A Model Used in Creating a Work-Rest Schedule for Laborers

Transcription

1 A Model Used in Creating a Work-Rest Schedule for Laborers Machine Hsie a, Wen-Ta Hsiao a, and Tao-ming Cheng b a Department of Civil Engineering, National Chung-Hsing University, Taiwan. b Department of Construction Engineering, Chaoyang University of Technology, Taiwan. Abstract This paper presents a mechanism in developing work-rest schedules for construction labors. Two objectives are balanced in the optimization processes. These objectives include minimizing the time for completing jobs as well as minimizing total extra energy that labors expend due to inappropriate work assignment which forces labors to working longer than maximum acceptable work duration. Experiments on examples demonstrate that the proposed mechanism effectively locates work-rest schedules. Key words: Work-rest schedule, job rotation schedule, physical energy expenditure, maximum acceptable work duration, genetic algorithms, multiobjective optimization 1. INTRODUCTION Construction workers have done much work outside which is easily affected by environmental factors such as humidity and temperature. These conditions would increase mental workload or physical workload or both to workers. In addition to these workloads, construction workers usually perform jobs with over-exertions and awkward postures in restricted working environment with less use of machinery. Their work, as a result, is very physical demanding (Koningsveld and Molen 1997, Abdelhamid and Everett 2002, Abdelhamid and Everett 1999, Imbeau et al. 1995). Physically demanding work not only leads to physical fatigue but causes negative problems such as the loss of productivity, poor quality work, and cumulative trauma disorders (National Safety Council 2000, Nechaev 2001). Possible preventive measures such as organization of work can be strived for avoiding the cause of workers physical fatigues (Beynon et al. 2000). Proper job rotation is one of good Corresponding author: tmcheng@cyut.edu.tw, Tel: ext. 7580, Fax:

2 means in improving the organization of work (Tharmmaphornphilas et al. 2003, Tharmmaphornphilas and Norman 2004, Kuijer et al. 1999, Dababneh et al. 2001, Gallis 2006, Corominas et al. 2006, Konz 1998). The purpose of job rotation scheduling is to balance productivity demands and safety concerns or physical workload of the personnel involved in meeting this demand in manufacturing environment (Carnahan et al. 2000). For instance, Tharmmaphornphilas et al. (2003) proposed a mathematical model to create job rotation schedules in minimizing noise exposure for labors working in sawmill. Another example is shown in Tharmmaphornphilas and Norman (2004). They explore the advantages of rotating tasks to reduce worker s fatigue. In spite of decreasing worker s physical fatigue, job rotation but has no effect on recovery once fatigue is accumulated and over one s limitation. Recovery is the key factor not causing the accumulation of fatigue (Kuijer et al. 2004). As a result, work-rest schedule is usually designed when recovery is considered (Wood et al. 1997). A work-rest schedule involves the frequency, duration, and timing of rest breaks. Proper design of work-rest schedule may be effective in improving worker s comfort, health and productivity (Genaidy and Al-Rayes 1993, Kopardekar and Mital 1994). A good example can be found in Dababneh et al. (2001). They conducted an experiment involving of providing extra break time to meat processing workers. The experimental results show no negative effect on production but reduce their discomfort. Construction workers (such as those in Taiwan frequently working 7 days a week without adequate rest to recover from fatigue) particularly need proper design of schedules allowing labors having rests. However, research for designing work-rest schedule in construction environment is rarely reported. On the other hand, work-rest schedule permits a recovery from fatigue but neglects the time constraint for finishing job as those frequently seen in construction scheduling. It is necessary to develop a scheduling mechanism for arranging job for construction worker to safeguard them away from over-exertion in dealing physical demanding works. Meanwhile, time constraint should also be cope with in the such scheduling mechanism. Hence, this research aims at developing a model to be used in the generation of construction workers schedules. The model would rotate the workers through different activities and provide workers break but balance the time-span that is needed to complete the job as well. A genetic algorithms-based modeling mechanism is used to create such schedules. In addition, the worker s energy expenditure is used as an index in representing worker s fatigue level. Therefore, the schedules balance two objectives, which minimize both the time for completing jobs and extra energy that labors expend due to inappropriate work assignment.

3 2. BACKGROUND The scheduling mechanism adopts energy expenditure as a criterion to judge three things: labor s work capacity, maximum acceptable work duration if job s physical demand exceeds labor s work capacity, and rest time needed for recovery from fatigue. The related theories or models used in this research are presented in this section. 2.1 Measuring individual s work capacity To evaluate an individual s physical workload is to express his/her energy expenditure relative to an individual s physiological capacity. The physiological capacity is based on the maximum aerobic capacity which is usually expressed by the maximum volume of oxygen (VO 2max ) that a person can take in a minute (Wu and Wang 2001). An individual s VO 2max can be determined by actual testing procedure or predicted by experimented equation such as shown in Equation (1). A person s VO 2max is related to his/her gender, age, and body composition. VO 2max (l/min)=[ (1.951*sre)-(0.754*bmi)-(0.381*age)+(10.897*gender)]*w/1000 (1) In this equation, W represents one s weight (kg) and gender equals to 1 for male and 0 for female, respectively. BMI (body mass index) and SRE (self-report level of aerobic exercise) measure one s body composition. BMI is calculated by having one s weight (kg) to be divided by square of one s height (m). SRE is used to rate one s scale of physical activity and readers may refer to Jason s and Ross s (1996) paper for the details of acquiring self-report scale of SRE. For instance, if an individual regularly participates in recreation such as weight lifting for 10 to 60 minutes a week, his/her SRE is rated as 2. If a 32-year-old man s weight, height, and SRE are 75 kg, 1.70 m, and 3, respectively, his VO 2max can be estimated around 3.1 l/min based on equation (1). 2.2 Energy expenditure A kilocalorie (kcal) is an energy unit, defined as the quantity of heat necessary to raise temperature of 1 kilogram of water by 1 (Coletta, 1995). It is used as the unit for measuring energy expended by an individual at rest or during work. In general, every liter of oxygen consumed by an individual, 4.83 kcal of energy is produced (Murrell 1965). Thus, the energy expended when human is at rest or during work can be obtained by multiplying oxygen uptake (liter) with Maximum acceptable work duration

4 Normally, one could not sustain their physical activity without causing fatigue if required workload is higher than 33% of one s VO 2max (Saha et al. 1979, Wu and Wang 2001). In other words, fatigue can be accumulated if physical requirement exceeds 33% of one s VO 2max. In construction operations, high physical demanding activities such as making brick wall are frequently seen. The workload for such activities usually are over one s 0.33 VO 2max (Abdelhamid and Everett 2002). In order to avoid the accumulation of fatigue, maximum acceptance work duration (MAWD) should be applied when one performs such operations. Equation (2) describes the estimation of MAWD according to one s relative oxygen uptake rate (RVO 2 ) (Wu and Wang 2001). e RVO2 MAWD( min) = (2) where RVO VO VO 2 work 2 rest 2 = and VO2 work (l/min) and VO2 rest (l/min) represents VO 2 max VO 2 rest the oxygen uptake rate during work and rest, respectively. In usual, the oxygen uptake rates during rest for men and women are 0.34 l/min and 0.3 l/min, respectively. If a man, whose VO 2max is estimated around 3.1 l/min, works on a job that requires the man to uptake oxygen in 1.8 l/min, his MAWD is expected to be min based on the calculation using equation (2). 2.4 Rest time Once an individual works on a job requiring him/her to consume oxygen is more than his/her 0.33VO 2max and in addition, he/she works longer than his/her MAWD, fatigue increases exponentially with time (Konz 1998). Under such circumstance, enough rest can prevent one from the accumulation of fatigues and loss of productivity. Equation (3) shows the calculation of rest time needed if one works longer than his/her MAWD (Konz 1998). Assuming a man s VO 2max is 3.1 l/min and he works 30 min on a job requiring him to uptake oxygen 2.0 l/min (greater than this man s 0.33VO 2max ), the man can only work no longer than min (MAWD) without causing fatigue and thus he needs min break for recovery according to the calculation by using this equation. R (min)=work time (min)*(vo 2work -0.33VO 2max )/(VO2 max -VO2 rest ) (3) where (VO 2work VO 2max )<0, then R=0. 3. SCHEDULING MECHANISM The scheduling process is demonstrated in Fig. 1. The steps of producing such schedule are described in the following.

5 Step 1: Create job sequence at random. Step 2: Put labors in queue. Step 3: Assign labors in queue to perform tasks based on first-in-queue-and-first-out principle until no labor in queue. Step 4: Examine if all tasks are completed. If so, go to step 7, otherwise, go to next step. Step 5: Check individual labor s working time whether exceeds his/her MAWD (obtained from the calculation using equations (1) and (2)). If not, return to step 2, otherwise, go to next step. Step 6: Force labor to take a rest in R (computed based on equation (3)) minute, then return to step 2. Step 7: Stop the labors assignment operations. Fig. 1 Flowchart of scheduling scheme 4. MULTIOBJECTIVE OPTIMIZATION The goal for the job rotation schedule generation model is to acquire a job assignment schedule, which is to minimize both duration for finishing the job and extra energy that labors spend in over-exertion activities. Thus, the model involves in solving a multiobjective optimization problem. Multiobjective optimization concerns the problem of seeking solutions over a set of possible choices to optimize more than one criterion. Various approaches, such as using multiobjective weighting and the use of a utility function can reduce the multiobjective problem to a scalar optimization problem, but it involves selecting a preference among objectives. However, establishing a Pareto front, as in this study, is perhaps one of the most effective methods for solving multiobjective optimization problems (Gen 1997). A Pareto front is a set of solutions in the multiobjective case that cannot be simply compared with each other. In other words, no objective function

6 can be improved without sacrificing at least one of the other objective functions for any Pareto solution in the Pareto front. Figure 2 displays the concept of the Pareto front in a two-objective optimization problem. Z 1 and Z 2 are objectives to be minimized. In this study, the total time required for completing a job is minimized while the total extra energy expenditures workers spending in performing the job is minimized as well. Therefore, establishing the Pareto front is effective in a GA-based evolutionary process. In addition, the calculation of total extra energy expenditure (TEEE) is described in equation (4). The unit of TEEE is converted to Kcal by multiplying 4.83 because every liter of oxygen consumed by an individual, 4.83 kcal of energy is produced. ( WT j MAWDij ) ( VO work j n m ( Kcal) i= 1 j 1 TEEE ) = (4) where WT j : working time needed for carrying out activity j; MAWD ij : maximum acceptable work duration that labor i performs activity j; (VO 2work ) j : oxygen uptake rate needed for performing activity j; n: the number of labor: m number of activity. Fig. 2 Example of Pareto front 5. GENETIC ALGORITHMS Genetic Algorithms (GA) is the search algorithm developed by Holland (Gen 1997), which is based on the mechanics of natural selection and genetics to search

7 through decision space for optimal solutions. In GA, a string represents a set of decisions (chromosome combination), a potential solution to a problem. Each string is evaluated on its performance with respect to the fitness function (objective function). The ones with better performance (fitness value) are more likely to survive than the ones with worse performance. Then the genetic information is exchanged between strings by crossover and perturbed by mutation. The result is a new generation with (usually) better survival abilities. This process is repeated until the strings in the new generation are identical, or certain termination conditions are met. The following sections present details of the use of GAs to determine job rotation schedules. 5.1 Fitness function The fitness function is designed for solutions that are close to the Pareto front with a high probability of being selected in the next generation. Equation 4 defines the fitness value. Fi = d max d i (4) Where d max : maximal distance between d i in the generation such that d i =min(d ij, for all j); d ij :distance between parent i and each point j of the Pareto front, given by d ij ( i j ) + ( i j ) Z1 Z 2 Z 2 = (see Fig. 2) Z 5.2 Selection Proportional selection is adopted to choose the strings with favorable fitness value. Equation (5) gives the selection probability according to the fitness value generated in the above steps. P = i F i Pop _ size i= 1 F i (5) 5.3 Chromosome structure The proposed scheduling mechanism involves in solving resource-constrained project scheduling problem because labors are available in limited quantities and perform activities with precedence constraints. Priority-based encoding technique as described in Gen s and Cheng s (1997) book is used in locating the sequence of operating the activities. The chromosome structure, which represents the job sequence created at random, is real-number-encoding and presented by two dimensions. The length of the chromosome is defined as the total number of activities. As presented in Fig. 4, a string represents seven activities from 1 to 7 (network of these activities shown in Fig. 5). Each activity is randomly assigned an integer indicating the priority of activity to be executed when the activity can be performed. The larger the integer, the higher the priority. For instance, when starting activity (i.e., activity 1) is finished, activity 2 and 3 are the candidates that can be performed. The priorities are 4 and 5 for activities 2 and 3, respectively. As a result, activity 5 wins the position to be operated.

8 Fig. 4 Chromosome structure Fig. 5 Network used in forming the chromosome structure as indicated in figure Crossover and mutation The position-based crossover operator applied to the chromosomes. The process of the position-based crossover, presented in Fig. 5, is described as follows: First, two parent strings are selected at random. Then, child string takes some genes from one parent at random and fills vacuum positions with genes from the other parent by a left-to-right scan. Moreover, this study employs bit-wise mutation. When a chromosome is selected for mutation, one gene is randomly selected to have its values changed. In addition, the swap mutation mechanism is applied in mutation operation. For example, two positions of a chromosome are simply selected at random to swap their priority integer as shown in Fig. 6. Fig. 5 Example of crossover operation Fig. 6 Example of mutation operation 5.5 Convergent status

9 The completion of the evolution process using GAs is usually set in terms of the number of generations. However, the convergent curve generated during the evolution process can also be observed to determine whether the evolution is completed. In this study, the area enclosed by the Pareto front, the abscissa and ordinate (Fig. 6) is recorded to determine if the completion of the evolution process is reached. Z 2 extreme point in Z 2 Pareto Front extreme point in Z 1 Area enclosed by Pareto Front, abscissa, and ordinate Z 1 Fig. 6 Example of area enclosed under Pareto front 6. CASES STUDY Several examples are tested to see the efficiency of the proposed mechanism. Two of them are introduced in this section. 6.1 Example 1 activities without precedence relationships The demonstrated example involves ten independent tasks that are performed by seven multi-functional labors (i.e., each labor is able to perform a given subset of types of tasks). The information including gender, age, height, weight and SRE for every labor are provided in Table 1. Additionally, Table 2 shows each task s quantity, demanded oxygen consumption rate and number of labor needed to perform it, and duration required to finish one unit of such task as well. For example, it requires two labors to carry out activity 1. Each labor has to expend 0.5 l/min oxygen while doing this work. In addition, it takes 15 minutes for those labors to complete a unit of this task. Table 1 Labors physiological information Labor Gender Age Height (m) Weight (kg) SRE A M B M C M

10 D M E M F M G M H M I M J M K M L M Table 2 Tasks information used in first example Task Duration (min) Quantity Number of labor needed VO 2work (l/min) The generation, population, crossover rate, and mutation rate are set to 5000, 100, 0.3, and 0.05, respectively for obtaining optimal solutions. As illustrated in Fig. 7, there are four Pareto solutions obtained in the final generation. The required extra energy expenditure and duration to complete the entire schedule for those solutions are given in Table 3. Solutions 1 and 4, as shown in Table 3, represent two extreme arrangements. Solution 1 indicates that the total seven labors would expend the least extra energy (12,606 kcal) but spend the longest time (1,184 min) to finish the work. On the other hand, solution 4 forces labors to input the most extra energy (12,943 kcal) but complete the job in the least duration (1,176 min). There are some interesting findings during the evolution process. For instance, there are 6 different job schedule (not shown in the paper) indicating 1,179 minutes that are required to complete the whole work but the least energy (12,785 Kcal) can be selected as solution #2 listed in Table 3. This indicates the effectiveness of the proposed mechanism. Table 4 shows the individual labor s job assignment for solution #1. For example, the previous 3 tasks and time for labor A to perform and spend would be task 5 for five minutes, task 3 for five minutes, and task 4 for twenty minutes, respectively. The solutions are converged around the 1800th generation, as plotted in Fig. 8. In addition, around 3.62* (10 (200-9) *9!) possible solutions in this example must be sought but only very few portion (500,000/3.62* ) of the solution space was examined, which yields favorable results.

11 Table 3 Completed time and extra energy labors spending for Pareto solutions Solution No Duration (min) 1,184 1,179 1,178 1,176 Energy (kcal) 12,606 12,785 12,937 12,943 Fig. 7 Pareto solutions for the first example Table 4 Job rotation schedule for Pareto solution #1 Task No. Labor No. Beginning of Event Time (min) End of Event Time (min) 3 A B C D E F G H I 0 5

12 2 J H I J K A : : : : 6 H A E K Fig. 8 Convergent curve for the demonstrated example 6.2 Example 2 activities with precedence relationships The scenario of second example is almost the same as the previous example but there exists precedence relationships between activities. The labors physiological information shown in Table 1 is still suitable to be used in this example. The precedence relationships between activities (network shown in Fig. 9) are described in

13 Table 5. This project is divided into 20 sections that must be completed. Each section is completed as 10 activities are gone through. Other information, such as duration for completing one unit of each activity and quantity needed to be implemented for each activity, are shown in Table 5 as well. Table 5 Task information used in second example NO. Precedence Duration (min) Quantity (section) Number of labor needed VO 2work (l/min) Fig. 9 Network represents the precedence relationships between activities The generation, population, crossover rate, and mutation rate are also set to 5000, 100, 0.3, and 0.05, respectively for obtaining optimal solutions. There are four Pareto solutions (see Fig. 10) obtained in the final generation. The required extra energy expenditure and duration to complete the entire schedule for those solutions are given in Table 6. Planner may have labors to take extra 14,132 Kcal energy to implement this project in 1,199 minutes or take less extra energy (13,173 Kcal) but complete all works in a longer duration (1,220 min) such as solutions #1. Additionally, the schedule representing solution #1 is described in Table 7.

14 Fig. 10 Pareto solutions for the first example Table 6 Completed time and extra energy labors spending for Pareto solutions in the second example Solution No Duration (min) 1,220 1,213 1,202 1,199 Energy (kcal) 13,173 13,192 14,104 14,132 Table 7 Schedule for the second example Task No.* Labor No. Beginning of Event Time (min) End of Event Time (min) 0101 A B C D E F G H I 0 20

15 0104 J K L C D E : : : : 2009 C F E J CONCLUSIONS Construction workers usually perform jobs which is highly physical-strength demanding. Theses physically demanding work not only leads to physical fatigue but causes the loss of productivity. As a result, the organization of labors work should be coped with minimizing both workers physical demands and time for completing their jobs. This work presents a GAs-based mechanism for providing work-rest schedule that balances the optimization of aforementioned objectives. Cases study reveals that the proposed mechanism can effectively locate the solutions. Labors energy expenditure can be reduced and work can be completed within a reasonable time span. However, to practically apply this scheduling mechanism, more fundamental researches regarding ergonomics in construction area should be explored. For example, a thorough survey of energy required for carrying out different construction works is necessary. This information is needed before such scheduling mechanism is applied. On the other hand, the proposed scheduling mechanism is prone to arrange worker with high physical capacity to perform jobs that are in high physical demanding. Therefore, the relationship between cost and labor productivity is worthy to figure out when different paid rates to workers having different physical capacities is adopted. REFERENCES Abdelhamid T S, and Everett J G., Physiological demanding during construction work. Journal of Construction Engineering and Management, 2002, 128(5), Abdelhamid T S, Everett J G. Physiological demands of concrete slab placing and finishing work, Journal of Construction Engineering and Management, 1999, 125(1):

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