Applying genetic algorithms for construction quality auditor assignment in public construction projects

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Applying genetic algorithms for construction quality auditor assignment in public

construction projects

Yu-Ren Wang

a,

⁎

, Siang-Lin Kong

b a

Dept. of Civil Engineering, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung 807, Taiwan b_{Construction Ofﬁce, Public Works Bureau, Kaohsiung City Government, No.2 Shiwei 3rd Rd., Kaohsiung 802, Taiwan}

a b s t r a c t

a r t i c l e i n f o

Article history:

Accepted 27 November 2011 Available online 26 December 2011 Keywords:

Assignment problem Quality audit Optimization Genetic algorithms

Random third party quality audits are mandatory by the regulations for public construction projects in Tai-wan. This project and auditor selection process is normally carried out based on personal experience and the quality of the selection outcome is hard to predict and control. This is a difﬁcult work assignment problem because there are normally hundreds of projects and dozens of auditors to choose from. The purpose of this research is to establish a genetic algorithm-based model to assist with the project selection and auditor as-signment process. The model is set up toﬁnd the optimal match between the project characteristics and au-ditor expertise from approximately 5.09E + 29 possible combinations. Information provided by the Kaohsiung County Government is used to validate the model. The results show that the model is not only valid but also able to produce a“much better match” between projects and auditors when comparing to man-ual assignment.

1. Introduction

In order to improve the quality of the public construction projects, the Taiwan government has enforced a three-level quality manage-ment system since 1993. The goal is to promote the awareness of the importance of construction quality among all the participants in the public construction projects. Theﬁrst level is the quality control system carried out by the contractor. The second level is the construc-tion quality assurance system implemented by the local government construction department. The third level is quality audit system enforced by the national government construction department[1]. The structure of the three-level quality management system is shown inFig. 1.

To conduct the third-level quality audit, a quality audit committee is established in the Kaohsiung County Government. The committee is composed of one chairperson, two vice-chairperson, one secretary andﬁve staffs, 17 internal auditors and 45 external auditors. The au-ditors are nominated by the committee and approved by National Construction Council. Approved auditors are either experienced ex-perts (from government or from private sector) or knowledgeable scholars. The quality audit committee is responsible for selecting pub-lic projects to be audited and assign auditors for quality audits every month. In general, there are more than 150 construction projects in the list and eight projects are to be selected for audit each month. For each project, three auditors (one internal and two external)

should be assigned from the approved auditor list to conduct the quality audit. This is a complex assignment problem as there are many potential project and auditor combinations (approximately 5.09E + 29) to choose from. It is a very tough task confronting the quality audit committee and at times, the committee just randomly (or by gut feelings) selects projects and assigns auditors. As a result, some auditor expertise might not match the project characteristics well and thus the“quality” of the construction quality audit is in jeopardy.

To assist with this assignment problem, this research adopts ge-neric algorithms to develop a public construction project selection and auditor assignment model that aims atﬁnding optimal matches between the auditor expertise and project characteristics. With data provided by the Kaohsiung County Government, the model is proven to provide better recommendations regarding project selection and auditor assignment when comparing with traditional manual selec-tion and assignment process. Built in the MS Excel environment, this model can be easily utilized by the members in the quality audit committee to assist with the public construction project quality audit process.

In Japan, the Metropolitan Government of Tokyo also conducts au-dits on public construction projects to ensure no wasteful spending, shoddy workmanship and so forth at each stage of project execution

[2]. The proposed model can be adopted to assist the Tokyo City of ﬁ-cials select projects for audit and assign appropriate auditors. In other countries, private companies (often consulting companies) hired by the public agencies would perform the quality audits for public con-struction projects. With some customization, these private companies will be able to use the modi_{ﬁed model to assist the quality audit}

Automation in Construction 22 (2012) 459–467

⁎ Corresponding author. Tel.: +886 7 3814526x5250; fax: +886 7 3831371. E-mail addresses:yrwang@cc.kuas.edu.tw(Y.-R. Wang),dozekidd@kcg.gov.tw

(S.-L. Kong).

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process. With a better match between auditor expertise and project characteristics, it is expected that the“quality” of the quality audit will be improved.

2. Assignment problem

Generalized assignment problem (GAP) deals withfinding the op-timal solution among many different combinations, which are con-cerned with assigning n jobs to m agents under constraints. Every agent has different capabilities and resource constraints. When per-forming each job, the cost occurred and efficiency achieved is differ-ent for each agdiffer-ent. The purpose of solving GAP is to assign appropriate agent to complete the n jobs so that the lowest total cost or the highest overall profit is achieved. It can be expressed in the following equations[3]:

Maximize or minimize f xð Þ ¼X m i¼1 Xn j¼1 cijxij ð1Þ subject to X m i¼1 xij¼ 1; j¼ 1;2;…;m ð2Þ Xn j¼1 rijxij≤ bi; i ¼ 1;2; …;n ð3Þ

Eq.(1)is the objective function and Eqs.(2) and (3)are problem constraints. n is the total number of jobs to be performed and m is the total number of agent available to perform the jobs. Cijrefers to the cost occurred or proﬁt obtained for agent i to complete job j. When Xijequals one, it means that agent i is assigned to perform the job j. On the other hand, when Xijequals zero, agent i is not appointed to perform the job j. rij is the resource consumed by agent i to perform the job j and biis the total resource available for agent i. Eq.(2)makes sure that each job is performed by only one agent and Eq.(3)makes sure that the resource consumed by each agent does not exceed the capacity limit.

This research intends to investigate effective techniques for assigning auditors and selecting projects for public construction audit under constraints. That is, to optimize the match between audi-tor expertise and project characteristics. Several researches have been conducted to solve this sort of assignment problems with different techniques/algorithms. Nevertheless, none has been applied to solve quality auditor assignment problem before. Algorithms aiming at re-solving assignment problems can be summarized as exact algorithms and heuristic algorithms, which will be discussed in the following sections.

2.1. Exact algorithms

Exact algorithms are one of the algorithms used to_{find exact} solu-tions to optimization problems. Savelsbergh proposed a Branch-and-Price algorithm tofind the maximum profit when assigning n jobs to m agents under capacity constraints[4]. The algorithm considers the linear programming relaxation of the disaggregated formulation for the generalized assignment problem (GAP) and allows column gener-ation at any node of the branch and bound tree. The optimal integer solutions to a set partitioning formulation of the problem can thus be obtained[5]. Narciso and Lorena applied Lagrangean/surrogate re-laxation to the problem of maximum profit assignment of n tasks to m agents (n > m), such that each task is assigned to only one agent sub-ject to capacity restrictions on the agents[5].

A Branch-and-Bound algorithm is proposed by Haddadi and Ouzia to solve the generalized assignment problem with largest-upper-bound-next branching strategy[6]. Lagrangean relaxation is achieved by dualizing the second set of constraints. An upper bound is obtained using a standard subgradient method at each node of the decision tree to solve the lagrangean dual. By solving a smaller generalized as-signment problem, the algorithm exploits the solution of the relaxed problem[6].

Gomar et al. proposed a linear programming model to optimize the multi-skilled workforce assignment and allocation process in con-struction[7]. Their objective is toﬁnd the minimum total number of workforce, switching and hires/ﬁres. The model is able to suggest ac-tivity assignments that minimize switching and can be used to set strategic targets for combination of multi-skills[7].

2.2. Heuristic algorithms

Different from the exact algorithms, heuristic algorithms only_ﬁnd approximate solutions to the problem. As a result, optimal solutions are not guaranteed under heuristic search but“good” solutions can still be obtained within reasonable run times. Pearl states that heuris-tic methods are based upon intelligent search strategies to control problem solving in human beings and machines[8].

Chu and Beasley proposed a genetic algorithm (GA)-based heuris-tic for solving generalized assignment problem[3]. Comparing to other heuristic algorithms in terms of solution quality, the GA-based algorithm is able to provide the best possible heuristic solutions when assigning n jobs to m agents under capacity constraints. The re-sults show that the near-optimal solutions found are on average less than 0.01% from optimality[3].

Diaz and Fernandez applied Tabu search heuristic to solve the GAP

[9]. Different from other search techniques, Tabu search enhances the performance of a local search method by using memory structures. The proposed algorithm uses recent and medium-term memory to dynamically adjust penalty weights when constraints are violated. The most distinctive feature of the proposed algorithm is the permis-sion of solution search in the infeasible solution space. Comparing to other heuristic methods, the Tabu search heuristic provides good quality solutions in competitive computation times[9].

A GA-based algorithm is proposed by Tororslu and Arslanoglu to solve an extended version of the standard assignment problem, which has additional constraints for matching the nodes of the parti-tions[10]. When solving the GAP, both the hierarchical-ordering and set-restriction constraints are taken into consideration for large hier-archical organizations. The results show that GA-based algorithm provides good solutions for the multi-objective optimization problem

[10].

Exact algorithms are only effective in certain GAP instances where the constraints are loose. For highly capacitated problems, exact algo-rithms can only solve problems involving up to a few hundred vari-ables before the search trees grow prohibitively large. The large-sized problems are often tackled by applying heuristics to obtain Fig. 1. Three-level quality management system.

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there are approximately 2.5 × 1027 _possible _combinations (C219× C332× C3105× C817× C1645). The data from October of 2008 is taken as the input for the proposed GA model toﬁnd the optimal assign-ment of construction project and corresponding auditors. The GA pa-rameter setting are: (a) population in each generation set as 50, (b) crossover rate set as 0.5, (c) mutation rate set as 0.05, and (d) stop-ping condition set as less than 0.1% change in last 5000 valid trials. The model simulation results from 10 trials are summarized in

Table 5.

FromTable 5, the average of bestfitness value found from 10 trials is 5512. Comparing to thefitness value (2431) of manual assignment in October 2008, the model results obtained are much better. The best fit-ness value found overall is in the 10th trial (in bold italics) with the highestfitness value of 5865. In order to examine the quality of the search results, the model is applied again with smaller solution space (fewer model variables) to see if better results can be obtained. In order to do this, the selected projects for the bestfitness value obtained in the 10 trials arefixed before applying the GA model again. Thus, the total number of variables is reduced from 32 to 24 as the model only has to search for corresponding auditors. The GA model results are listed in

Table 5under the column“Fix project”. The deviations indicate the dif-ference of the search results before and after the projects areﬁxed in the search process. The average deviation, 0.81%, is small and this shows

that the proposed GA model yields relatively good results comparing to results obtained with smaller search space.

The best assignment results from October are taken as the input for the proposed GA model to search for the optimal project and au-ditor assignment for November of 2008. The average best fitness value found for 10 trials is 4478. This is lower than the average from the previous month. The major contributing factor for this de-crease is that penalties will be applied to thefitness function if audi-tors are already selected in previous months. To avoid the penalty, the auditors chosen in November must be different from the ones in Oc-tober and as a result, they might not be the best candidates to per-form the quality audits. This is to ensure that total number of assignments for each quality auditor is equally distributed. Similarly, the assignment results from October and November are taken as input for the model to obtain audit assignment for December of 2008. The average best value found for 10 trials is 4359. Taking the three month's quality audit data as the model input, the GA model de-veloped is capable of making suggestions for auditor and project as-signment with high _{fitness values. This shows that the model} developed is able assist with the Kaohsiung County Government Con-struction Office during the quality audit project selection and auditor assignment process.

6. Conclusions

To ensure the quality of the public construction projects, random third-party quality audits are required by the regulations in Taiwan. In practice, the project selection and auditor assignment is arranged manually by quality audit committee staffs. The manual selection re-lies heavily on personal experience/judgment and oftentimes, the au-ditor expertise does not match the project characteristics well. In fact, this is a complicated assignment problem because for each month, there are typically more than 150 on-going projects and 62 registered auditors to choose from. In order to solve this problem, this research proposes a GA-based model to assist with the project selection and auditor assignment process. With actual data input from Kaohsiung County Government, the model is developed and validated by com-paring model outputs with manual assignment results. The results show that the GA model outputs have a much better match between auditor expertise and project characteristics. It is believed that with a better match between auditor expertise and project characteristics, the“quality” of the quality audit will be improved. In this research, the proposed GA model is proven to be successful in solving the con-struction project selection and quality auditor assignment problem. Built in the Excel environment, this model can be easily adopted by public construction ofﬁcials or private consulting companies in other countries to assist with their quality audit process for public construction projects.

References

[1] The Executive Yuan, Public construction project quality management system,

http://www.pcc.gov.tw/1993.

[2] The Secretariat to Audit and Inspection Commissioners of the Tokyo Metropolitan Government,http://www.kansa.metro.tokyo.jp/03kouji/kouji_en.html2011. [3] P.C. Chu, J.E. Beasley, A genetic algorithm for the generalized assignment

prob-lem, Computers and Operations Research 24 (1) (1997) 17–23.

[4] M. Savelsbergh, A Branch-and-Price algorithm for the generalized assignment problem, Operation Research 45 (6) (1997) 831–841.

[5] M.G. Narciso, L.A.N. Lorena, Lagrangean/surrogate relaxation for generalized as-signment problems, European Journal of Operation Research 114 (1999) 165–177.

[6] S. Haddadi, H. Ouzia, Effective algorithm and heuristic for the generalized assign-ment problem, European Journal of Operation Research 153 (2004) 184–190. [7] J.E. Gomar, C.T. Haas, D.P. Morton, Assignment and allocation optimization of

par-tially multiskilled workforce, Journal of Construction Engineering and Manage-ment 128 (2) (2002) 103–109.

[8] J. Pearl, Heuristics: Intelligent Search Strategies for Computer Problem Solving, New York, Addison-Wesley, 1984.

[9] J.A. Diaz, E. Ferandez, A Tabu search heuristic for the generalized assignment problem, European Journal of Operational Research 132 (1) (2001) 22–38. Table 4

Manual assignment results vs. model assignment results. Assignment method Project no. 3 13 21 27 28 44 61 98 Fitness Manual assignment Internal auditor 16 9 13 1 17 2 3 1 2,351 External auditor 1 7 1 3 39 2 20 8 30 External auditor 2 28 34 17 27 23 34 11 33 Match index 0.75 0.5 0.5 0.25 0.25 0.5 0.75 0.25 GA model assigns selected auditors Internal auditor 9 2 16 1 13 1 17 3 3,997 External auditor 1 33 28 3 11 34 8 34 20 External auditor 2 2 39 17 7 27 30 1 23 Match index 1 1 1 1 1 1 1 0.75 Auditors selected freely by GA model Internal Auditor 9 2 16 1 3 6 12 14 4,849 External auditor 1 32 13 3 7 19 33 4 16 External auditor 2 2 12 17 41 34 14 11 40 Match index 1 1 1 1 1 1 1 1 Table 5

Test results for the case simulation.

P0P = 50 Last 5000 changeb0.1% Fix project Deviation Trial Best value

found Occurred on trials Time to ﬁnd (s) Stop time (s) Best value found 1 5713 25,193 158 190 5775 1.09% 2 5416 15,871 103 135 5508 1.71% 3 5350 14,944 91 121 5434 1.58% 4 5076 11,281 70 104 5123 0.93% 5 5807 23,975 146 177 5850 0.74% 6 5304 18,712 111 144 5340 0.68% 7 5517 21,195 136 166 5522 0.10% 8 5685 17,370 116 147 5738 0.94% 9 5382 17,594 114 146 5404 0.40% 10 5865 24,937 205 250 5865 0.00% Average 5512 19,107 125 158 5,556 0.81%

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[10] I.H. Toroslu, Y. Arslanoglu, Genetic algorithm for the personnel assignment with multiple obectives, Information Sciences 177 (2007) 787–803.

[11] J. Holland, Adaption in Natural and Artiﬁcial Systems, The University of Michigan Press, Ann Arbor, MI, 1975.

[12] Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, New York, 1996.

[13] D.E. Goldberg, Genetic algorithms in search, Optimization and Machine Learning, Addison Wesley, Reading, MA, 1989.

[14] D.A. Coley, An introduction to genetic algorithms for scientists and engineers, WorldScientiﬁc, Singapore, 1999.

[15] Government Kaohsiung County, 2008 Project Audit Plan, Kaohsiung, Taiwan, 2008, 2008

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