Six optimization models are developed and sequentially applied to select appropriate .... applied; 0 otherwise yhjl ...... barrier costs US $225 and it reduces noise.
International Journal of Occupational Safety and Ergonomics (JOSE) 2006, Vol. 12, No. 4, 355–367
Design of Optimal Noise Hazard Control Strategy With Budget Constraint Krisada Asawarungsaengkul Suebsak Nanthavanij Sirindhorn International Institute of Technology, Thammasat University, Pathumthani, Thailand An analytical design procedure to determine optimal noise hazard control strategies for industrial facilities is presented. Its objective is to determine a set of appropriate noise controls to eliminate or reduce noise levels so that workers’ daily noise exposure does not exceed a permissible level. From a given noise control budget, engineering controls will be firstly implemented, followed by administrative controls, and then the use of hearing protection devices. Six optimization models are developed and sequentially applied to select appropriate noise controls without exceeding the budget. Numerical examples are presented to demonstrate the application of the proposed design procedure.
noise control strategy
industrial noise hazard
1. INTRODUCTION Noise-induced hearing loss is one of the most common occupational diseases and the second most self-reported occupational illness or injury [1]. Exposure to high noise levels is a leading cause of hearing loss and may also result in other harmful health effects. In the USA, it has been estimated that 30 million workers are currently exposed to noise hazard on the job and an additional 9 million workers risk getting hearing loss [1]. A major cause that contributes to this problem is a lack of effective noise hazard control program in the workplace. Regarding noise hazard prevention, three preventive approaches are generally recommended: (a) engineering approach, (b) administrative approach, and (c) the use of hearing protection devices (HPDs). The engineering approach has been discussed at length in many textbooks. Details of engineering controls can be found in several publications [2, 3, 4, 5, 6, 7]. More specifically, topics such as development of
job rotation
optimization
quieter machines, noise reduction methods, noise absorption materials, and process change for noise reduction have also been discussed in the literature [8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. Sutton [18] has presented a procedure to identify possible methods of noise reduction and to select the best method using a cost–benefit analysis. Discussion on the administrative approach is relatively scarce. Job rotation is usually recommended as a practical means of preventing noise hazard exposure. Nanthavanij and Yenradee [19] developed a minimax work assignment model to determine an optimal set of work assignments for workers so that the maximum daily noise exposure that any worker received was minimized. For large job rotation problems, a genetic algorithm was developed to determine near-optimal minimax work assignments [20]. Yaoyuenyong and Nanthavanij [21] also developed a simple heuristic for solving large minimax work assignment problems. For industrial facilities where noise levels were excessively high, Nanthavanij and Yenradee [22] recommended that
This research was sponsored by the Thailand Research Fund (TRF) through an RGJ-PHD grant PHD/0184/2545. Correspondence and requests for offprints should be sent to Suebsak Nanthavanij, Management Technology Program, Sirindhorn International Institute of Technology, Thammasat University, Pathumthani 12121, Thailand. E-mail: .
356 K. ASAWARUNGSAENGKUL ET AL.
the number of workers be greater than the number also follows OSHA’s hierarchy of noise control. of machines/workstations. They also developed In section 2, we describe optimization models used in the proposed procedure. The analytical a mathematical model to determine a minimum number of workers and their work assignments design procedure is explained in detail in for working at noisy worker locations so that section 3. Then, section 4 shows how different levels of budget will affect the noise hazard their daily noise exposure did not exceed the permissible level. control strategy. Finally, we give conclusions in Various types of HPDs and their properties section 5. have been extensively discussed [2, 3, 4, 5, 6]. In addition, there have been research studies on the 2. MATHEMATICAL MODELS OF development and testing of effective HPDs [23, NOISE CONTROLS 24, 25, 26]. Resistance to using HPDs by workers was also studied by Feeney [27]. Consider an industrial facility where workers According to the U.S. Occupational Safety are present at various locations during an 8-hr and Health Administration (OSHA), a noise workday. Suppose that the only noise sources in conservation program is required in situations this facility are machines. At any worker location, where noise levels exceed 90 dBA [28]. To the noise level to which an assigned worker is reduce noise levels, engineering controls are to exposed is a combined noise level at that location be implemented first. If they are not feasible, (transmitted from all noise sources). A formula administrative controls such as job rotation to compute the combined noise level at location should be implemented next. The use of HPDs j, Lj (dBA), from multiple noise source ts (where is specified as the last resort of noise reduction. t = 1, ... , q) is shown here. They should be applied only when engineering Letting Lab be ambient noise level (dBA), Lt be and administrative controls fail to prevent daily noise level (dBA) measured at 1 m from machine noise exposure from exceeding the permissible t, and dtj be Euclidean distance (m) between level. HPDs should be used to assist, not machine t and location j, Lj is computed from to replace, engineering and administrative controls. Often, managements choose not to � Lt �120 � � � � L �120 � � � q � � ab � � 10 � � follow OSHA’s hierarchy of noise control due 10 10 � � � �1 L j � 10 log �10 � to large capital investment that is normally 2 � � d t �1 tj required for engineering controls and difficulty �� �� (1) in implementing engineering and administrative � L j �90 � controls. As a result, only HPDs (earplugs, � Lt ��120 � �� � � L �120 � � 1 � ��10 5 �� ��� � � ab � w q� earmuffs, etc.) are often provided to workers for �2 . 10 j 10 � � � p � � � L 10 log 10 � 120. j noise hazard control. � � d tj2 t �1 � ��� Sanders and McCormick [29] recommended �� ��� Wi � 16.61�log10�� w k �� � 90. that a combination of noise controls be used to ��k�S ���� � � L j �90 � � For simplicity, � we can� refer to the combined achieve a desired level of abatement. However, � 5 � 1 q rt �. as �noise load. By� dividingsa workday �� L�t �120 �� � � 2 �noise level finding the appropriate combination of wnoise j � 120 ��cb q� yb �� �cstu �� ys��tuLa�ab��formula � p � v for v� 10 � � into p equal� work periods, 10 � controls is usually difficult especially when 10 � t� 1 u� �110 log �10 v �1 � � � � �� L j � � �� computing the� per work period at d 2 requirements such as the allocated budget � noise load � � r t � 1 tj t W � 16.61�worker log10 �location w k �� � 90. �� and permissible exposure level need toi be ��k�S L��t���j,�wLj, tis� ���NRstu � ystu � ; t � 1, ... , q; �� simultaneously considered. u �1� L �90 � s � q rt �� j � In this paper, we introduce an analytical � L t� �120 � � (2) 1 v ��� �� � L5 ���120 � �cstu � ystu � � �cb � yb � �� �� v ab � � 2 . w q � �� � j � 10 � � design procedure to determine an optimal 10 v �1 10 p �� t �1 u �1 � �� � � 12 L j � 10 log �10� strategy for industrial noise hazard control with 2 rt d � �� tj 1� �� to t ���worker assigned respect to a given budget and noise levels Lint� the �NRstuthat �W; ti ��worker �� ��, q�;log � Lt � Note � ystuany 116 , ....61 w � 90 . � � 10 � j will receive the�noise load wkj.��For a facility. The order of priority of noise controls � u �location 1 k � S � � � � � L j � 90 � � � L �120 � ��� q5 r��t��Lt� �120 �� � s � �� 10 � s , yb � �0,1� ; �t , u, � 2� q � � ab � �1, ... �, n; ystu � � cs1;tuj �� ystu � cbvv � ybv �� � 10� � 10 � � L j � 10 log �10 NRb jv � yb � � � L �902 � � � 120 � JOSE 2006, Vol. 12, No. 4 �� v ; j � v �1 � t �1 u �j1dtj � � � t �1 � v �1 � 5 �r � 1 �� � t� w � max; j � 1, ... , n; � 2�
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1 OPTIMAL NOISE HAZARD CONTROL STRATEGY
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� Lt �120 � � � � L workers � stay � work system in which may not NRbjv amount of noise (dBA) reduced at worker q � � ab �120 �� � 10 � � 10 10 at one Llocation throughout the workday, it is � � � � � 120. location j after installing barrier v j � 10 log �10 2 � � NRhl amount of noise (dBA) reduced after necessary to determine an 8-hr time-weighted d t �1 tj �� dBA) sound level that �� average (8-hr TWA, wearing HPD l each worker receives. NRstu amount of noise (dBA) reduced at machine t � L j �Let 90 � S be a set of worker � � � 5 �i is alternately present; locations js where after applying engineering control method u 1 worker �. w j � � 2� the 8-hr TWApthat worker i receives, Wi, is q number of machines (noise sources) rt number of engineering control methods to � �� ��� reduce machine noise at machine t (3) Wi � 16.61�log10 � w k �� � 90. ��k�S ���� �� s number of engineering control methods to block the noise transmission path r q s t � � For example, consider worker W1 who works � � � � � � � cs ys cb yb TB total noise control budget (TB = EB + HB) � tu tu v v � at two worker workday which �� t �1 u �1locations in an 8-hr �� v �1 wmax maximum noise load per work period is divided into four equal work periods. Noise rt xijk 1 if worker i is assigned to worker location loads per at the two locations are �NRs Lt� work � Lt �period tu � ystu � ; t � 1, ... , q; j in work period k; 0 otherwise assumed to be 0.28u �and 1 0.15, respectively. Let us yi 1 if worker i is assigned; 0 otherwise further assume that�worker W1 works at �the L � �first 120 � � �� �� t yb 1 if noise reduction using barrier v is � L ab �120 � v s 10 � � � rotates location in the first�two� periods,� andq then 10 10 � � 120 � applied; L j � 10location log �10� in the �last NRb jv0 �otherwise ybv ; j � 1, ... , n; � two periods. to the second 2 d � � 1 if HPD l is used at worker location j; yh t �1 jl v �1 Using Equation 3, �the 8-hr TWA of workertj W1 � 0 otherwise � � can be computed: ystu 1 if noise reduction at machine t using � L j � 90 � � � WW1 = 16.61[log � 5 � 10{0.28 + 0.28 + 0.15 + 0.15}] engineering control method u is applied; � � 1; j � 1, ... , n; ys , yb � �0,1� ; �t , u, v. � 2 + 90 = 88.91 dBA. tu v 0 otherwise � L j �90 � � � z number of HPD types Generally, the permissible daily noise exposure � 5 � 1 � w max; j � 1noise , ... , n;hazard prevent level is � 902 � dBA. � To p exposure, a total noise load that any worker 2.1. Models of Engineering Controls rt receives in one workday must not exceed 1. Selection Lt� � Lt � �NRstu � ystu � ; t � 1, ... , q; The developmentu �of the optimization models is 1 For engineering controls, we consider only based on the following notations. � L t� �120 � � � � L �120 � controlling at the machine and controlling along �� 10 �� q s � � ab � � � � 10 the path (i.e., using the barrier to block the 10 v � cbv cost installing � L j of � 10 � � 120 � NRb jv � ybv ; j � 1, ... , n; log �10�barrier path). The former implies chl cost of using �hearing protection dtj2l � noisev �transmission 1 t �1device � � cstu cost of reducing � noise at machine t using � that machine noise is reduced. Thus, all worker locations will benefit from such noise control. engineering control method s u � q rt � EB budget for�cs engineering �cbv � ybv �� � EB; Note that for a given machine, there could be � tu � ys tu � �controls � �� several engineering control methods for reducing � 1 � 1 � 1 v t u EC total � cost of engineering controls machine noise. The latter, however, will reduce F total ystuworker–location , ybv � �0,1� ; �t ,changeover u, v. noise levels at some worker locations (only those fj number of worker–location changeovers at locations where the barrier can block the noise workerp �location 1� mj � transmission path). � � � f 1 x x ; j � 1 , ... , n . HB budget for�HPDs ijk j i , j ,k �1 � � � k �1 of HPDs i �1 used The problem of selecting appropriate HC total cost � 1 p n m engineering controls is formulated as cost- and � � noise level (dBA) measured at machine t � � � F 1 x x . � � , j , k �1 ijk ireduction safety-based models. Two mathematical models (at 1-m distance) after noise j �1 k �1 � i �1 � are developed. The first model (E1) is the costm number of workers in the current based model which is intended to minimize the workforce total cost for implementing feasible engineering M number of available (current + additional) controls (i.e., reducing machine noise and/or workers blocking the noise transmission path by barriers) n number of worker locations such that the combined noise level at any worker
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JOSE 2006, Vol. 12, No. 4
u�1
358 K. ASAWARUNGSAENGKUL ET AL.
� L t� �120 � � � � L �120 � �� �� q s � � ab � � 1 10 � � 10 10 �� � L j � 10 log �10� � 120 � NRb dtj2 � � t �1 v �1 1 �� �� s � q rt � �cstu � ystu � � �cbv � ybv �� � EB; � �� t �1 u �1 v �1 1 �� ystu , ybv � �0,1� ; �t , u, v.
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location does exceed 90 dBA. �120 �second � LtThe � not � �� � Lab �120 � q 10 � � � � �� model (E2) is the safety-based10 model which is 10 � � � � � L 10 log 10 � 120. � Lt �2120 � �� load j intended to �minimize the maximum noise � d � � 1 Lab �120 � tq�1 tj 10 �� �� among � worker �locations � � such per work period all 10 � 10 � � �� � 120. L j � 10 log �10 � 2 exceed an that the resulting total cost does not �� L �90 � � d tj t �1 allocated engineering EB. p �1 � ���� j �� control budget � m � � Lt �120 � � 5 1 � Lt �120 � � � � � � � f 1 x x ; j � 1, ... , n. � � 2���L ���90Lab�� .�120 �� � � wj � j ijk i , j , k � 1 q 2.2. Job Rotation Models � q 10 � 10 � � p �� j � �10 � � 1 � 1 k i 10 � 10 � �2.1.1. � � � � 10 � E1: of � 120. �L�j120 5 ��minimizing total cost � . log���10 1Model 2 2 � d n p �1administrative m The only control � considered in � 2� . w j � engineering � t � 1 � � tj � � d � controls � 1 t �1 tj p � � � W 16 . 61 log w � 90 . � � � � � F 1 x x �. this paper is� job rotation. because k� �� i � 10 � � ijk This i , j , k �is1 mainly ��k�S ��� � 1 j �1 k �1 � hasi �been Minimize ��� L �90� � � job rotation widely recommended in � �� � j �log � W 16 . 61 w � 90 . � � r q � � s i 10 k t � � � � the literature, and mathematical models of the 1 � 5 � �� � ybL ���120 w � j � ��cs2��tu� � ystu��k.���S ���cb � vt ��1 v job rotation problem have been well defined. p � � �� � � �� Lab �120vs���1 q 10 � 10 �� tq�1 urt�1 � Basically, workers are allowed to rotate among � �10 � � � v � ybv �� � � 120. �log ���cb � ys cstu�r�t10 �L j � 10to tu� � � ��� subject 2 worker locations so that a maximum daily noise W .61�log10 � �w � � 90. d tj,��q; � ��Ltt��i 1��u16 �L1t � � �NRs vys �k1tu��t;�t1 � 1, ... �� � 90. tu � � � � �� �� exposure that any worker receives does not �k�S �� ���� � Lt �120 � � ur�t� 1 � � exceed 90 dBA. r q s � ; t � 1�, ... q � t� � Lt t � �� L�jNRs �120 L � �, q ; �� � �90 � � ys 10 � 10� � �L � � L ab�tu�120 � tu � t � � �� � � ��cb � yb 2�� � �� 1201. �csutu��� 1� 5�ystu� � � � �cbq v � yb s Two mathematical models are developed for � v10 v ��Lt �j 1��u10 �� � � 120 � jobNRb dv tj� � w � 2 �� 10� �10 . v �� 1� 10� L � �120 �1 log t �1 � 1, ... , n; (A1) is intended to rotation. model �� jv � ybThe v ; j first � � j p �� � L �120 � �� � �� dt 2 r�t � ab � tj t � 1 v � 1 q s determine a set of feasible work assignments for � � 10 � � � � 120 � � ����; t 10 � �10 � ys ���10�NRs � � L � L � � 1 , ... , q ; 10 log , n; that a total worker– � � � t t tu tu j jv � yb v ; j � 1, ... theNRb current workforce such u � ; t � 1, ... , q; W�i L� �16 .61�log w k �t��1� 90. dtj2 � v �1 90 � u �1 10 � j location changeover is minimized. At any worker ��k�S ���� � � � � � �� � � L t� �120 � � � L t� �120 � � 2 � 5 � � 1; j��L 1, � � � location, a worker–location changeover occurs 120 0�,1� ;�� � ab ... , n��s; ystuq, ybv � � �10 � �� q rt � t , u, v. s � q 10 �� � � �� L j � 90 �� s � �� 10 � 10 � when current worker moves out to another � 10 cs NRbthe � L�log �� ys tu � � �90�10 j �510 jv � ybv ; j � 1, ... , n; � �L ���120 � ybv �;�cb j �v1�, ...yb,dnv2;��� �� � 120 � ���� � 90. 2 �� ��j tuNRb � jv � � location and a new worker moves in. To some � � � 2 � 1 ; j � 1 , ... , n ; ys , yb � 0 , 1 ; � t , u , v . v �1 tu tj � t �1 v v �1 dtj � �1t �1 u ���1 v �51 �� ����t �1 � � � 2 � w j � 1 , ... , n ; max; extent, productivity of a work system might be �� p � L j �90r�t � � � � L1��t� L �j ���L90t ���5 r �� �NRstu � ystu � ; t � 1, ... , q; decreased due to possible needs for learning and � w max; j � 1, ... , n; �cbv � ybv �� Lp�����25 L ��� u �t 1 ��NRs adapting to a new task. Thus, it is logical to keep � ystu � ;,tyb � 1,�...�0, q,1;� ; �t , u, v. tu v � L t� �120 � � stu , ybv � �0��,1� ; �t2, ut , v. t �ur�1�;1 j � 1,tu... , n; ys the number of worker–location changeovers as �� 10 �� � L j �90�t � �� L ab �120 �� q s � � � � � 101�, ... few as possible. The second model (A2) covers a 120 L � �, q L� t � �� � �NRs ; �� �� 10 � tu � ; t � � tu � ys �� t � ; t � 1, ... , q; LL1t�j ���210 5 10 L �120 � � � 120 � s NRb jv � ybv ; j � 1, ... , n; � log 2 �1� ��� wabmax; ��j � 1q, ...10 u� � situation in which additional workers need to be � �� �; d 10 , n � 1, ... , n; tj 10 v �1 � minimizing � � t �1 maximum 2.1.2. Model Lp j � 10 NRb jv � yb ; j rotation � 1, ... , ndue ; to excessive noise log��10E2: � L t� �2120 � �� � 120 � considered inv job � L t� �120 � � �120work � L abper � �� �� �� d10 noiser���t load period tj � 1 � 1 t v q �� �� s � � �� � levels in the facility. The model’s objective is q 10 � 10 � � �� L j � 90 �s � � � � � � ; t 10 10 Lt log � 1, ...2, q; �� � 120 � L NRb jv � ybv ; j � 1, ... , n; �� �10NRstu � ys �tj ��10 tu � ; t � 1 , ... , q ; Minimize subject �� to determine a minimum number of workers (in NRb �1205 � � w�max u jv � ybto v ; jt ��11, ... ,dntj; � 2 � � u � 1 � 1 v t , u, v. dtj � 2� q rt v �1��1; j � 1, ... , n;s ystu , ybv � �0�,1� ; � t �1 the increased workforce) such that none of them � � ; �jcs�90tu� �� �ysLabtu ��120 �cbv � ���ybLt�v��120 � � � ���EB � L t� �120 � � � L � � � �� � �� s receives a daily noise exposure above 90 dBA. q � tq�1 urt��� 1 s5 � �� �� 10 v��s�1 q 10� 10�� � � 10� 10 � � L1 j ��210 � It is jvworth that � log �10 � �w � � 120 � NRb � ybv noting ; j � 1, ... , n; the two job rotation nyb ;, nv 2;�� � EB; � ys tu � ��ys120 � � �cs NRb �t�,�yb ;�cb j1�,v... 1�,,... �max; u, vvj. � tu , ybv �tu��0,1� ;jv 2 d � p tj v �1models do not consider costs since the �� v �1 t �1 stut �,1ybv �d�tj0,1� ; ��t��, tu�,1vu. �1 v �1 � �� �� r�t implementation of job rotation does not require ystu , yb ,1� ; �t , u, v. p �1v� � �0m � � � � L � L � NRs � ys ; t � 1 , ... , q ; r q s tu tu any equipment investment or workplace �f t � t t 1 � � ; jyb � 1�,��...�, nEB . ; �csu �1� ysxijk� �� xi , j ,�kcb �1 �� � ��cb 1, ...�, nyb ; �� � EB�;j v v tu tu modification. It is assumed that any incurred costs v v �� t �1 upk��11 �� � im�1 �� � � �� � L t� �120 v �1 �� � due to decreased productivity will be absorbed by �120 � f j � n p�1�1�� �� Lmxab , ... ,���n�. s ijk � xi�, j ,k �1q � ; j���� 110 � � ys , yb � 0 , 1 ; � t , u , v . 10 10 tu v production department. If additional workers � � � � xijk � �xi , j , k �1 � . i ��1 � � 120 � theNRb � ; t � 1, ... , q; LFj �� k10�1 log�110 jv � ybv ; j � 1, ... , n; 2 � � � �1 jn�1 pk �1 � im t �1 v �1are needed in job rotation, it is also assumed that � dtj � p �1 � ��1 m � � � F x x . they are existing workers (perhaps from other � � � � ijk i , j , k �1 � �� L t� �120 ��� � f � � � 1 x x ; j � 1 , ... , n . � � � 1 � 1 � 1 j k i j ijk i , j , k � 1 � � q � ; j�� � 1 10, ... ,�n�. q rt s departments), not new workers. If skill training is s k �1 10 � k �1 � i �1 �, ... , n; � � � 120 � NRb � yb ; j � 1 � � � � � cs � ys � cb � yb � EB ; required, the cost of training will be absorbed by jv v � � v v tu tu dtj2 �� n vp��11 � m t �1 � � � 1 � 1 � 1 v t u � the human resources department. � �� �F � xijk � xi , j , k �1 � . �1 � i , j , k �1 � . � � ystu ,jyb � 0 , 1 ; � t , u , v . �1 vk �1 � i �1 � � � �cbv � ybv �� � EBJOSE ; p2006, �1 � Vol. m 12, No. 4 � �� � fj � 1 xijk � xi , j ,k �1 � ; j � 1, ... , n. � � k �1 � i �1
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� L j �90 � OPTIMALn NOISE HAZARD CONTROL STRATEGY 359 � � � � � � xijk � 1; i � 1, ... , m; k � 1, ... , p; � � � � � � 5 w Wi �w16j .�611�log � 210 . k �� � 90. � j �1 2 ��k�S ���� p�� m n p �1 � m The following assumptions are required for the � � 1 p n m � � �� s ��� xijk ��1 � 1; j � 1x,ijk...�, n�x;ik, j ,�k �11, ... � q rt � � , p; implementation oflog job rotation. � � 1 x x 16 . 61 w � 90 . � � � � � � , , � 1 ijk i j k � � � � � � ys cb yb � Wi ��cs � 10 k � � ij�1 k �1 i �1 v n tup �1 � tu m � �� ���� v(for � � �� working � 1 � 1 � 1 j k i k�� S duration � �� t �The 1. workers 1 u �1maximum v 1 p n p xijk � xi , j , k �1 �� n �1 � r xijkj xijk � p�;ni1;�i p1�, 1..., ... , m,;mx;ijk � ( 0,1); �i, j, k . and is 8s hrs. � � qmachines) � w 1 j �1t rkt �1 � per i �day w xijk � 1; i � 1, ... , m; � � � � � ys cb yb � j � 1 � 1 j k �can � Lt� A��workday Lt �n �pcs NRs � ys ; t � 1 , ... , q ; tu � tu v v p equal periods. 2. be divided into j �1 k �1 tu tu �� t �1 u �u1�1 � � 1 � 1 j k v �1 M n Job rotation w occurs only 1; i �at 1the , ... end , m; of the� work j xijk � n r � L 120 � � � t � xyijk i � 1; i � 1, ... , m; k � 1, ... , p; period.j �1 �k �1 � Lt ab �120 � � 2.2.2. Model A2:xijk minimizing �� � 1; i � 1, ...number , m; k � 1of , ... , p; q � ;��t �10 s Lt� �n L�t � � �NRstu� � ys 1 , ... , q ; i � 1 � j �1 tu10only one� worker 3. Each worker location requires 10 � � workforce L j � 10 log �x10 u��11; i � 1, ... � ybv j �;1in j �the 1, ...increased , n; � , m; k � 1, 2... , p; � � 120 � mNRb jvworkers ijk work period. to attend �per dtj � L � �120 � � v �1 n xp � 1; j �m � � L �120t �� 1 1, ...noise , n; k is� 1excessive, , ... , p; it might be Whenijk workplace j �1 � �� � �� t worker � 4. Each worker can attend only one ab x � 1 ; j � 1;, ... , n; k � 1, ... , p; q � s 10� � � � � � ijk � w x � y ; i � 1 , ... , M i �1 j to ijk addi additional workers 10 m necessary to increase 10 � � location per work period. � 1 i � � � 120 � �k � 1, ... , p2; � L jL � 90 j n�1 k p�1NRb jv � ybv ; j � 1, ... , n; j ��� 10xlog�10 1 ; j � 1 , ... , n ; � M be number of available thev �workforce. Letting ijk � � p t �1 5.�� Workers’ efficiency is independent ofdtjthe task 5 �� n 1 xijk � p;ni � 1, ... , m; xijk � ( 0,1); �i , j , k . 1 1; j �� 1, ... , n; ys , yb � �0,1� ; �t , u,�v. i �� 2 workers in the increased workforce where M > n, x ;k� tu v Similarly, task � � they are to perform. � 1p,; i...�, 1p,;... , m; xijk � ( 0,1); �i, j, k . 1 � 1; i � 1, ... , Mijk j �1 kx�ijk p n assigned model A2 can jbe as follows. �1 kexpressed �1 �� ��� L j �is90 90independent output �� xijk � p; i of � 1the , ...workers. , m; xijk � ( 0,1); �i, j, k . jM�1 � M � 5 ��� 1 yi � 2 � j �1 k ��1� 1w; max; j �, n1;, ys ...tu, n,;ybv � �0,1� ; �t , u, v. mMinimize j � 1, ... y subject to x p i � 1 ijk � 1; j � 1, ...i , n; k � 1, ... , p; M 2.2.1. Model i �1 � L j �A1: 90 � minimizing total worker– i �1 � ryt i � location � 5 changeover � 1 n � � p Lt� � L�t i�2�1 �NRs�tu w � max; ystu � ;jt��11,,... ...,,nq;; n p xijkj xijk � p�n�yyi ;ipi; i��11, ,......, M , M; ; xijk , yi � (0,1); �i, j, k . p work w u �1 system in which job rotation is not For the w x � yi ; i � 1, ... , M ; j ijk � 1 � 1 j k rt j �1 k �1 �� n � p workers implemented, are fixed at�� Ltheir t� �120assigned �� � 1 � 1 j k � L ab �120 � � q 1,�... s n Lt� �locations. L�t � w NRs 1;, ...worker– � j x�ijk �,�q; � tu�yi � ; i ys � ,� M10 tu10;�ttotal worker 10 Thus, � � � the � � L j � 10 log � 120 � NRb n;1, ... , p; 10 u � 1 xijkjv��1;yb i �v 1n;, j...�, 1M, ... ; k, � �1 k �1 location jchangeover is zero. Whend 2job rotation x � 1 ; i � 1, ... , M ; k � 1, ... , p; � � ijk tj � 1 � 1 t v � 120 L � j n�1 z �� � t n � be � may is implemented, �� � different � � L ab �120 � workers � 1 j � � � ; k q� 1, ... m s yh jl xijk �� 1; i� � 110 , ... , M p10;� � � 10� ,location. �to the same � � worker alternately assigned � � L � � 120 � , n,; p; 10 log 10 j �1 x l �ijk 1NRb � 1;jvj �m1yb , ... k 1�,1..., ... s v ,;nj; � � q rtj j �1 � d2 x � 1 ; j � 1 , ... , n; k � 1, ... , p; � � Each time a worker is replaced by another ijk 1 �� �tjEB; �cs �cbv �t �yb i �n1v �1z � m tu � ys tu � � v � � � 1 i worker, changeover � occurs. � � n p yh jl � chl � HB; �� t �1 u �1 the xworker–location ijk � 1; j � v1�,1... , n; k � 1, ...� , p; n p A formula to determine the number of worker– r q �1 l �1 xijk � p � yi ; i � 1, ... , M ; xijk , yi � ( 0,1); �i , j , k . j s � ystu ,�ybvi ��1t �0,1� ; �t , u, v. xijk � p � yi ; i � 1, ... , M ; xijk , yi � (0,1); �i, j, k j� � � �location cbv � ybj,v f�j�, is � EB; � changeovers location z 1 k �1 n �pcs tu � ysat tu worker � 1 � 1 j k �� t �1 u �1 xijk � p � yi ;vi��1 1, ... , M ; xijk��, yi � (0,1); �i,yh j, kjl. � 1; j � 1, ... , n; p �1 � m � l �1 1 k �1� �0,1� ; �t , u, v. j,�yb ys f j � tu�1 � v xijk � xi , j ,k �1 � ; j � 1, ... , n. (4) z � � n z k �1 � i �1 � 2.3. Models�� of 90z � Use L nj �the yh jl � � NRhofl �HPDs � yh jl � n p �p1��1 � m m �1 lyh � �� jl j �1 l �use 1 The of � HPDs should be �considered as a z�1 5 worker–location � nn�1locations, xijkthe � f jall � � xijk ��xixtotal F For , ji, kj ,�k1�1� �. ; j � 1, ... , n. � j �1 l �1 � n pz supplementary hazard control approach. � changeover j �1 k �k1��1F� isyh i �i1jl�1 �� 1 �� n noise z ��x � 2 � 1; iwhen � 1, ... , m; yh � ch � HB ; j �n1 l � 1 l That is, applied ijk only p �1 � m � yh be p jl it should jl � chl � HB; � 1 j k � 1 � 1 l F � n z �1 � xijk � xi , j , k �1 � . engineering controls j �1 l �1 and job rotation fail to (5) z 1 l � HB; j �1 k �1yh � jl �i �ch � prevent workers’ daily noise exposure from yh jl � 1; j �z1, ... , n; j �1 l �1 Additionally, exceeding 90 dBA. yh 1; j � 1, ... ,22 n; the number Model A1 can be expressed as follows. jl � l �1 z l �1 of worker locations Minimize yh jl � 1; j � 1, ... , n; z where the� use of HPDs � � L � 90 � NRh� � yh � z is enforced should be as�l few � jl � as possible. �� In j n p �1 � l �1 m � � � 90 � � NRhl � yh jl L j l �1 � � � � n p �1 1 � m x � x practice, HPDs should be worn only � ijk � i , j , k �1 �z subject to� � � � � l �1at very noisy 5 �xL � 90 � � NRh � yh � � � 1 x � � � � � 5 jl � l j �1 k �1 � i �1 ijk � i ,j j , k �1 � � worker There are many types of HPDs n p locations. � � � � 1 l��1 j �1 k �1 � i �1 � � p � n different noise ��x � �1, ... , m; n p available, with reduction ratings � 2 � 1 ; i � 1 � � ijk 5 � ��x � 2 � 1; i � 1, ... , m n p w x p � � , ... , m; j �1 k �1 and prices. Atpany given location, suitable ijk (NRR) jn ijk p� 1; i � 1 � � 1 � 1 � 1 j k w x � ; i � 1 , ... , m ; � � j �1 k �1 j ijk �2 � xijk � 1; i �types 1, ... , m of; HPDs to be used must be specified. jn�1 k �1 p j �1 k �1 Two mathematical models for selecting n x ijk � 1; i � 1, ... , m; k � 1, ... , p; appropriate HPDs are developed. Note that both j �1 xijk � 1; i � 1, ... , m; k � 1, ... , p; models consider job rotation and the use of HPDs jm�1 concurrently. m x ijk � 1; j � 1, ... , n; k � 1, ... , p; x � 1 ; j � 1 , ... , n ; k � 1 , ... , p ; i �1 ijk
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JOSE 2006, Vol. 12, No. 4
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yh jl �� n�1 p j � 1 l n p � ;yi ; i � 1, ... , M ; ijk, M zy ; i �w1j,x... i �� w j xijkn ��� �1 � ch � HB; j �1 kyh ET AL. 1 ASAWARUNGSAENGKUL j �1 k �K. jl l �� 360 j �1 ln�1 n , ..., p, ;M ; k � 1, ... , p; xijk � 1; i z�� 1, ...xijk , M�; k1;�i �1,1... � � 1 j yh jl minimizing � 1; j � 1, ... ,number n; 2.3.1. Model of j �1 �H1: m � 1 l HPDs (m = n) m n; k � 1, ...� , p; x � ijk � 1; j ��1, ...xijk, n;�k1�� ;�Lj1��,90...1,�,...pz;,NRh � yh �
n z j �1 l �1
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� L � 90 � � NRhl � yh jl � � j � l �z 1 � � �� L � 90 � NRh � yh �� � 1, ... , p; �5 l jl �� �� j Model H1 is intended to i �1 l �1 � al minimum jl � � �� n p � jdetermine i �1 1 �� l �1 HPD budget ��x 5 �on the given � p n based number of HPDs � 2 � � ijk � 1; i � 1, ... , M ; � � n p 5 p n p � � 1, ... , p; x � p � y ; i � 1 , ... , M ; x , y � ( 0 , 1 ); � i , j , k . � � 1 � 1 � 1 j k ijk i ijk i current HB andxijkthe�nnumber ��x p �p yi ; i �of1�, workers ... , M ; xijkm, y(the � ); �i , j , k . i � ( 0,1 � 2� ijk � 1; i � 1, ... , M ; �1 j �1 k1 ��x p workforce). The model ofijk � 1; ij n��11k,�... � 2� also yields type(s) , M ; j �1 k �1 1 p xijk � 1; i � 1, ... , M ; k � 1, ... , p; j �1 k �1 n .. , M ; xijk , yi � (0,HPDs 1); �i, and j, k . those worker locations where HPDs � 1 j n must be worn. x � 1; i � 1, ... , M ; k � 1, ... , p; M ijk xnijk z� 1; i � 1, ... , M ; k � 1, ... , p; n z j �1 Minimizej �1 xijk � 1; j � 1, ... , n; k � 1, ... , p; yh jl subject to yh jl M � 1 i j � 1 l � 1 M j �1 l �1 x � 1; j � 1, ... , n; k � 1, ... , p; n pijk xnijk z� 1; j � 1, ... , n; k � 1, ... , p; n z i �1 xijk � p � yi ; i � 1, ... , M ; yh; jl � chl � HB; 1 � HB yh jl �i �ch n p l � 1 � 1 k j n j �p1 l �1 xijk � p � yi ; i � 1, ... , M ; j �1 l �1 z x xj �ijk1 k,�y1i , yh jl � ( 0,1); �i, j, k , l. ijk � p � yi ; i � 1, ... , M ; z yh jl � 1;j �j 1�k1�,1yh ... ,jln;� 1; j � 1, ... , n; x ijk , y i , yh jl � ( 0,1); �i, j, k , l. l �1 x ijk , y i , yh jl � ( 0,1); �i, j, k , l. l �1 z � � z � � 90� � NRh � yh � � jl � j � � l � L � 90 � NRh� �Lyh � �l jl � l �1 � j � l �1 � � 3. DESIGN PROCEDURE 3 � � 5 � � 5 � � � p n � � � hl � yh jl � 1 �� n p � ��x � 1 �� � 2 1; i �analytical 1, ... , m; design procedure to determine the � � � 2 � x � 1 ; i � 1, ...ijk , m�;The ijk p n � j �1 k �1 p optimal noise hazard control strategy requires the j �1 k �1 � x ijk � 1; i � 1 , ... , m ; k � 1 , ... , p ; � six optimization models described in section 2 to ��x � 11, ... , m; ijk � 1; ij � be applied in sequence by following the OSHA’s
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n j �1 l �1 HPDs (n ≤x m �≤1M) n ; i � 1, ... , m; k � 1, ... , p; n z ijk xijk yh � 1; i��ch 1�,1...�,HB m; k; � 1, ... , p; j Model H2jl is used to determine the minimum l j �1 m � 1 � 1 j l number of HPDs when all available workers m xijk � 1; j � 1, ... , n; k � 1, ... , p; Mz are considered in job rotation. Nevertheless, xijk ��11;; jj ��i �11,,... yh ...,,nn;;k � 1, ... , p; jl not i �1 all of them need to be assigned to worker x ijk , yh jl � ( 0,1); �i, j, k , l l �1 locations. x ijk , yh jl � (�0,1); �i, zj, k , l � � L n � 90z � NRh � yh � � jl j l nMinimize z � yh jl subject�� to yh jl �� j �1 l �1 l �15 � � � j n�1 l �p1 � n z � 1 n z � 2� � xijk yh jl � chl �� HB ; � 1; i � 1, ... , M ; p j �1 k �1 yh jl � ch �1HB; j �1l l� jn�1 l �1 z z x � 1 ; i � 1 , ... ; k1;�j 1�, ... yh, M 1, ,...p;, n; ijk jl � j �1 yh jl � 1; j � 1 , ... , n; l �1 �1 lM z � � � L � 90 � NRh � yh � z � � � jl j l xijk � 1; j� � 1, ... , n; k � �1, ... , p� ; � L � 90 � � NRh�l � yh jl l �1 � � j � i �1 � � l �1 5 � � � � � n p � n p 5 � � � � 1 JOSE 2006, Vol. 12, No. 4 ��x n p xijk �� p � yi ; i � 1 �,2...� , M ; �� 1 � ijk � 1; i � xijk � 1; i � 1, ... , M ; j �1 k �1 � 2 j �1 k �1 p p j �1 k �1
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• number of work periods per workday p; • number of available workers M; • combined noise level at each worker location Lj (j = 1, ... , n); • ambient noise level Lab; • noise level generated by each machine (at 1-m distance) Lt (t = 1, ... , q); • feasible methods for reducing machine noise at each machine, costs, and amount of noise reduced; • feasible methods for blocking the noise transmission path, costs, and amount of noise reduced at affected worker locations; • types of HPDs, costs, and noise reduction ratings; • total noise control budget TB; • allocated budget portions for engineering controls and the use of HPDs (EB and HB, respectively).
� 1, ... , M ;
OPTIMAL NOISE HAZARD CONTROL STRATEGY
Step 2: Using model E1, find feasible engineering controls for reducing machine noise at the source and/or for blocking the noise transmission path that will prevent daily noise exposure at each worker location from exceeding 90 dBA; find a minimum total cost EC*. If EC* ≤ TB, go to step 13. Otherwise, proceed to step 3. Step 3: Using model E2 and setting EB = TB, determine feasible engineering controls that minimize the maximum daily noise exposure wmax among all n worker locations and a total cost EC. Assuming that such engineering controls are implemented, determine the new combined noise levels at all worker locations. Step 4: Implement job rotation using the current workforce (m workers). Using model A1, find a set of work assignments with the minimum total worker–location changeover F* such that all daily noise exposure does not exceed 90 dBA. If the optimal work assignment solution can be found, go to step 13. Otherwise, proceed to step 5. Step 5: From the increased workforce (M workers), use model A2 to find the minimum number of workers m* to attend all n worker locations on a rotational basis such that their daily noise exposure does not exceed 90 dBA. If m* can be found, proceed to step 6. Otherwise, go to step 7. Step 6: With the optimal workforce m*, set m = m* and use model A1 again to determine the work assignment solution with the minimum total worker–location changeover F*. Then, go to step 13. Step 7: If engineering controls and job rotation are insufficient in preventing noise hazard exposure, the use of HPDs is considered next. Firstly, use the current workforce (m workers) and the original set of noise data (by discarding the recommended engineering controls
361
in step 3). Model E2 is utilized once more with the budget for engineering controls EB = TB – HB to determine the maximum daily noise exposure that any worker receives and the total cost EC. Again, assuming that the recommended engineering controls are implemented, determine the new combined noise levels at all worker locations. Step 8: Setting the revised HPD budget HB = TB – EC and using the new combined noise levels, model H1 is utilized next to determine the work assignment solution with the use of HPDs among m workers, the minimum number of HPDs for the worker locations with excessive noise levels, and a total cost HC. If a feasible solution can be found, proceed to step 9. Otherwise, go to step 10. Step 9: With the use of HPDs at some worker locations, re-compute workers’ noise exposure. Model A1 is then utilized again to determine the work assignment solution with the minimum total worker– location changeover F* for the new workplace noise data. This step will help to find the solution that not only meets safety requirements but also enhances overall productivity of the work system. Next, go to step 13. Step 10: The use of HPDs is re-considered using the number of workers n ≤ m ≤ M. Model H2 is utilized to determine not only the work assignment solution with the minimum number of HPDs (based on the HPD budget HB = TB – EC) but also the number of workers (from M available workers) and their daily work assignments. If the solution (number of HPDs, total cost HC, number of workers, work assignments, and noise exposure levels at all worker locations) can be found, go to step 11. Otherwise, increase the noise control budget TB and, if necessary, revise EB and HB. Then, return to step 2.
JOSE 2006, Vol. 12, No. 4
362 K. ASAWARUNGSAENGKUL ET AL. Step 11: Re-compute noise exposure at the worker locations where HPDs are to be enforced (from step 10). Model A2 is utilized again to determine the work assignment solution with the minimum number of workers m* based on the new noise data (with the use of HPDs). Step 12: Next, set m = m* and use model A1 to determine the work assignment solution (with the use of HPDs) with the minimum total worker–location changeover F* from step 11. Step 13: The result will provide the optimal noise hazard control strategy based on the given total budget (and allocated portions for engineering controls and the use of HPDs). Depending on the given noise data and noise control methods, the solution will recommend a feasible combination of engineering controls, job rotation, and the use of HPDs that will prevent workers’ daily noise exposure from exceeding 90 dBA. Safety, cost, and productivity concerns have also been considered in this design procedure.
4. NUMERICAL EXAMPLES Consider the industrial facility that houses five machines (q = 5). At present, there are four workers (m = 4) being assigned to four different worker locations (n = 4). If necessary, an additional worker can be assigned to work in this facility (M = 5). An 8-hr workday is divided into four equal work periods (p = 4). Ambient noise level is assumed to be 70 dBA. Table 1 shows location co-ordinates of the five machines (M1, M2, M3, M4, and M5), their noise levels, and location co-ordinates of the four worker locations (WL1, WL2, WL3, and WL4). From the given data and using Equation 1, the combined noise levels at the four worker locations are found to be 93.02, 94.97, 93.59, and 93.86 dBA, respectively. Supposing that job rotation is not implemented, it is seen that all four workers (W1, W2, W3, and W4) are exposed to noise hazard. As such, an effective noise hazard
JOSE 2006, Vol. 12, No. 4
TABLE 1. Location Co-Ordinates of Machines, Machine Noise Levels, and Location CoOrdinates of Worker Locations Location Co-Ordinate (m) Machine Noise (dBA) Machine x y M1
2
2
M2
5
2
95
M3
7
4.5
98
M4
5
7
88
M5
2
7
96
94
Location Co-Ordinate (m) Worker Location
x
y
WL1
2
3.5
WL2
5
3.5
WL3
5
5.5
WL4
2
5.5
control strategy is required to reduce their daily noise exposure. Engineering controls for reducing machine noise at individual machines, costs, and noise reduction levels are presented in Table 2. Additionally, there are two types of barriers for blocking the noise transmission path. Type-1 barrier costs US $225 and it reduces noise levels at worker locations WL1 and WL4 by 10 and 4 dBA, respectively. Type-2 barrier costs US $250. When this barrier is installed, noise levels at worker locations WL2 and WL3 will be reduced by 4 and 9 dBA, respectively. There are two types of HPDs, type-A and type-B, which can be worn at any of the four worker locations. Type-A HPD costs US $2.50 and its effective NRR is 8 dBA. Type-B HPD costs US $12.50, with an effective NRR of 12 dBA. Readers should note that cost data in this paper is based on the estimated cost in Thailand. To convert the Thai currency (baht) into the U.S. currency (US $), we use the following currency exchange rate: 40 baht = US $1. Three levels of noise hazard control budget are evaluated. They are case I: TB = US $300, case II: TB = US $400, case III: TB = US $500. In all three cases, the budget for HPDs HB is US $25. The 13-step design procedure is applied
OPTIMAL NOISE HAZARD CONTROL STRATEGY
363
TABLE 2. Methods for Reducing Machine Noise, Cost, and Noise Reduction Method 1 Machine
Method 2
Cost (US$)
Noise Reduction (dBA)
Cost (US$)
Noise Reduction (dBA)
M1
150.00
9
300.00
14
M2
237.50
11
262.50
13
M3
225.00
10
262.50
15
M4
175.00
9
250.00
15
M5
212.50
12
287.50
16
to determine the optimal noise hazard control strategy for this facility under each budget level.
4.1. Case I: TB = US $300 After solving model E1 in step 2, the following engineering controls are recommended: • reducing noise at machine M2 using engineering control method 1, • reducing noise at machine M3 using engineering control method 1, • using type-1 barrier to block the noise transmission path. As a result, the reduced noise loads per work period at all four worker locations are 0.08066, 0.20341, 0.23608, and 0.22294, respectively. Since each noise load per period is less than 0.25, it indicates that workers’ daily noise exposure does not exceed 90 dBA. However, the total cost of engineering controls EC* is US $687.50, which is beyond the total budget of US $300. Thus, the solution is infeasible. Next, model E2 is used to determine feasible engineering controls that will minimize the maximum noise load per period under the given budget. The new solution recommends that noise level at machine M3 be reduced using engineering control method 2, incurring the total cost EC of US $262.50. Also, the four noise loads per period at the four worker locations are 0.35254, 0.36997, 0.25901, and 0.40155, respectively. Since all noise loads per work period exceed 0.25, noise hazard still exists. Assuming that the recommended noise control (reducing noise at machine M3) has been
implemented, job rotation is next considered using model A1 with the number of workers m = 4 (the current workforce). However, each noise load per period is still greater than 0.25. Thus, job rotation using only four workers (m = 4) is insufficient. Model A2 is then utilized with all available workers considered in job rotation. The solution shows that there is no feasible work assignment solution for m = 5. Since engineering controls and job rotation fail to prevent noise hazard exposure (under the given budget), the use of HPDs is now considered. Using the original noise data and setting the HPD budget HB = US $25, model E2 is applied with the new engineering controls budget EB = US $300 – US $25 = US $275. The solution is found to be identical to the previous one (when model E2 was used with EB = US $300). Once again, assume that the recommended noise control has been implemented. Next, model H1 is applied (using the number of workers m = 4). The solution recommends that two sets of type-B HPD be worn at worker locations WL2 and WL4 and the total HPD cost HC is equal to the HPD budget HB. Therefore, the total noise control budget is EC + HC = US $262.50 + US $25 = US $287.50 (
