute Rating Technique (SMART) is used at the strategic level for evaluating the feasibility of prefabrication based on the judgment of experts. The Multi-Attribute Utility Theory (MAUT), which associate attitude to uncertainty and risk, is then used at the tactical level to evaluate the appropriate level of prefabrication for the defined project according to the judgment of 135 multi-decision makers. However, this decision support tool requires a lot of input from the decision makers and preference values need to be precise.

Scheduling Models in Construction Applications
A schedule presents what work needs to be performed, which resources of the organization will perform the work and the timeframes in which that work needs to be performed. This consists 140 of a list of multiple entities called jobs that need to be scheduled. Each job has an order of tasks, called operations, to go through and each operation takes a specific amount of time to finish using a particular resource. An operation is called the execution of a task by a resource. Each job can comprise of a single operation or a set of operations which must be done using shared resources. The shared resources are usually machineries, cranes, and workforce. In resource scheduling, two 145 distinct decisions have to be made: the assignment of operations to resources (e.g. machineries, cranes, and workforce) while sharing resources, and the sequencing and timing of operations. Resource scheduling has been studied broadly because of its practical application in different fields such as production line [14,15], vehicle and crew scheduling in transit systems [16] and assembly line [17,18,19,20,21]. Job shop scheduling, flow shop scheduling, and flexible job shop schedul-150 ing are popularly used to model the rules which govern the MtA sectors separately. The classical Job Shop Scheduling (JSS) deals with sequencing operations of jobs on predefined resources with the aim of minimising the makespan. The JSS problems are known as one of the hardest combinational optimisation problems since resource orderings can be different for each job. In the Flow Shop Scheduling (FSS), the operation order on resources is the same for all jobs. For in-155 stance, a production-line for double-curved precast concrete panels is a job with eight operations in the following order: mould assembly, embedded placing, reinforcement fixing, concrete casting, cleaning/finishing, mould stripping, concrete curing and handling. The order of operations in this production-line is the same (fixed) for all jobs (e.g. precasting concrete panels or walls). However, the execution of each operation may require different resources in each job and certain resources 160 may need to be shared between a number of operations in a factory. The processing time of an operation also varies using different resources. The Flexible Job Shop Scheduling (FJSS) problem is a modified version of the JSS problem where the fixed operation sequences can be processed by alternative identical or non-identical resources in parallel and not by predefined resources. A non-identical resource is the one which has the flexible capability to be set up to process more 165 than one type of operation. The FJSS is to assign each operation to an identical or non-identical resource out of set of resources capable of performing it (a routing problem), and to sequence the job operations in order to obtain a feasible schedule which satisfies one or multiple objectives (a scheduling problem). An extension of FJSS problems allows having a set of operations with arbitrary precedence relations [22] which is similar to real problems in the precast construction. 170 The JSS and the FJSS are NP-complete problems [8,23,24], they are computationally demanding to solve. The approaches for solving FJSS problems are classified into two main categories: a hierarchical approach and an integrated (concurrent) approach [25]. In the former, operations are assigned to their respective resources first and after that the scheduling procedures starts. Whereas in an integrated approach the assigning and scheduling processes are made concur-175 rently. Integrated methods are more complex and difficult to solve but can produce better results. There are two well-known classes of solution methodologies to tackle FJSS problems and fulfill the scheduling requirements of the industrial projects: mathematical programming (e.g. Mixed Integer Linear Programming (MILP)) and hybrid meta-heuristics (e.g. evolutionary algorithms).
Different MILP models for solving the FJSS and its extension is explored in many stud-180 ies [26,27,28,22]. A MILP can find the exact solution, however, they are computationally time consuming. Evolutionary algorithms, first defined by Rosenberg [29], are optimisation methods which search scenarios iteratively over time and uses different strategies or multiple searching points to explore various solutions in order to find a non-exact optimal solution. Evolutionary algorithms do not have knowledge of the specific problem; hence they investigate many possible 185 solutions. One type of evolutionary algorithms is the Genetic Algorithm (GA) which is adopted in this study. In general, a GA is composed of an initial population, genetic operations (e.g. crossover and mutation), and an objective function [30,31,32]. GAs are briefly explained and crossover, mutation and migration operators are discussed in Section 5. GAs allow combining different strategies and exploring various solutions both in the initial solution phase and in the generation phase. 190 As the summary in Sections 2.1 and 2.2 shows, there is no decision support tool available which does resource scheduling for the MtA sectors as a unified system and allows for comparing the optimal schedule of multiple levels of prefabrication. Scheduling a unified MtA system presents additional challenges of size, which is larger than the capabilities of the existing algorithms. In this paper, an integrated MtA system is modelled as a REFJSS problem with arbitrary 195 precedence relations. A multi-objective Genetic Algorithm (GA) is developed to solve the REFJSS problem with the objective of minimising makespan and cost while maximising safety. Safety can be maximised by minimising the number of on-site workers on congested construction sites. The output of this GA-based REFJSS model provides an optimal allocation of resources on operations in a unified MtA system. 200

Problem Description
In a unified MtA system of a prefabricated construction project, a number of different components are (semi-)prefabricated in a factory, transported to the site and assembled on-site according to the project's planning horizon H. These components are produced using a combination of resources. The production of the required number of each component is called a job. In the 205 manufacturing industry, product orders are released in a cyclic manner (cyclic jobs) and delivered in batches according to the horizon of the project. An example is shown in FIGURE 2 illustrating the prefabrication process for building a 3m run of a precast component. This component is made of two precast units type 1 and one precast unit type 2 using steel moulds and prefabrication cages. Details of the manufacturing and assembly lines are shown in TABLEs 1 and 2. The manufacturing 210 line is similar to a FSS problem; the assembly line is equivalent to a FJSS problem. A job is made of a set of tasks linked by precedence constraints and executed by a subset of resources. The set-up and processing times of each operation corresponding to each resource and the demand sizes for the project are stated in TABLEs 1 and 2.
In a unified MtA system, operations have arbitrary precedence relations which can be repre-     Operation dependencies for the assembling line problem is an extension of a FJSS problem with a set of operations with arbitrary precedence relations. Applying a GA-based optimisation method to this type of problem will return a good result 220 quickly. The multiple input, output, and optimisation process overview of a unified MtA system in a multi-objective DfMA project is summarised in TABLE 3. Scheduling a unified MtA system requires specifying the following inputs for different sectors (manufacturing, transportation and assembly) in a construction project: 225 • a list of product types, weights and quantities; • a list of operations that have an effect on the overall project finish date; 8 • a list of available resources for each operation in the project; • an estimation of completion time and cost for each operation using specific resources; • the operation dependencies and strategies (e.g., predecessor or successor) in the MtA 230 sectors for different product types and different levels of prefabrication.
In precast construction projects, the deliveries are based on the assembly strategies and the transportation options (road, rail and sea) considering the weight and size limitations. Late deliveries will cause penalties and early deliveries will contribute to holding costs. The project horizon H can be divided into short periods with a number of shipments from one sector to another (e.g., 235 manufacturing sector to the transportation sector to the assembly line). Each prefabrication method may require a different set of resources as well as different delivery and assembly strategies. Thus, the precedence relation of the operations between the MtA sectors differs according to the selected prefabrication method. Considering a unified MtA system for optimisation, the following assumptions are made: 240 • All resources are available and can be set up to process more than one type of operation (non-identical resources).
• Operations can start at different times during the project's planning horizon.
• Setting up times of resources are considered.
• Resources and operations are independent from each other. 245 • The order of operations is predefined and fixed (precedence relations).
• A resource (or machinery) can execute one operation at a time (resources constraints).
• A started operation cannot be interrupted during its processing time on a given resource (or machinery). Thus, preemption of operations is not allowed.
• A number of non-identical resources are available in all MtA sectors. These can be used 250 simultaneously to process similar operations.
• Actual/fixed start dates, early start dates, and late finish dates are specified for all operations.
• Projects' due dates are identified.

9
• Any operation can be executed by a combination of more than one resource at a time.
• Any resource can process only one operation simultaneously.
• Product orders are released in the specified cyclic manner.
Based on these assumptions, the unified MtA system is considered to be a REFJSS problem and is modelled with the objectives of minimising time and cost while maximising safety. The mathematical description is presented in Section 4. The multi-objective assignment problem is optimised subject to a set of constraints. Constraint (1) determines the makespan. Constraint (2) estimates the processing time of O jh on the 280 selected machine i. Constraint (3) ensures a specified operation sequence. Each machine is only able to process one operation at a time (see constraint (4)). Constraints (5) and (6) ensure that each operation O jh starts after its assigned machine is available and the previous operation O jh−1 is completed. Constraint (7) specifies the suitable machines for each operation. Constraint (8) assigns each operation to machines and identifies the sequence of operations on the machines. Each 285 operation can be performed on one machine only with the priorities defined in constraints (8), (9), and (10). As the FJSS problem is NP-hard, solving the above model, which is an extended FJSS problem, is also NP-hard. In the next section, a multi-objective GA is presented for solving the problem efficiently.
The start time for processing O h T m ik The start of working time for machine i in priority k k i The number of assigned operations to machine i Ps jh Processing time of operation O jh after selecting a machine Objective T m ik ≥ 0

290
A GA mimics the natural process of evolution over a period of time. It uses string coding of variables (chromosome encoding), randomly generates a set of possible solutions (initial population) to the problem, ranks possible solutions of the population (generation) after calculating the fitness function for each one (chromosome evaluation), keeps the best solutions and uses these to generate new possible solutions (genetic operators). A GA iteratively applies genetic operators 295 (such as crossovers and mutations) to change the current population to a new population. By repeating chromosome evaluation and applying genetic operators, either an acceptable solution will be found or the GA will iterate a given number of cycles.
The critical elements of GAs are the chromosome definition, the design of genetic operators, and the mechanism for population management to decide which chromosomes are selected 300 in each population for applying the genetic operators. Also, a fitness function is defined in GAs to measure the quality of each chromosome. After randomly choosing two chromosomes (parent set), a crossover operator (or marriage) combines the genes of the parent set to generate off-springs. The chromosomes with lower fitness value are then replaced with off-springs generated from crossover of more fit chromosomes. To avoid local optima during the search process, a mutation operator 305 makes a perturbation to the genes of off-springs. The chromosome encoding and decoding method, objective function, initial population generation, genetic operators of the proposed GA for solving REFJSS problems are presented in Sections 5.1, 5.2, 5.3 and 5.4, respectively.

Chromosome Encoding and Decoding
A new modified encoding scheme based on the work by Falkenauer and Bouffoix [33] is   3. Thus, operation 3 must be processed before operation 4, opera-325 tion 10 must be processes before operation 11, and operation 16 must be processes before operation 17. All predecessor operations of each operation have to be completed before this operation can start. Any solution that does not satisfy the predecessor-successor relations is not feasible. Unlike the method proposed by Falkenauer and Bouffoix [33], the assignment of operations to resources is based on the precedence relations for generating the initial population. Hence, only without any predecessors or with completed predecessors are added to a list called "ready for process". An operation is randomly selected from the "ready for process" operation list for resource assignment. The available resources that are suitable to execute the selected operation are identified with one of them being assigned. Operations that require more than one resource are added to 335 a "simultaneous" list. The same sequential steps applied to the "ready for process" operation list are followed here until all the operations are assigned to their required set of resources. The decoding method by Falkenauer and Bouffoix [33] is adopted to achieve feasible solutions. In this method, operations are selected based on their sequence in each sub-string and scheduled sequentially at the earliest possible time by considering the precedence relations. The 340 ones that do not satisfy the precedence relations are scheduled at a later time that satisfies the predecessor constraints. The scheduling process also considers actual/fixed start dates, early start dates, late finish dates, and a maximum number of on-site workers per day. In this way, infeasible chromosomes are changed to feasible ones in the decoding process and, therefore, valid solutions 13 are created. It is evident that the operations which require more than one resource can only be 345 processed when all the required resources are available.

Objective Functions
The evaluation criteria for prefabrication are cost, time and safety. The dominate objective function is minimising the completion time of a project f 1 . The second objective function is minimising the total project cost f 2 while utilising resource allocation. The number of workers on 350 the construction site has a significant impact on safety in precast construction projects as mentioned earlier. Hence, the number of on-site workers per day is constrained. The two objective functions f 1 and f 2 are computed for all chromosomes in each generation. The chromosomes are then ranked according to f 1 . Solutions with identical completion times are ordered according to their total project cost f 2 . 355

Generating Initial Population Subject to Objective Functions
The overall structure of the proposed GA is shown in FIGURE 6. Firstly, an initial population is generated of N feasible chromosomes. These chromosomes are then ranked according to the evaluation criteria (see Section 5.2). A number of the fittest chromosomes are preserved and transferred into the next generation. The preserved chromosomes remain eligible for selection 360 as parents when breeding the remainder of the next generation. At each step, the crossover and mutation operators define new chromosomes by preserving the assignment property of the parent chromosome/s and changing the sequence of operations in the set of operations assigned to resources (see FIGUREs 7 and 8).

365
As mentioned, a number of genetic operators such as the crossover, mutation and migration operators are applied here. The resource based crossover operator proposed by Qing-dao-er-ji and Wang [34] is used in this paper. An example is given in FIGURE 7: Suppose parent 1 and parent 2 are selected to create two offsprings, the crossover operator randomly divides the sub-strings of the parents into two resource based sets and swaps the genes in the sub-strings of each set. Hence, 370 the children inherit the sequence of operations processed on resources from their parents. After applying the crossover operator to parent 1 and parent 2, it can be seen in FIGURE 7 that child 1 inherits the operation sets (with the same order) of resource C and resource G[1] from parent 1 while resource G [2], resource S and resource T obtained the operation sets (with the same order) from parent 2. The symmetric process is applied to create child 2. The new children that are 375 created using the crossover operator will be then decoded to get a feasible schedule. The mutation operator by Qing-dao-er-ji and Wang [34] is adopted to get a feasible schedule. First, A single chromosome is chosen to create a new offspring. Then, the mutation operator randomly selects a sub-string from the selected chromosome and changes the position of two operations within the sub-string of the parent chromosome considering the precedence relations 380 (see FIGURE 8). This operator preserves the assignment property of the parent chromosome and changes the sequence of operations. The new child will be then decoded to get a feasible schedule. The genetic operators can be stopped by the user, if an acceptable solution which satisfies 385 the total project's time and the project's cost is found. In this case, the corresponding schedule including the utilised number of on-site workers over time are reported as the output. Otherwise, the algorithm will continue searching for a better solution.

Case Studies
To assess the performance of the developed GA, a solution for a number of precast con-390 struction scenarios has been determined. Our GA-based algorithm is applied to 1. a FSS and FJSS problem presented in TABLEs 1 and 2: The FSS problem consists of two cyclic jobs using 5 machines (FO, FG, JG, OG, and CG) and 8 operations for each job. The FJSS problem is made of one job using 9 machines (2×OG, CG, PG, JG, E, C, P, and S) and 8 operations. 395 2. an extended FJSS problem shown in FIGURE 3: This scenario is made of 5 machines (2×G, C, S, and T) and 26 operations.
3. a number of FJSS benchmarking problems from the literature: Solutions to several sets of FJSS problem instances designed by Fattahi et al. [26] and Brandimarte [25] have been reproduced. The data sets consist of 10 small problems, 10 medium problems and 400 10 large problems. The small problems are composed of 2-4 jobs using 2-5 machines and performing 2-5 operations for each job. The medium problems consist of 5-12 jobs, 6-8 available machines and 3-4 operations for each job. The large problems have 10-20 jobs using 4-15 machines and executing 5-15 operations for each job. The population size of 100 is used in this paper for running the small and medium size instances 415 based on the study by Roeva et al. [35]. Looking at TABLE 6, the best makespan for large size instances is achieved by the GA-based work of Pezzella et al. [36]. Hence, the same population size of 5000 is used here for these large size instances. The listed crossover, mutation and migration values are found most effective from computational experiments. The results for the FSS and FJSS problems are reported in FIGUREs 9 and 10. The re-420 sults calculated by the GA-based algorithm are identical to the actual manufacturing and assembly schedules.
In FIGUREs 11, the results of the conceptual exercise of a unified MtA system shown in FIGURE 3)is illustrated using the proposed GA-based algorithm. It can be seen that the proposed algorithm is capable of solving extended FJSS problems which have higher degree of flexibility to 425 capture real world scenarios. TABLE 5 summarises the results obtained by the developed GA in comparison with results from the literature with respect to small and medium size instances. Starting from the left, the columns specify the instance name, the number of jobs (n), the number of machines (m) for each example, and the Lower Bound (LB). In the eighth column, the best makespan gained available heuristic algorithms, TABLE 5 shows that our GA performs well for small problems and outperforms by +9.41% for medium instances. However, our GA deviates by −6.67% in medium 440 instances from an exact solution determined by MILPs. With regards to the 10 large FJSS problem instances by Brandimarte [25], TABLE 6 presents our results compared to the results by the tabu algorithms reported by Brandimarte [25] and Mastrolilli and Gambardella (MG) [37] (MG), the results by the CP model presented by Behnke and Geiger [28], and the results by the GA algorithms proposed by Pezzella et al. [36], Chen et al. [38], 445 Jia et al. [39] and Ho and Tay (HT) [40] using Composite Dispatching Rules (CDRs). The arrangement of the data in TABLE 6 is equivalent to TABLE 5. In summary, our proposed algorithm underperforms on average of about 15% in comparison to current available algorithms. The proposed structure for a chromosome allows having a set of operations with arbitrary relations and, therefore, is able to solve complex extended FJSS problems. However, it requires more time for 450 finding a good solution compared to available non-exact methods for solving FJSS problems. It should be considered that reported results are returned within ten minutes. Thus, the proposed algorithm has a higher degree of flexibility to capture real world scenarios in comparison to other non-exact algorithms.

455
This paper contributes to the development of a heuristic method for the holistic Manufacturing, transportation and Assembly (MtA) resource scheduling problem. The holistic/unified MtA system of precast construction projects is defined like a Resource-constrained Extended Flexible Job Shop Scheduling (REFJSS) problem. A multi-objective Genetic Algorithm (GA) has been developed to optimise cost and time associated in different precast construction techniques. Hence, 460 it allows constraining the number of on-site workforce per day from congested construction site. Using this multi-objective GA-based optimisation model, the most advantageous solution for different levels of prefabrication is determined and compared with respect to overall time and cost. The performance of the developed algorithm was evaluated using results of 30 small, medium and large problem instances reported in the literature. It can be concluded that our GA algorithm 465 outperforms available heuristics in small and medium size instances. However, this GA-based algorithm requires further improvements to outperform the current available scheduling algorithms in large size FJSS instances. However, the developed algorithm has a higher degree of flexibility to capture real world scenarios in comparison to other algorithms. The proposed model is capable of solving complex extended FJSS problems with arbitrary precedence relationships among their 470 operations. The optimisation architecture explored in this paper allows introducing further objectives that are essential to be optimised as part of future work. In future work, the proposed model will be combined with exact models. Hence, the flexibility of the presented GA-based algorithm will remain; at the same time, the performance with respect to large size FJSS instances might improve. Also, a Pareto frontier based on the non-dominant ob-475 jective functions will be calculated to solve complex extended FJSS problems using the proposed method.