Hybrid procedure to determine optimal workforce without noise hazard exposure

https://doi.org/10.1016/j.cie.2006.08.018Get rights and content

Abstract

Hearing loss is a major occupational health problem among industrial workers. Repetitive exposure to loud noise increases the risk of hearing loss. An administrative noise control such as job rotation can help to reduce workers’ daily noise exposures. In a case where noise levels are excessively high, it is often necessary to assign additional workers to the current workforce to alleviate daily noise exposures that individual workers receive. This paper presents four solution algorithms (three approximations and one exact) to determine a minimum number of workers and their work assignments to attend noisy workstations without noise hazard exposure (that is, daily noise exposure does not exceed 90 dBA). Then, a hybrid procedure which utilizes the four algorithms successively is proposed to improve the solution procedure. Based on a computational experiment on 300 test problems, it is found that the hybrid procedure outperforms all four algorithms (when utilized separately) and is able to find an optimal solution for 88% of the test problems.

Introduction

It is known that a cumulative effect of repetitive exposure to loud noise is occupational hearing loss. According to the National Institute for Occupational Safety and Health (NIOSH, USA), approximately 30 US million workers are currently exposed to noise hazard on the job and an additional 9 million are at risk of hearing loss. Noise-induced hearing loss is one of the most common occupational diseases and the second most self-reported occupational illness or injury. Some examples of an economic impact of hearing loss are in British Columbia: from 1994 to 1998, the Workers’ Compensation Board paid $18 million in permanent disability awards to 3207 workers suffering hearing loss. An additional $36 million was paid out for hearing aid (NIOSH, 1998).

For industrial facilities having high noise levels, appropriate noise controls must be implemented to prevent workers’ daily noise exposures from exceeding a permissible level. Engineering controls are the most effective noise hazard prevention, which can be done through proper design, maintenance, lubrication, and alignment of machines. The use of barriers or shields can reflect high-frequency noise. Isolating machines from areas where workers are likely to be present also helps to reduce noise levels. The use of hearing protection devices (HPDs) is another common noise control approach. Earplugs and earmuffs are widely used in industry. While the application cost of HPD is attractively inexpensive, its effectiveness is usually the poorest. Noise reduction ratings (NRR) tend to be overly stated by manufacturers (Gasaway, 1984). Wilson, Solanky, and Gage (1981) reported that workers typically adjust their HPDs for comfort rather than to achieve maximum attenuation. In many manufacturing facilities, workers choose not to use HPDs unless strictly enforced and routinely monitored. Comfort seems to be a major factor that influences whether or not HPDs are worn by workers (Casali, Lam, & Epps, 1987).

Other than using engineering controls or HPDs, job rotation is popularly recommended to reduce workers’ daily noise exposures. Job rotation is an administrative noise control that offers a trade-off between safety concern and cost effectiveness (Olishifski & Standard, 1988). Briefly, job rotation requires workers to rotate among workstations within one workday in order to reduce their daily noise exposures. In a few special situations, job rotation not only helps to reduce noise hazard exposure but also increases productivity by sharing very demanding tasks among workers (Royster & Royster, 2003). Despite being an effective yet inexpensive noise control, job rotation has not received much attention from industrial engineers and/or safety practitioners. This is perhaps due to difficulty in implementing job rotation to achieve its optimal level of effectiveness. In practice, the number of workstations where individual workers will attend, work duration at each workstation, and the order of assignment must be defined. Since a major goal is to reduce workers’ daily noise exposures, it is necessary to search for a feasible set of work assignments such that none of the workers receives daily noise exposure exceeding 90 dBA. In a case where there is no feasible set of work assignments with the current number of workers (which is usually equal to the number of workstations), the number of workers must be increased. However, the number of workers who are exposed to high noise levels should be minimized (NIOSH, 1998).

In this paper, we consider an optimization problem of finding the minimum number of workers and their daily work assignments to attend a set of workstations such that none of the workers receives daily noise exposure exceeding 90 dBA. The problem is called the one-dimensional minnum work assignment problem based on noise exposure (1DMAP-N). 1DMAP-N can be viewed as a variant of the one-dimensional bin packing problem (1BPP). The paper is organized as follows. We initially discuss a measure of daily noise exposure and the use of job rotation to reduce it. Next, we review research work on existing 1BPP algorithms. After that, we describe a mathematical model of 1DMAP-N and evaluate the relationship between 1DMAP-N and 1BPP. Then, we explain four solution algorithms and a hybrid procedure for solving 1DMAP-N in detail. Finally, results of a computational experiment with 300 test problems are reported and discussed.

Section snippets

Daily noise exposure and job rotation

Daily noise exposure is measured in terms of an 8 hour time-weighted average (8 hour TWA, dBA) sound level. Letting hj be work duration (in hour) at workstation j, n be number of workstations, and L¯j be combined noise level (dBA) measured at workstation j, the 8-hour TWA can be determined using the following formula (adapted from OSHA, 1983).8-hour TWA=16.61log10j=1nhj82L¯j-905+90Note that the permissible daily noise exposure is equivalent to the 8-hour TWA of 90 dBA (OSHA, 1983).

The

The 1DMAP-N model and its relation to 1BPP

For readers who are not familiar with 1BPP, its objective is to find a minimum number of equal-sized (i.e., fixed-height) bins that is sufficient for being packed by a set of one-dimensional items with various sizes. When comparing between 1BPP and 1DMAP-N, one can see that an item in 1BPP is analogous to an amount of noise exposure per work period that a worker receives when attending a given workstation in 1DMAP-N, whereas a bin is analogous to a worker. In 1BPP, all bins are identical.

Review on selected algorithms for solving 1BPP

Since 1DMAP-N is a variant of 1BPP, an understanding of existing algorithms for solving 1BPP and their concepts could be useful for the development of solution algorithms for 1DMAP-N. Because 1BPP is also one of the first combinatorial optimization problems in the literature, there are a number of research papers on the bin packing problem and its variants. As reported by Hochbaum (1995), there are over 100 research papers written on the bin packing and related problems since 1960s, and the bin

Solution algorithms to determine optimal workforce

In this section, a method for identifying the lower bound of 1DMAP-N is firstly explained. Then, three approximation algorithms and one exact algorithm are described. Their applications are demonstrated through a series of numerical examples that are based on the same noise data. Work assignment solutions (consisting of number of workers and daily noise exposure) are also compared.

Hybrid procedure

As seen in the previous section, individual algorithms can be separately utilized to solve 1DMAP-N. While the first three approximation algorithms may not guarantee the optimality of the work assignment solution (when UB > LB), the exact algorithm (DA-BnB) will yield the work assignment solution that is optimal. Depending on the problem size, DA-BnB may take a few seconds to yield the optimal solution or may need hours of computation time. To improve the solution approach (to find the optimal

Test problems

Three sets (A, B, and C) of test problems (1DMAP-N) were randomly generated. Each set consisted of 100 problems, which were grouped into five levels of the number of workstations (n), i.e., 10, 20, 30, 40, and 50 workstations, respectively. For each n, there were 20 test problems. The number of work periods per day p was assumed to be four equal periods. In each problem set, the values of noise weight were randomly generated using a uniform distribution between these following ranges:

  • Set A:

    wj  

Discussion

The hybrid procedure clearly outperforms all four algorithms when considering the number of optimal solutions (hits) and the maximum computation time. In terms of the number of optimal solutions or hits, the hybrid procedure achieves the highest hits, which is 265 out of 300 problems, followed by M-LPT swap (236), BnB-H (224), DA-BnB (212), and mFFD (119). In each set of test problems, the hybrid procedure also achieves the highest hits. These results show that the hybrid procedure successfully

Conclusion

The hybrid procedure for solving the one-dimensional minnum work assignment problem based on noise exposure (1DMAP-N) is proposed. The procedure consists of four algorithms. Firstly, the lower bound (LB) for 1DMAP-N is determined using the same method as that in 1BPP (Martello & Toth, 1990b). Next, the first fit decreasing (FFD) heuristic is modified to identify the upper bound (UB) for 1DMAP-N. If UB > LB, then the M-LPT swap heuristic tries to decrease UB using the following algorithms: M-LPT

Acknowledgements

The authors wish to express their gratitude to the Thailand Research Fund for financially supporting this research study through the RGJ-PHD grant (Grant No. PHD/0138/2544). The authors are also indebted to the anonymous referee for the valuable comments.

References (31)

  • Falkenauer, E., & Delchambre, A. (1992). A genetic algorithm for bin packing and line balancing. In Proceeding of The...
  • S.P. Fekete et al.

    New classes of fast lower bounds for bin packing problems

    Mathematical Programming

    (2001)
  • M.R. Garey et al.

    Computers and intractability: A guide to the theory of NP-completeness

    (1979)
  • D. Gasaway

    NIOSH compendium hearing protector attenuation

    National Safety News

    (1984)
  • J.N.D. Gupta et al.

    A new heuristic algorithm for the one-dimensional bin-packing problem

    Production Planning and Control

    (1999)
  • Cited by (15)

    View all citing articles on Scopus
    View full text