Modeling of the harmonization method for executing a multi-unit construction project

Michał Tomczak

doi:10.1515/eng-2019-0036

Article Open Access

Modeling of the harmonization method for executing a multi-unit construction project

Michał Tomczak

Published/Copyright: July 25, 2019

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From the journal Open Engineering Volume 9 Issue 1

Abstract

One of the key problems in managing the realization of a construction project is the selection of appropriate working crews and coordinating their activities in a way that ensures the highest degree of implementation of defined goals (minimizing the project duration and/or reducing downtime and related costs). Most of the existing methods of work harmonization used in construction industry allow obtaining the desired results only in relation to the organization of the processes realization in repetitive linear projects. In case of realization of non-linear construction objects or construction units, it is usually necessary to choose between the reduction of the project implementation time and maintaining the continuity of crews work on the units. It was found that there is a lack in the literature of developed method enabling harmonization of crews’ work, while minimizing the downtime at work and the duration of the entire project taking into account additional constraints, e.g. the need to not exceed the deadlines for the realization of the project stages.

The article presents the concept of a multi-criteria optimization method of harmonizing the execution of non-linear processes of a multi-unit construction project in deterministic conditions. It will enable the reduction of realization time and downtimes in work, taking into account the preferences of the decision maker regarding the relevance of the optimization criteria. A mathematical model for optimizing the selection of crews and order of completion of units in multi-unit construction projects was also developed. In order to present the possibility of usage of the developed concept, an example of the optimal selection of crews and their work schedule was solved and presented. The proposed method may allow for better use of the existing production potential of construction enterprises and ensure synchronization of the crews employed during the work, especially in the case of difficulties in acquiring qualified staff in construction industry.

Keywords: construction project management; project scheduling; renewable resource leveling; repetitive non-linear activities; schedule optimization

1 Introduction

The conditions for the realization of construction projects are specific and significantly diverge from those that occur while carrying out projects in other areas of the economy. Long duration of construction project realization, variability of environmental conditions, influence of atmospheric conditions, high material consumption, individuality of design projects, internal and external organizational problems make planning the realization of construction projects a task that causes many problems. Specific and more complex conditions for the realization of construction projects make it pointless to apply the methods and tools of work organization known from industrial production (Tomczak, 2013; Jaskowski and Tomczak, 2015; Tomczak and Rzepecki, 2017; Tomczak and Jaskowski, 2018). Whereas, methods traditionally used for scheduling in construction industry (network planning methods CPM, PERT, PD) give good results only in the case of planning processes with the same labor intensity on all construction units. In practice, projects containing only homogeneous processes are rare. Functional and aesthetic aspects of construction objects result in the need of changing the spacing of load-bearing elements of constructions, and thus makes it impossible to level the times of realization of processes and makes it difficult to harmonize the work of crews. In such cases, construction managers, using traditional methods of scheduling, based in many cases on the use of network planning methods, cannot simultaneously take into account the relevant criteria for optimizing schedules: minimizing the time of completion of the entire project and downtime of crews work and seeking compromise solutions. The first optimization criterion is characteristic of the resource-constrained project scheduling problem (RCPSP) known in the literature, while the second is the resource leveling problem (RLP) (with the defined directive completion date of the project). Applying such methods may result in obtaining schedules that do not satisfy the contractors and do not meet their requirements. The schedule prepared with only the continuity of the crews’ work taken into account is often characterized by an unacceptably long period of realization of the project. That results in the need to incur additional avoidable financial resources as part of indirect construction costs. While the minimization of only the time of completion of construction works will lead to poor organization of crews and incurring unnecessary costs associated with their downtime on the construction site. Another criterion often taken into account when setting the work schedule is to ensure the continuity of work on the construction units. Long downtime of work on the construction units may cause the client to feel that the contractor does not have sufficient resources to carry out the project, or result in increased costs dependent on time, such as the rent of machinery and equipment. In case of bothersome public projects, e.g. road repairs, long-term stoppages on construction units may cause dissatisfaction of public opinion.

Determining appropriate schedules and allocating resources is the responsibility of operational research, discrete optimization and combinatorial programming, especially in industrial engineering. The RCP problem can be presented as a flow shop problem known from operational research. In this case, the crews correspond to the machines, the units correspond to the jobs, and the construction activities correspond to the operations (Jaskowski, & Biruk, 2019). There are many variants of permutation flow shop problem, and the following can be used to describe construction repetitive projects (Makuchowski, 2015):

regular permutation flow shop problem to determine the minimum duration of the project (here the continuity of the crew and the continuity of the work in the work units are not of interest) (Liu et al., 2016),
the no-wait flow shop problem, where the emphasis is on the continuity of work in the work units (Li et al., 2008; Ruiz et al., 2009; Samarghandi, & Behroozi, 2017),
the no-idle flow shop problem to ensure the continuous work of crews (Goncharov, & Sevastyanov, 2009; Billaut et al., 2019).

Within the framework of operational research, we can also distinguish the problem of repetitive projects, which is broadly described in the literature (Krüger, & Scholl, 2010; Azaron et al., 2011; Yaghoubi et al., 2011; Yaghoubi et al., 2015). The topic of scheduling and selection of crews in construction projects, both considered as RCSP and RLP, has been repeatedly undertaken in world literature (Mattila and Abraham, 1998; Kolisch and Padman, 2001; Herroelen and Leus, 2005; Kim et al., 2005; Anagnostopoulos and Koulinas, 2010; Jaskowski and Sobotka, 2012; Benjaoran et al., 2015; Biruk and Jaskowski, 2017; Kassandra and Suhartono, 2018; Kannimuthu et al., 2018).

Jaskowski and Tomczak (2017) developed a mathematical model of the problem of minimizing work downtime among the crews of the general contractor at a directively fixed time and cost limit of the project realization, taking into account the limitations in the availability of crews and the possibility to subcontract the works. Thanks to subcontracting of specialized works, it became possible to obtain a greater degree of work harmonization of the resources involved, and consequently to ensure continuous and steady production, while fully exploiting the general contractor’s executive potential.

Nikoofal Sahl Abadi et al. (2018) have developed a multiobjective integer nonlinear programming model that optimizes two criteria: the costs of fiuctuating employment of work crews and the duration of the entire project. Three algorithms were used to find solutions that met the Pareto condition of the developed model: non-dominated sorting genetic algorithm-II (NSGA-II), strength Pareto evolutionary algorithm-II (SPEA-II), and multiobjective particle swarm optimization (MOPSO), and then their effectiveness was compared.

Tang et al. (2018) proposed a linear project resource leveling model (Line of Balance-based Resource Leveling Model, LOBRLM) based on the Line of Balance and constraint programming (CP) techniques. The LOBRLM includes synchronized scheduling of activities and leveling allocation of resources without the need to specify a fixed schedule. In addition, to facilitate the implementation of LOBRLM and the visualization of tasks in a manner known to construction managers, a scheduling support system called LOBSS was developed.

Jaskowski and Biruk (2018) considered the effect of introducing soft relations into the model of a construction project. In the example they define, the part of the sequence relations between the processes has been defined as fixed (hard), and the part as soft relations, which allow execution of processes in reversed order or that can be canceled. The introduction of a new type of relationship between processes is aimed at increasing the use of the production potential possessed by the contractor.

Podolski (2017) presented the problem of scheduling the multi-unit construction project as a permutation flow shop problem. In order to obtain shorter realization dates of the project, the developed model allows any order of realizing the units for each process. This concept assumes that resources are available all the time, which is rare in practice. The Tabu Search algorithm was developed to solve the model.

The impact of learning and forgetting effect during the completion of repetitive construction processes was considered in the works (Biruk and Rzepecki, 2017; Rzepecki and Biruk 2018). The learning theory is used to mathematically describe the relationship between the number of repetitions and performance. It is used for homogeneous production operations, during which the employee continuously improves his or her skills or seeks to ensure a better ergonomics of his or her workplace. An increase in the number of repeated operations leads to the acquisition of more and more practice, and thus to a reduction in the time and cost of their implementation. Due to the discontinuity of the work of working teams, the forgetting effect, which is proportional to the duration of breaks (the period in which the team does not perform the same type of work), should also be taken into account. Biruk and Rzepecki have developed a simulation program for planning repetitive processes carried out in random conditions to determine the learning and forgetting effect for the duration of the project. As a result, it was possible to shorten the time of the project realization.

Whereas García Nieves et al. (2018) have developed multimode RCPSP model,which achieved makespan minimization considering the optimum execution of crews and starting times for all subactivities. For this purpose, the authors have introduced multiple execution modes for the same activity through the use of unidirectional changes in optimum crew size throughout an activity execution, which is called acceleration routines.

Birjandi and Mousavi (2019) studied RCPSP with multiple routes (RCPSP-MR) for flexible project parts in order to optimize the cost of the entire construction project. Flexible activity means the activity that has multiple routes (i.e., technology) for its carrying out. The method developed by them is based on nonlinear programming under the fuzzy environment. The fuzzy mixed integer nonlinear programming problem model was solved using a genetic algorithm, particle swarm optimization and the CT-PHA meta-heuristic algorithm, and then comparing their effectiveness.

It was observed that despite the popularity of discussed topics in the literature there are no multi-criteria methods to obtain compromise solutions and enable harmonization of crews work in realization of repetitive processes while minimization of downtime at work and time of realization of the entire project taking constraints. The example may be the need to not exceed the directive deadlines for the realization of the project stages.

2 The mathematical model of the problem

2.1 Method Approach

Definitions the sets, parameters and variables of the mathematical model are included in Table 1.

Table 1

Model indices, sets, parameters and variables.

Indices:
j ∈ {1, 2, . . . , n}	Activities (construction processes)
p ∈ {1, 2, ..., o}	Construction objects
l_p ∈ {1, 2, ..., m_p}	Construction units in p object
l ∈ {1, 2, ..., m₁, m	₁ + 1, ..., ..., m₁ + m₂, m₁ + m₂ + 1, ..., m} Construction units in the entire project
r ∈ {1, 2, ..., 𝛩}	Contractors
Sets:
V	Set of activities
R	Set of contractors
R_j	Set of contractors that can execute the activities j; R_j ⊂ R
J_r	A set specified for each contractor r, which involves of activity pairs (u, v); J_r ⊂ V × V
Parameters:
n	Number of activities
o	Number of construction objects
m_p	Number of construction units in p object
m	Number of construction units in the entire project
𝛩	Number of contractors
c_p	Predefined order of unit execution
t_jlr	Execution time of activity j on the unit l by crew r
	The activity pairs (u, v) that meet the following
(u, v)	conditions(u, v) ∈ J_r ⇔ u ∈ V_r ^ v ∈ V_r ^ u < v – activities u and v can be executed by the
	contractor r
T	Directively fixed deadline for completing the project
T_p	Deadline for the completion of working on individual object p
	The weightings of decision-maker criteria, which reflects his preferences. It is fixed for
{w₁, w₂, w₃}	following criteria: minimizing the time of completion of the entire project, reducing downtime
	in crews work and reducing downtime at unit of works, respectively.
z_jlr	Deadline for completing the activities j on the nit l by the crew r
zrmax	Deadline for completing of the work by the crew r
Zlmax	Deadline for completing of the work on the unit l
srmin	Deadline for starting of the work by the crew r
Slmin	Deadline for starting of the work on the unit l
ρ	Sufficiently small number
M	Sufficiently large number
Variables:
s_jl	The start dates of activity j on construction unit l
SXjr	Binary variable, which indicates decision on the selection of contractors for the realization of activities. It will take the value 1, when the activity j will be executed by the contractor r, and the value 0 otherwise.
y_uv	Binary variable, which indicates the order of execution of activities u and v. It will take the value 1, when the activity u will be executed before the beginning of the activity v, and the value 0 otherwise.
p_jlr	Additional variable, which establishes the deadlines in the model for each crew r and for each activity j on each unit l. If the activity j will be realized by the crew r, this variable will take the value equal to the start date of realization of activity j on the unit l, otherwise value 0. It is equal to p_jlr = s_jl · x_jr. Due to the nonlinear nature of the discussed relation, in the model it was replaced by additional linear relations (17) - (19) (see Table 2), which allowed to maintain the linear character of the model.

The paper introduces a case, which is made of the following sets, in hierarchical order:

Construction project,
Objects (sometimes referred to as zones) – p ∈ {1, 2, ..., p, ..., o},
Units – l_p ∈ {1, 2, ..., m_p}; The scope of work on the construction units and the dependencies of precedence relations between them are modeled using an activity-on-node network,
Activities – j ∈ {1, 2, . . . , n}; as in many publications in this field (Kolisch, & Padman, 2001; Podolski, 2017; Jaskowski, & Biruk, 2018) the project activities and precedence relations between them are represented by a graph G = 〈V, E〉, with one start and finish node, while graph arcs E ⊂ V × V reflect the order of Finish to Start relations between activities on one construction unit.

Construction projects with such a hierarchical structure are quite common in the construction industry. An example of such a project may be e.g. construction of a housing estate: objects are separate buildings, units – parts of buildings between consecutive construction expansion joints (the least structurally detachable part of the building), activities – construction processes.

Some crews can execute several different activities, but not simultaneously. In case when to a pair activities (u, v) ∈ J_r will be assigned the contractor r (x_ur = 1^x_vr = 1), these activities cannot be executed simultaneously (in parallel). The order of execution of these activities will be modeled using the binary variables y_uv ∈ {0, 1}. It also means that the sequence of performing the activities by the same crews will be fixed on different units, which is desirable for organizational reasons – repeatedly performing the same activities several times allows for increasing the effectiveness of the crews.

Table 2

Constraints of the mathematical model.

C1=snm+Dnm	(11)	Definition of the project completion date
C2=∑r∈R(zrmax−srmin−∑j∈V∑l∈Ltjlr⋅xjr)	(12)	Definition of the total downtime for the crews work
C3=∑p∈O(Zpmax−Spmin−∑j∈V∑r∈Rj∑l∈Lptjlr⋅xjr)	(13)	Definition of the total downtime on the unit of works
Djl=∑r∈Rjtjlr⋅xjr,∀j∈V,∀l∈L	(14)	Determining the duration of performing the activity j on the unit l
∑r∈Rjxjr=1,∀j∈V	(15)	Only one crew can be assigned to each activity
s11=0	(16)	The first activity begins on time 0 The condition makes it possible to set deadlines for starting
sil+Dil≤sjl,∀(i,j)∈E,∀l∈L	(17)	activity on the unit (with the exception of the first one) l
sjk+Djk<sjl,j∈V,∀k,l:k,l∈L∧l=k+1	(18)	Condition for the completion of the units on objects in a fixed order
suk+Duk≤svl+M⋅(1−yuv)+M⋅(2−xur−xvr),∀(u,v)∈Jr,∀r∈R,∀k,l∈L	(19)	Allow setting deadlines for starting activity that cannot be carried out in parallel by the same contractor
svk+Dvk≤sul+M⋅yuv+M⋅(2−xur−xvr),∀(u,v)∈Jr,∀r∈R,∀k,l∈L	(20)
snmp+Dnmp≤Tp,∀p=1,2,...,o	(21)	Limitation on the date of completion of individual objects Condition for completing the project before the declared latest
snm+Dnm≤T	(22)	possible date of realization of the entire project
pjlr≤M⋅xjr,∀j∈V,∀l∈L,∀r∈Rj	(23)
pjlr≤sjl,∀j∈V,∀l∈L,∀r∈Rj	(24)	Defining the variable p_jlr
pjlr≥sjl−M⋅(1−xjr),∀j∈V,∀l∈L,∀r∈Rj	(25)
sjlr≤pjlr+M⋅(1−xjr),∀j∈V,∀l∈L,∀r∈Rj	(26)	Deadline for starting the activities j on the unit l by the crew r Upper limit of variable s_jlr for cases, when for a given crew r and
sjlr≤∑r∈Rpjlr,∀j∈V,∀l∈L,r∈R	(27)	8j 2 V, 8l 2 L variable p_jlr is equal to 0
zjlr=pjlr+tjlr⋅xjr,∀j∈V,∀l∈L,∀r∈Rj	(28)	Defining deadline for completing the activity j on the unit l by the crew r
zrmax≥zjlr,∀j∈V,∀l∈L,∀r∈Rj	(29)	Defining deadline for completing of the work by the crew r
Zlmax≥zjlr,∀j∈V,∀r∈Rj,∀l∈L	(30)	Defining deadline for completing of the work on the unit l
srmin≤sjlr,∀j∈V,∀l∈L,∀r∈Rj	(31)	Defining deadline for starting of the work by the crew r
Slmin≤sjl,∀j∈V,∀l∈L,	(32)	Defining deadline for starting of the work on the unit l
Boundary conditions:
srmin≥0,∀r∈Rj	(33)	Start of work by the crew r take only non-negative values
Spmin≥0,∀p∈O	(34)	Start of work on the object ptake only non-negative values
sjl≥0,∀j∈V,∀l∈L	(35)	Activities’ start dates can take only non-negative values
pjlr≥0,∀j∈V,∀l∈L,∀r∈Rj	(36)	Variable p_jlr take only non-negative values
xjr∈{0,1},∀j∈V,∀r∈Rj	(37)	Activity j is realized by the crew r, or is not
yuv∈{0,1},∀(u,v)∈Jr	(38)	Activity is realized before the Activity v, or is realized after it

2.2 The Optimization Criteria

The selection of activity contractors and setting deadlines for their realization will be made in a manner ensuring that three criteria are taken into account: minimizing the time of completion of the entire project, reducing downtime in crews work and reducing downtime at unit of works by means od mixed-integer-linear programming (MILP) approach.

In general, the problem of multicriteria optimization can be formulated as follows: find a vector of decision variables

(1)x∗=[x1∗,x2∗,...,xα∗]T

the one that optimizes the vector function

(2)F(x)=F1(x),F2(x),...,Fη(x)]T

and meets the imposed constrains

(3)gγ(x)=0,γ=1,2,...,ς

(4)hφ(x)=0,γ=ς+1,...,σ

where α = 1, 2, ..., ω – set of decision variables indexes, η = 1, 2, ..., ξ – set of criteria indexes. The analyzed object is described by decision variables, which are subject to change in the optimization process, and by parameters – values determined earlier (assumed project objectives) remaining as constant in the whole optimization process. Decision variables are defined in the ω-dimensional space of decision variables A ⊂ R^ω. The area of acceptable solutions X determines the limits imposed on decision variables and forms part of the decision variables space (Montusiewicz, 2012).

For non-dominated solutions no goal function can be improved without simultaneously deteriorating one of the other goal functions. Non-dominated solutions form a set of non-dominated solutions (a Pareto set), which is a subset of feasible solutions, and the calculated criteria values form a set of assessments of non-dominated solutions, which is a subset of assessments of feasible solutions (Montusiewicz, 2012). The problem of choosing the best solution from the Pareto set is not trivial because it depends on many aspects (e.g. the importance of the goal functions, the nature of the construction project, etc.) This process is known as multi-criteria decision making (Nguyen et al., 2014).

One of the most popular methods of determining non-dominant solutions is using a Chebyshev weighted distance (Jaszkiewicz et al., 2001; Clímaco, & Pascoal, 2016; Jaszkiewicz, 2018). It expresses the size of losses resulting from the differences between the implementation of objectives in the generated solutions and ideal levels of their implementation. This approach requires solving single-criterion tasks in advance with constraints of the multi-criteria optimization task. Since the default start date of the project equals zero, the minimum time of completion of the entire construction project is equal to the date of completion of the last activity on the last unit:

(5)C1o=min(snm+Dnm)

The total time of downtime in each crew’s work will be calculated as the difference between the dates of starting the work of a given crew in the realization of the analyzed project, completion of its work and the total time of execution of the activity entrusted to it. The minimum total downtime at work can be represented by the following equation:

(6)C2o=min[∑r∈R(zrmax−srmin−∑j∈V∑l∈Ltjlr⋅xjr)]

Complying with the principles of organizing construction works, it is desired that the crews performing particular construction activity fill the entire front of construction works on the construction unit. Defining a construction project using a directed graph G illustrates a more general case that allows simultaneous carrying out of various activities on the same construction units. In practice, this is a rare situation - most often construction activities make up to a series of activities carried out one after the other. Another common case is the presentation of a construction project using a general graph directed G with an additional constraint preventing simultaneous execution of various activities on one construction unit. Of course, although cases where several activities are executed on one unit at a time are not frequent, they occur in construction projects. This situation requires introducing additional variables into the model, e.g. binary variables equal to 1, when at a given time (after starting of works on the unit and before their completion) work is not carried out on the given construction unit and equal to 0 otherwise. The mathematical model containing these variables becomes very complex and the use of commercial solvers to work it out seems to be ineffective, and it becomes legitimate to use metaheuristic algorithms. In the developed model it was assumed that the activities will be carried out in series. The downtime on the construction units will be calculated as the difference between the dates of starting the work on the given unit, completion of the last activities unit and the total time of execution of all activities defined by the sequence of activities. The shortest possible down time on working unit is:

(7)C3o=min[∑l∈L(Zlmax−Slmin)−∑j∈V∑r∈Rtjlr⋅xjr]

The goal function (substitute criterion) of the issue of selecting multi-skilled crews to carry out the activities and setting completion deadlines in a multi-object project (with assumed directive project deadlines and individual objects). At the same time minimizing the duration of the entire project, downtimes in crews’ work and downtimes at unit of works takes the following form:

(8)minCS:CS=maxw1⋅C1−C1oC1o,w2⋅C2−C2oC2o,w3⋅C3−C3oC3o+ρ⋅C1−C1oC1o+C2−C2oC2o+C3−C3oC3o.

The weighted Chebyshev metric is not linear in itself, but is a minimax task (in this case). Transforming a minimax task into a linear programming task is very simple and well known. The goal function takes on the form:

(9)min=λ,

subject to:

(10)wk⋅Ck−CkCko+ρ⋅∑k=13Ck−CkCko≤λ,∀k=1,2,3.

2.3 Model Constraints

Model constraints are given in the Table 2.

3 Example

The proposed approach used to determine the optimal schedule and selection of the most appropriate crews to carry out various construction processes (activities) in an exemplary construction project. The analyzed project includes the construction of two objects – the first consists of four construction units and the second of five (units are marked as UX, X = 1, 2, ..., 9). A sequence of six activities (activities are marked as PY, Y = 1, 2, ..., 6) should be executed on each unit. There are five crews available – A, B, C, D and E. Possible assignment of crews to particular activities is given in Table 2 (crew A or B can be assigned to activity 2 and crew C or D can be assigned to activity P4).

The times of activity execution by individual crews on objects and units have been summarized in Table 3. The project must end within a maximum of 170 days.

Table 3

Execution times of activities by crews on objects and construction units expressed in days.

Object 1									Object 2
Activity	P1	P2		P3	P4		P5	P6	Activity	P1	P2		P3	P4		P5	P6
Unit/Crew	A	A	B	A	C	D	B	E	Unit/Crew	A	A	B	A	C	D	B	E
Unit 1	5	7	3	4	6	7	5	10	Unit 5	5	7	3	4	6	7	5	10
Unit 2	6	8	5	5	7	7	6	10	Unit 6	8	10	8	9	11	10	9	13
Unit 3	4	6	3	3	6	6	4	8	Unit 7	2	1	1	2	2	1	2	5
Unit 4	7	8	4	3	7	7	6	8	Unit 8	6	5	3	5	5	7	7	9
									Unit 9	4	7	3	5	6	7	5	10

To demonstrate the proposed mixed-integer-linear programming (MILP) approach and to compare its solution with single goal proposals the mathematical model was solved in two stages. In the first stage, for each single-criterion alternative:

minimization of the realization time of the entire project (Solution 1; S1),
minimization of downtime in crews work (Solution 2; S2),
minimization of downtime of work on units of works (Solution 3; S3),

and in the second stage for the Compromise Solution, with weighting criteria values equal to w₁ = w₂ = w₃ = 0.333 (Compromise Solution; CS). The Lingo14.0 (LINDO Systems, 2014) program on PC Intel Core i5, CPU 2 gigahertz was used for the calculations. For a task of this size (2 objects, 9 units, 6 activities on each unit, 5 crews) the task contains 630 variables, 1308 linear constraints and 6539 non-zeros. The elapsed runtime of computations amounted to 11.84 seconds. The solutions of the three-criteria optimization model and the compromise solution are presented in Table 4. A detailed schedule of a compromise solution is presented in Figure 1, and the crew employment schedule for a compromise solution in Figure 2.

Figure 1

Schedule of the project in the three-criteria optimization problem (CS) with weighting criteria amounting to w₁ = w₂ = w₃ = 0.333.

Figure 2

The schedule of employment of crews in solving the compromise optimization schedule.

Table 4

Values of individual criteria (C1, C2, C3) for solutions of single-criterion alternative (S1, S2, S3) and a compromise solution (CS) (expressed in days).

	S1	S2	S3	CS
C1	121	170	170	122
C2	60	0	286	65
C3	120	624	9	84

The results for this particular example with specific criteria weights, which are presented above indicate that it is justified to simultaneously take into account three, above-mentioned criteria, for minimizing which (in the task of three-criteria optimization) the most balanced result was obtained. This result ensures beneficial organization of works in multi-unit construction projects through rational selection of work crews and deadlines for activity realization. As predicted, aiming only at minimizing downtimes of crews work or downtimes on unit of works leads to obtaining results that are not very efficient in practice. Schedules of the example project obtained for the tasks of single-criterion optimization, separately taking into account the above mentioned criteria looks like very unfavourable in terms of the time of completion of the entire project and the organization of construction works. As demonstrated, they can also lead to protracted construction work on individual units, and each investor wants the construction objects to be commissioned as soon as possible – this means quicker capital recovery and / or repayment of the loan. Moreover, the analysis of the solution in the various alternatives can provide indications of the project costs, including active and idle crews.

4 Conclusions

The article presents a method enabling harmonization of the crews work (their selection and synchronization of their work over time), while minimizing downtime at work and the time of realization of the entire project taking into account additional limitations. This method allows to obtain compromise solutions by taking into account three criteria: minimizing the time of realization of the entire project, minimizing downtimes in the work of crews and minimizing downtimes in work on the construction units. It is a combination of two traditional approaches to the harmonization of work on the construction site: RCPSP and RLP are both adequate for repetitive processes. The obtained results were compared to analogous examples with the minimization of each criterion separately. The results obtained using the approach described in the article, while minimizing all three criteria, proved to be the most desirable.

Acknowledgments

The author gratefully acknowledges the financial support by the Ministry of Science and Higher Education in Poland (S/63/2019).

References

[1] Anagnostopoulos, K. P., & Koulinas, G. K. (2010). A simulated annealing hyperheuristic for construction resource levelling. Construction management and economics28(2), 163-175. https://doi.org/10.1080/01446190903369907https://doi.org/10.1080/01446190903369907Search in Google Scholar

[2] Azaron, A., Fynes, B., & Modarres, M. (2011). Due date assignment in repetitive projects. International Journal of Production Economics129(1), 79-85. https://doi.org/10.1016/j.ijpe.2010. 09.004https://doi.org/10.1016/j.ijpe.2010.09.004Search in Google Scholar

[3] Benjaoran, V., Tabyang, W., & Sooksil, N. (2015). Precedence relationship options for the resource levelling problem using a genetic algorithm. Construction management and economics33(9), 711-723. https://doi.org/10.1080/01446193. 2015.1100317https://doi.org/10.1080/01446193.2015.1100317Search in Google Scholar

[4] Billaut, J. C., Della Croce, F., Salassa, F., & T’kindt, V. (2019). No-idle, no-wait: when shop scheduling meets dominoes, Eulerian paths and Hamiltonian paths. Journal of Scheduling22(1), 59-68. https://doi.org/10.1007/s10951-018-0562-4https://doi.org/10.1007/s10951-018-0562-4Search in Google Scholar

[5] Birjandi, A., & Mousavi, S. M. (2019). Fuzzy resource-constrained project scheduling with multiple routes: A heuristic solution. Automation in Construction100 84-102. https://doi.org/10.1016/j.autcon.2018.11.029https://doi.org/10.1016/j.autcon.2018.11.029Search in Google Scholar

[6] Biruk, S., & Jaskowski, P. (2017). Scheduling linear construction projects with constraints on resource availability. Archives of Civil Engineering63(1), 3-15. https://doi.org/10.1515/ace-2017-0001https://doi.org/10.1515/ace-2017-0001Search in Google Scholar

[7] Biruk, S.&Rzepecki, Ł. (2017). Wpływ zjawiska uczenia i zapominania na czas realizacji powtarzalnych procesów budowlanych realizowanych w warunkach losowych Influence of the phenomenon of learning and forgetting for the time of implementation of repeat construction processes carried out in random conditionsPrzeglad Naukowy Inzynieria i Kształtowanie Srodowiska 26 (2), 202-209. https://doi.org/10.22630/PNIKS. 2017.26.2.18https://doi.org/10.22630/PNIKS.2017.26.2.18Search in Google Scholar

[8] Clímaco, J. C., & Pascoal, M. M. (2016). An approach to determine unsupported non-dominated solutions in bicriteria integer linear programs. INFOR: Information Systems and Operational Research54(4), 317-343. https://doi.org/10.1080/ 03155986.2016.1214448https://doi.org/10.1080/03155986.2016.1214448Search in Google Scholar

[9] García-Nieves, J. D., Ponz-Tienda, J. L., Salcedo-Bernal, A.,&Pellicer, E. (2018). The Multimode Resource-Constrained Project Scheduling Problem for Repetitive Activities in Construction Projects. Computer-Aided Civil and Infrastructure Engineering 33(8), 655-671. https://doi.org/10.1111/mice.12356https://doi.org/10.1111/mice.12356Search in Google Scholar

[10] Goncharov, Y.,&Sevastyanov, S. (2009). The flow shop problem with no-idle constraints: A review and approximation. European Journal of Operational Research196(2), 450-456. https://doi.org/10.1016/j.ejor.2008.03.039https://doi.org/10.1016/j.ejor.2008.03.039Search in Google Scholar

[11] Herroelen, W., & Leus, R. (2005). Project scheduling under uncertainty: Survey and research potentials. European journal of operational research165(2), 289-306. https://doi.org/10.1016/j.ejor.2004.04.002https://doi.org/10.1016/j.ejor.2004.04.002Search in Google Scholar

[12] Jaskowski, P., & Sobotka, A. (2012). Using soft precedence relations for reduction of the construction project duration. Technological and Economic Development of Economy18(2), 262-279. https://doi.org/10.3846/20294913.2012.666217https://doi.org/10.3846/20294913.2012.666217Search in Google Scholar

[13] Jaskowski, P., & Biruk, S. (2018). Reducing renewable resource demand fluctuation using soft precedence relations in project scheduling. Journal of Civil Engineering and Management 24(4), 355-363. https://doi.org/10.3846/jcem.2018.3043https://doi.org/10.3846/jcem.2018.3043Search in Google Scholar

[14] Jaskowski, P., & Biruk, S. (2019). Minimizing the Duration of Repetitive Construction Processes with Work Continuity Constraints. Computation7(1), 14. https://doi.org/10.3390/computation7010014https://doi.org/10.3390/computation7010014Search in Google Scholar

[15] Jaskowski, P., & Tomczak, M.(2014). Assignment problem and its extensions for construction project scheduling. Czasopismo Techniczne, Budownictwo Zeszyt 2-B (6) 2014, 241-248. http://dx.doi.org/10.4467/2353737XCT.14.133.2583Search in Google Scholar

[16] Jaskowski, P. & Tomczak, M. (2017). Problem minimalizacji przestojów w pracy brygad generalnego wykonawcy w harmonogramowaniu przedsiewziec budowlanych The problem of minimizing downtime in crews work of the general contractor in scheduling construction projectsPrzeglad Naukowy Inzynieria i Kształtowanie Srodowiska 26 (2), 193-201. https://doi.org/10.22630/PNIKS.2017.26.2.17https://doi.org/10.22630/PNIKS.2017.26.2.17Search in Google Scholar

[17] Jaszkiewicz, A. (2018). Many-Objective Pareto Local Search. European Journal of Operational Research271(3), 1001-1013. https://doi.org/10.1016/j.ejor.2018.06.009https://doi.org/10.1016/j.ejor.2018.06.009Search in Google Scholar

[18] Jaszkiewicz, A., Hapke, M., & Kominek, P. (2001,March). Performance of multiple objective evolutionary algorithms on a distribution system design problem-Computational experiment. In International Conference on Evolutionary Multi-Criterion Optimization (pp. 241-255). Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44719-9_17https://doi.org/10.1007/3-540-44719-9_17Search in Google Scholar

[19] Kannimuthu, M., Raphael, B., Palaneeswaran, E., & Kuppuswamy, A. (2018). Optimizing time, cost and quality in multimode resource-constrained project scheduling. Built Environment Project and Asset Management https://doi.org/10.1108/BEPAM-04-2018-0075https://doi.org/10.1108/BEPAM-04-2018-0075Search in Google Scholar

[20] Kassandra, T., & Suhartono, D. (2018). Resource-Constrained Project Scheduling Problem using Firefly Algorithm. Procedia Computer Science135 534-543. https://doi.org/10.1016/j.procs.2018.08.206https://doi.org/10.1016/j.procs.2018.08.206Search in Google Scholar

[21] Kim, J., Kim, K., Jee, N., & Yoon, Y. (2005). Enhanced resource leveling technique for project scheduling. Journal of Asian Architecture and Building Engineering4(2), 461-466. https://doi.org/10.3130/jaabe.4.461https://doi.org/10.3130/jaabe.4.461Search in Google Scholar

[22] Kolisch, R., & Padman, R. (2001). An integrated survey of deterministic project scheduling. Omega29(3), 249-272. https://doi.org/10.1016/S0305-0483(00)00046-3https://doi.org/10.1016/S0305-0483(00)00046-3Search in Google Scholar

[23] Krüger, D.,&Scholl, A. (2010).Managing and modelling general resource transfers in (multi-) project scheduling. OR spectrum32(2), 369-394. https://doi.org/10.1007/s00291-008-0144-5https://doi.org/10.1007/s00291-008-0144-5Search in Google Scholar

[24] LINDO Systems (2014). LINGO Optimization Modeling Language 14.0 LINDO Systems, Inc., Chicago, IL.Search in Google Scholar

[25] Liu, W., Jin, Y., & Price, M. (2016). A new Nawaz–Enscore–Ham-based heuristic for permutation flow-shop problems with bicriteria of makespan and machine idle time. Engineering Optimization48(10), 1808-1822. https://doi.org/10.1080/0305215X.2016.1141202https://doi.org/10.1080/0305215X.2016.1141202Search in Google Scholar

[26] Li, X., Wang, Q., & Wu, C. (2008). Heuristic for no-wait flow shops with makespan minimization. International Journal of Production Research46(9), 2519-2530. https://doi.org/10.1080/00207540701737997https://doi.org/10.1080/00207540701737997Search in Google Scholar

[27] Lucko, G. (2008). Productivity scheduling method compared to linear and repetitive project scheduling methods. Journal of Construction Engineering and Management134(9), 711-720. https://doi.org/10.1061/(ASCE)0733-9364(2008)134:9(711)https://doi.org/10.1061/(ASCE)0733-9364(2008)134:9(711)Search in Google Scholar

[28] Makuchowski, M. (2015). Permutation, no-wait, no-idle flow shop problems. Archives of Control Sciences25(2), 189-199. https://doi.org/10.1515/acsc-2015-0012https://doi.org/10.1515/acsc-2015-0012Search in Google Scholar

[29] Montusiewicz, J. (2012). Wspomaganie procesów projektowania i planowania wytwarzania w budowie i eksploatacji maszyn metodami analizy wielokryterialnej Lublin: Wydawnictwo Politechniki Lubelskiej.Search in Google Scholar

[30] Nikoofal Sahl Abadi, N., Bagheri, M., & Assadi, M. (2018).Multi-objective model for solving resource-leveling problem with discounted cash flows. International Transactions in Operational Research25(6), 2009-2030. https://doi.org/10.1111/itor.12253https://doi.org/10.1111/itor.12253Search in Google Scholar

[31] Nguyen, A. T., Reiter, S., & Rigo, P. (2014). A review on simulation-based optimization methods applied to building performance analysis. Applied Energy113 1043-1058. https://doi.org/10.1016/j.apenergy.2013.08.061https://doi.org/10.1016/j.apenergy.2013.08.061Search in Google Scholar

[32] Mattila, K. G., & Abraham, D. M. (1998). Resource leveling of linear schedules using integer linear programming. Journal of Construction Engineering and Management124(3), 232-244. https://doi.org/10.1061/(ASCE)0733-9364(1998)124:3(232)https://doi.org/10.1061/(ASCE)0733-9364(1998)124:3(232)Search in Google Scholar

[33] Podolski, M. (2017).Management of resources in multiunit construction projects with the use of a tabu search algorithm. Journal of Civil Engineering and Management23(2), 263-272. https://doi.org/10.3846/13923730.2015.1073616https://doi.org/10.3846/13923730.2015.1073616Search in Google Scholar

[34] Ruiz, R., Vallada, E., & Fernández-Martínez, C. (2009). Scheduling in flowshops with no-idle machines. In Computational intelligence in flow shop and job shop scheduling (pp. 21-51). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02836-6_2https://doi.org/10.1007/978-3-642-02836-6_2Search in Google Scholar

[35] Rzepecki, Ł.,&Biruk, S. (2018). Simulation Method for Scheduling Linear Construction Projects Using the Learning–Forgetting Effect. In MATEC Web of Conferences (Vol. 219, p. 04007). EDP Sciences. https://doi.org/10.1051/matecconf/201821904007https://doi.org/10.1051/matecconf/201821904007Search in Google Scholar

[36] Samarghandi, H., & Behroozi, M. (2017). On the exact solution of the no-wait flow shop problem with due date constraints. Computers & Operations Research81 141-159. https://doi.org/10.1016/j.cor.2016.12.013https://doi.org/10.1016/j.cor.2016.12.013Search in Google Scholar

[37] Tang, Y., Sun, Q., Liu, R., & Wang, F. (2018). Resource Leveling Based on Line of Balance and Constraint Programming. Computer-Aided Civil and Infrastructure Engineering33(10), 864-884. https://doi.org/10.1111/mice.12383https://doi.org/10.1111/mice.12383Search in Google Scholar

[38] Tomczak, M. (2013). Problemy w logistyce małych i srednich przedsiebiorstw budowlanych. TTS – Technika Transportu Szynowego, 10(2013), 637-645.Search in Google Scholar

[39] Tomczak, M., & Jaskowski, P. (2018). Application of type-2 interval fuzzy sets to contractor qualification process. KSCE Journal of Civil Engineering22(8), 2702-2713. https://doi.org/10.1007/s12205-017-0431-2https://doi.org/10.1007/s12205-017-0431-2Search in Google Scholar

[40] Tomczak, M., & Rzepecki, Ł. (2017, October). Evaluation of Supply Chain Management Systems Used in Civil Engineering. In IOP Conference Series: Materials Science and Engineering (Vol. 245, No. 7, p. 072005). IOP Publishing. https://doi.org/10.1088/1757-899X/245/7/072005https://doi.org/10.1088/1757-899X/245/7/072005Search in Google Scholar

[41] Yaghoubi, S., Noori, S., Azaron, A., & Fynes, B. (2015). Resource allocation in multi-class dynamic PERT networks with finite capacity. European Journal of Operational Research247(3), 879-894. https://doi.org/10.1016/j.ejor.2015.06.038https://doi.org/10.1016/j.ejor.2015.06.038Search in Google Scholar

[42] Yaghoubi, S., Noori, S., Azaron, A., & Tavakkoli-Moghaddam, R. (2011). Resource allocation in dynamic PERT networks with finite capacity. European Journal of Operational Research215(3), 670-678. https://doi.org/10.1016/j.ejor.2011.07.006https://doi.org/10.1016/j.ejor.2011.07.006Search in Google Scholar

Received: 2019-02-10

Accepted: 2019-05-22

Published Online: 2019-07-25

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/eng-2019-0036

Keywords for this article

construction project management; project scheduling; renewable resource leveling; repetitive non-linear activities; schedule optimization

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