Linear Programming for Optimizing Strategic Construction Workforce Management

First International Conference on Construction In Developing Countries (ICCIDC I) Advancing and Integrating Construction Education, Research & Practice August 4-5, 2008, Karachi,, Pakistan Linear Programming for Optimizing Strategic Construction Workforce Management Alireza Mohammadpour Student of MSc in Construction Engineering and Management, Department of Civil Engineering,Iran University of Science and Technology,Tehran, Iran mohammadpourmail@gmail.com Mostafa Khanzadi Assistant of professor, Department of Civil Engineering,Iran University of Science and Technology,Tehran, Iran Ehsanollah Eshtehardian Candidate of Ph.D in Construction Engineering and Management, Department of Civil Engineering,Iran University of Science and Technology,Tehran, Iran Abstract One of the most important factors in construction project management is to provide skilled labor relevant to the technical project requirements. Major problem in this field is shortage of skilled labor. A key reason for this problem is the absence of human resource management strategy for construction project. To choose an optimized strategy for making the best use of available workforce with the intent to reduce project costs. This paper presents a model to combine training and hiring workforce in different levels of skills. Linear programming is used for solving this model to achieve optimized solution. The input data to proposed model consists of certain available labor pool, cost configures for training workforce in different skills, the cost of hiring workforce, hourly labor wages, and estimates of affinities among the different considered skills and their levels. Therefore, project manager or decision maker by using this model and paying attention to condition of training and hiring workforce will be able to make best decision to minimize project costs. Keywords Resource Management, Linear Programming, Training, Hiring. 1. Introduction Therefore In the most part of the world the construction industry is facing skilled labor shortage. Skilled labor shortage problem by increasing construction projects, and limit of it has been intensified. This shortage has been considered in most countries that shows the significance of the issue. Tucker et al. attribute the problem to other factors such as the generally poor image of the industry, a working environment that is considered undesirable, the transient nature of the work, and the resulting unclear career paths in construction. Much of the workforce remains unskilled or under-skilled, therefore training must be considered as an option when staffing for a project. This study provides an optimization-based framework for matching supply and demand of construction labor most efficiently through training, 161

recruitment, and allocation. The objective of the model is to minimize labor costs while satisfying project labor demands. 2. Literature Review A more recent study by the Construction User Round Table (CURT 2001) in United States showed that owner companies considered the shortage of skilled labor as the most critical problem today s construction industry is facing. Recent statistics published by the Bureau of Labor Statistics of United States (BLS 2004) indicate that by 2010, there will be a need to replace 1,469,000 construction trade worker jobs. The recent BLS data indicate that the construction industry is projected to be the largest and fastest source of employment growth among goods producing industries. The construction industry in the United Kingdom for example is facing a skilled labor shortage (Mackenzie et al. 2000). The United Kingdom construction industry must draw from all labor sources irrespective of construction-related experience, age, gender, ethnic, or social background. A study of infrastructure in South Africa revealed a shortage of individuals to build and maintain infrastructure in underdeveloped areas (Philips et al. 1995). A study of railways in Japan linked the reduction in maintenance of the existing lines to the problem of labor shortages (Tarumi 1994). Several solutions have been used to alleviate the problem of skilled labor shortages in construction. These include increased wages and other incentives such as guaranteed overtime, implementation of training incentives, employing foreign labor or even outsourcing construction work to foreign sources, and reduction of demand through automation and technology (Pappas 2004). A recent collaboration between the Construction Industry Institute (CII) and the Center for Construction Industry Studies (CCIS) at the University of Texas at Austin produced a theoretical model for a revolutionary way to address the issue in a more comprehensive manner. Although the method, called Tier II, is new and future oriented, it may have a considerable impact on the construction workforce and industry (Castaneda 2002). The proposed Tier II strategy calls for training workers possibly in more than one skill, including management and other soft skills. This document focuses on the implementation of one of the main elements of the Tier II strategy, namely how to improve workers skill sets. The main objective is to provide a framework for making the best use of the available workforce and its skills set using an optimization-based approach. The use of optimization techniques is not limited to the construction industry. Optimization is a concept that has been extensively used in different fields such as communication, transportation, health care, manufacturing, finance, and others. The need for mathematical programming techniques to optimize strategic investment in the construction workforce has been noted in several studies (Gann and Senker 1998; and Gomar et al. 2002). Gomar et al. (2002) acknowledged this need and developed a model capable of optimizing the labor allocation and assignment process of a partially multiskilled workforce and a single-skilled workforce with the multiple objectives of minimizing hires, maximizing employee duration on project, and minimizing reallocation within the project. In another study which mentions the need for a multiskilled workforce multiskilled employees are needed increasingly, especially in repair and maintenance work. Srouri (2006) tried to present a model choosing a better choice between training and hiring that emphasized minimizing costs. This study uses mathematical modeling techniques to provide a strategy to work within the constraints of the ongoing construction labor shortage situation. It provides an optimal investment strategy for construction companies in their workforce. 3. Model Formulation Before writing a model there are some assumptions to reach the best results from the model. It is important to mention that for creating the model, Linear Programming is used. This linear model is solved by Lingo software. The level of training skills is divided into skilled (skilful) and helper, but labor hired in single or multiskills would do the work at skilled level. In continued it presents decision variables, objective function, and constraints. 162

3.1 Decision Variables X : The number of workforce who possess only skill i and will be trained k level from skill j. Y i : The number of workforce with only skill i to be hired. L t : The number of workforce possessing skills i and j in k(skilled) level, working in their primary skill i during time period t. N it : The number of workforce with skill i working during time period t. Z : The number of workforce possessing skills i and j the skilled level to be hired. M t : The number of workforce possessing skills i and j in k(skilled) level, working in their secondary skill i during time period t. note : k here means the workforce that is skilled level in his occupation. 3.2 Objective Function The objective function of the linear model is defined as follow : train cos t X + Yi hirecos ti + Z hcos t + i j k α i j i j n wage hrsperweek + L W hrsperweek + M W hrsperweek it i t t i t i j t i j t train cost X i j k α, The cost that will be incurred to train in k level from skill j, the workforce already possess skill i. train cost : cost in Rials ( Iranian unit of money) to train workforce who possess skill i in k level from skill j. α, skill affinity penalty between skills i and k level from skill j with values ranging between 0 and 1 ; Y i hire costi i : The cost that will be incurred to hire workforce with skill i, hirecost i : hiring cost in Rials of workforce with skill i ; Z hcost i j : The cost that will be incurred to hire workforce with skill i and j at skilled level, h cost : hiring cost in Rials of workforce who possess skills i and j at skilled level (k level) ; nit wagei hrsperweek i t :The incurred wages on site for workforce who possess only skill i, wage i :hourly wage in Rials of workforce with skill i ; hrsperweek :number of weekly hours of work ; t : time period index ; Lt W hrsperweek i j t, The incurred wages on site for workforce who possess skill i and j, at skilled level, working with skill i during time period t W :hourly wage in Rials of workforce with skill i and j at skilled level. M W hrsperweek, The incurred wages on site for the workforce who possess skill i and j,at i j t t 163

3.3 Constraints The constraint of the linear model is defined as follow : 3.3.1 Meeting the demand dit t for skill i during time period t using bi-skilled workforce (possessing skills i and j,both at the k level) and single-skilled workforce (possessing skill i, at k level): L + M + n d j t t it it j dit can be obtained from scheduling software. It consists of the daily demand loading as calculatedby scheduling software based on the project schedule, loading of all project activities with the resource requirements, and leveling the schedule using these resources.this equation may be interpreted as follows: the number of workers working with skill i during the time period t must be greater than or equal to the demand for workers with skill i during the same time period. 3.3.2 Training capacity of k (skilled) level from skill j: X traincap i k The reason for having this set of constraints is that there might be conditions in which there is a limitation on the number of workforce that can be trained during a short time period. 3. Hiring capacity : Yi hirecapi the number of workforce to hire with skill i is limited by a certain number of available workforce hirecap i. Z hirecap the number of workers to hire with skills i and j (bothof them at the k level) is limited by a certain number of available workforce. 3.3.4 Availability constraints: nit Si + yi + X j k A set of constraints which makes sure that the model does not use more workforce with skill i during time period t than the available pool, Si represents the number of workers with skill i who are already employed by the company. Lt + M t X + Z + P A set of constraints which makes sure that the model does not use more workforce with skills i and j (both of them at k level) during time period t than the available pool, and P represents the number of workforce with skills i and j who are already employed by the company. jk 4. Evaluation of Case Study 4.1 Input Data Among the skills used during the project, the skills are considered that have had more effect on the progress of the project. Such skills have training and certificate aspect. Meanwhile a five period of duration has been considered. The number of workforce for each skill during the week has been obtained from the schedule of the project. Selected skills from this project are: welding, electric work, and concrete finishing. Number of single skilled workforce needed at the beginning of the project at skills :welding, electric work, and concrete finishing respectively are : 4, 5, and 8.numberof bi-skilled workforce needed at the beginning of the project, shown at table 1. 164

Table1: Number of Bi-skilled Workforce at the Beginning of Project Electrician - 0 1 Concrete Finisher 0-1 Welder 1 1 - Hourly wages of single-skilled workforce for welder, electrician, and concrete finisher in Rials respectively are : 20000, 17000, and 12000. Hourly wages of bi-skilled shown at table 2. Table2: Hourly Wages of Single-skill Workforce in Rials Electrician - 10000 40000 Concrete Finisher 10000-40000 Welder 40000 40000 - For skills which have less relation or management is not willing between them, it is tried the model by showing partial view of decision maker not to draw toward unwanted choice. Therefore relevant parameters for two skills, it is used quantities, that the model doesn t follow such relation. For training workforce at secondary skill, there are some costs based on held training hours periods their quantities are shown at table 3. Table3: Workforce Training Costs in Rials Electrician - 150000,200000 50000,100000 Concrete Finisher 150000,200000-100000,200000 Welder 50000,100000 100000,200000 - It is supposed recruiting multiskills for each required skill is at the skilled level. hiring workforce costs for single-skilled, welder, electrician, and concrete finisher respectively are : 120000, 100000, 80000. Hiring costs for bi-skilled are shown at table 4. Table4: Bi-skilled Workforce Hiring Cost in Rials Electrician - 200000 1500000 Concrete Finisher 200000-130000 Welder 1500000 130000-165

It is necessary to know that for hiring single-skilled and bi-skilled based on project condition there are some limits for capacity of hiring. Maximum number of workforce with single-skilled that can be hire at welding, electric works, and concrete finishing respectively are: 3, 3, and 5. Maximum number of workforce with bi-skilled that can be hire are shown at table 5. Table5: Maximum Number of Workforce With Bi-skilled That Can Be Hired Electrician - 0 1 Concrete Finisher 0-0 Welder 1 0 - The number of needed workforce for each week based on project schedule is shown at table 6. Table6: Number of Workforce for Each Skill During The Five Period week skill 1 2 3 4 5 Electrician 1 0 3 0 1 Concrete Finisher 4 5 3 2 0 Welder 1 3 3 1 0 Since there are not same relations among some skills and their levels, α coefficient is used to show the affinities among skills. If there is more affinities among different skills and their levels, more quantities of α is required. The quantities of α are shown at table 7. Skill Table6: Skill Affinity Coefficient for This Study α Electrician (skilled, helper) Concrete Finisher (skilled, helper) Welder (skilled, helper) Electrician n/a 0.65,0.85 0.2,0.35 Concrete Finisher 0.65,0.85 n/a 0.55,0.75 Welder 0.2,0.35 0.55,0.75 n/a 4.2 Results From Case Study After modeling in modified software and running the model, the following out put has been obtained that it will be considered after presenting the output: - Two electricians should be trained in welding at helper level before the beginning of the project and vice versa. - One electrician skilled in welding and in his primary skill, electrician, work at first work. - Two persons at second week and one person at third week work at concrete finishing. - Three electrician skilled in welding and in secondary skill, welding, work in third week. - One electrician skilled in welding and in secondary skill, welding, work in fifth week. - One welder skilled in electric work and in secondary skill, electric work, work in first and fourth week. At the other quantities belong to decision variables are zero,it means that reach the minimum cost of this project shouldn t be accepted any quantities. 166

To consider the quantity and first purpose of training and hiring workforce important results have been presented.in this project the training skills with little affinity because of higher cost have been omitted, instead the model is continued with training related skills to reduce the cost of training.providing electrician and welder is the main necessity of the project that is tried as much as possible to overcome the shortage.the shortage of concrete finisher occurs at the middle weeks of the project. Therefore, it seems hiring workforce at the skilled level in compared with training workforce who are working in the project, has less economic justification. Meanwhile, hiring bi-skilled labor with more affinity between skills for the project helps to reduce the cost of this part, however, there are some biskilled workforce at the beginning of the project. 5. Conclusions As mentioned one of most important factor at management construction project is providing relevant skilled workforce in the project requirement.by using linear model presented in this paper, managers will be able to make better decision for overcoming the shortage of skilled workforce In construction projects. By using this model a manager will be able to choose one of the solutions whether training available workforce and hiring out of project, based on costs. Meanwhile, considering the leeling skills, manager are able to reduce and control training and hiring costs. 6. References Castaneda, J. C. _2002_. Workers skills and receptiveness to operate under the tier II construction management strategy. Dissertation, Univ. of Texas at Austin, Austin, Tex. Gann, D. and Senker, D. (1998) Construction skills training for the next millennium, Construction Management and Economics, 16, 569-580. Gomar, J.E., Haas, C.T., and Morton, D.P. (2002) Assignment and allocation optimization of a partially multiskilled workforce, Journal of Construction Engineering and Management, March-April, 103-109. Mackenzie S., Kilpatrick A.R. and Akintoye A. (2000) UK Construction skills shortage response strategies and an analysis of industry perceptions. Construction Management and Economics, 18, 853-862. Pappas, M.P.( 2004) An assessment of iimplementation requirements for the tier II construction workforce strategy.the University of Texas ataustin, Austin, TX. Philips, S.D., McCutcheon, R.T., Emery, S.J., Little, R., and Kwesiga, M.B., (1995) Technical Analysis of Employment Potential of a National Public Works Programme, Journal of the South African Institution of Civil Engineers, 37(3),18-24. Tarumi, H. _1994_. Review of research on ballast and roadbed. Quarterly Rep. of RTRI (Railway Technical Research Institute), Tokyo, 35_1_, 15 18. Tucker, R. L., Haas, C. T., Glover, R. W., Alemany, C., Carey, L. A.,Rodriguez, A., and Shields, D. (1999). Key workforce challenges facing the American construction industry: An interim assessment. Rep. No. 3, Center for Construction Industry Studies, Univ. of Texas at Austin, Austin, Tex. Srouri I.M, Hass C.T. and David P.Morton (2006) Linear programming approach to optimize strategic investment in the construction workforce. Journal of Construction Engineering and Management, Volume 132, Issue 11, pp. 1158-1166. 167