IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 31. NO. 2. MAY 1990 95

On the Optimal Safe Allocation and Scheduling of A Work Force in a Toxic Substance Environment

RAMIRO VILLEDA AND BURTON V. DEAN

Abstmct- Industrial firms, labor unions, governmental agencies, and the general population are concerned with the high risks and costs of safety management in the workplace. Specifically, manufacturers are interested in both 1) operating efficiently in situations where toxic sub- stances affect workers and 2) at the same time, complying with chang- ing Occupational Safety and Health Act (OSHA) regulations. How- ever, technological advances in manufacturing processes often produce deleterious changes in the number, varieties, and levels of toxic sub- stances affecting manufacturing operations. Consequently, manufactur- ing work force allocation and scheduling problems must be solved with each change in the production volume and/or process or OSHA regula- tions.

An approach to model and to solve the problem of safe allocation and scheduling of a manufacturing work force in a toxic substance envi- ronment using linear programming is presented. The firm’s objective is to maximize utilization of the work force, without violating any OSHA standards. Solutions are obtained in the form of optimal safe assign- ments and schedules of the work force to multiple jobs.

A variety of operational situations are analyzed to illustrate the mod- eling approach, the use of a low cost commercially available software package for a microcomputer, and the results obtained in realistic ex- amples.

INTRODUCTION

LMOST a century ago, when the Railway Safety Act was A being considered in 1893, a railroad executive said that it would cost less to bury a man killed in an accident than to put air brakes on a car [8]. This railroad executive was not an evil or malicious individual. He was expressing a common mind-set in those days-the safety of workers was considered only in direct monetary terms.

There have been many changes in industrial practices and many safety acts have been passed by Congress since 1893. For example, the passage of the Social Security Act (1935), assured the eventual acceptance in the United States of the phi- losophy that the worker had the right to earn a living without endangering his health. During the period since 1935 a num- ber of states adopted codes and regulations governing condi- tions of work to prevent injury to health and in many instances established threshold limit values which limited levels of ex- posures in the working environment [6], [ 131, [ 181.

Manuscript received May 16, 1988. The review of this paper was processed by Department Editor J. R. Evans. This work was supported by a grant from the School of Business, San Jose State University, San Jose, CA (1987-1988). R. Villeda was with the Department of Organization and Management, the

School of Business, San Jose State University, San Jose, CA 95192. He is now with the Mechanical and Industrial Engineering Department, the University of Texas at El Paso, El Paso, TX 79968.

B. V. Dean is with the Department of Organization and Management, the School of Business, San Jose State University, San Jose, CA 95192.

IEEE Log Number 8932156.

The most important act of legislation was the Occupational Safety and Health Act (OSHA) of 1970. This Act specifically instructed the National Institute for Occupational Safety and Health to 1) develop and establish recommended occupational safety and health standards and 2) perform all functions of the Secretary of Health, Education, and Welfare under Sections 20 (Research and Related Activities) and 21 (Training and Employee Education) of this Act [ 181.

More recently, in 1986, Congress extended the toxic waste law of 1980, requiring industrial plants to disclose to state and local communities detailed information on whether they are using and storing any of the more than 300 toxic and hazardous substances, as specified by the Act [9]. About 1.5 million factories and farms are subject to the new provisions, including more than 82 percent of all manufacturing plants in the U.S. It is estimated that manufacturers will spend some 13 million hours of effort in completing the forms required for reporting chronic releases of dangerous toxic substances [9, p. 381. (Dupont has an expert system on the market for $2600 to aid companies in the generation of these reports.)

Currently, both industrial firms and governmental agencies are concerned with the high risks and costs of safety man- agement in the workplace. Manufacturers are interested in 1) operating efficiently in situations where toxic substances af- fect workers and 2) complying with OSHA regulations so as to avoid harsh economic penalties and undue inspections or frequent interruptions in operations [ 151. Also, labor unions and governmental agencies seek to minimize risks to workers 1151.

Technological advances in manufacturing processes may produce deleterious changes in the number, varieties, and lev- els of toxic substances that affect manufacturing operations. Also, annual changes and updating in federal, state, and local toxic substance legislation impose increasing restrictions on manufacturers’ processes and procedures. Furthermore, there is some evidence that the effects of industrial chemicals on the workers’ metabolism is enhanced or further complicated by their drinking or smoking habits. For example, Cherry et al. [4] found that a concentration of toluene of 80 parts per mil- lion (ppm), which is below the OSHA limit (200 ppm), had no effect on workers’ performance on pursuit tracking and visual search tasks and also in mood; however, there was a tendency for performance and mood to deteriorate more when alcohol and toluene (at 80 ppm) were administered together than when alcohol was taken alone. Johns-Manville Corp., citing a study that reports that smokers who are occupationally exposed to asbestos have a 92 times greater chance of developing lung

0018-9391/90/0500-O$Ol .00 0 1990 IEEE

96 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 31, NO. 2, MAY 1990

cancer than the general population, has banned smoking in its asbestos facilities [ 101.

Most of the research and prevention efforts in manufactur- ing safety management have focused on the work activities involved in manual load handling. This is due to the fact that musculoskeletal injuries to the trunk account for 32 percent of all compensable injuries and 42 percent of the compensation costs in the U.S. [ l l ] . It has been difficult to study the case of toxic substances due to the presence of many confound- ing effects, and also because the effects of low concentra- tions of toxic chemicals on the work force may show up only decades after the initial exposure has taken place. Employers and workers tend to ignore the effects and consequences of toxic substances in the workplace because they are not able to observe the relationship between cause and effect [lo, p. 41 11. To the best of our knowledge, the only published work that provides managers with recommendations on how to de- sign work shifts in compliance with OSHA’s standards is that of Villeda [ 191. The purpose of the present study is to demon- strate the use of an approach to model and optimally solve the problem of safe allocation and scheduling of a work force in a toxic substance environment.

STATEMENT OF THE PROBLEM

Although previous use of work force scheduling practices have been concerned with increasing work force efficiencies [ 11, [3], [20], no such published studies have been specifically related to toxic substance situations.

In this study, the basic assumption is that engineering con- trols (e.g., substitution of a less harmful substance, modifi- cation of the machine or process, etc.), the preferred OSHA methods of reducing worker exposure, are either technolog- ically not possible or operationally too costly. Advances in manufacturing technology which do not require the use of toxic chemicals for printed circuit board production involving a single layer of circuit patterns should reduce worker expo- sure [21]. This study considers that only managerial controls, the reduction of the exposure time of workers, are possible.

The corporate manufacturing objective is to optimize the utilization of the work force, without violating any OSHA constraints or specifications. The firm’s control and noncon- trollable variables are as follows.

Control variables: 1) number of employees who are available to be assigned

to jobs; 2) schedule of workers’ assignments to jobs; 3) allocation of the work force to jobs.

Noncontrollable variables :

product technology is fixed, based on product engi- neering design characteristics; process technology is fixed, along with the specific toxic substances associated with each stage of the pro- cess level or manufacturing engineering considerations; number and types of jobs (workstations) in the work shift are specified; applicable federal and/or state OSHA standards and limitations are specified.

Threshold Limit Values (TLV) OSHA prepares and updates for each identified toxic sub-

stance, threshold limit values (TLV), which workers may be exposed to without violating legislation or regulations. TLV refer to airborne concentrations of substances measured in parts per million (ppm) or milligrams of particulate per cubic meter of air (mg/m3), and represent conditions under which it is believed that nearly all workers may be exposed eight hours a day for a 40-hour week over a working lifetime with- out adverse effect. Because of the wide variation of individ- ual susceptibility or exposure of an occasional individual, the threshold limit may not prevent discomfort, aggravation of a preexisting condition, or occupational illness to individual workers at different intervals following initial or sustained ex- posure. Therefore, it is up to management to decide whether the prescribed TLV or a lower value should be used in prac- tice. For a particular work force the OSHA TLV may be too high and a reduction from the OSHA TLV is advisable.

Current TLV found in OSHA’s 1910.1000 Air Contami- nants [ 181 are used in this study to illustrate the proposed ap- proach and to provide specific parameter values in the exam- ples. Additional restrictions may also apply in specific manu- facturing situations, based on local community or state toxic substance control statutes.

MODEL CONSTRUCTION The problem may be divided into two different cases. Case

I is where workers are exposed to a single toxic substance, and case I1 is where they are exposed to several toxic sub- stances. Case I, with the following four variations, is analyzed in this study. Situations involving case I1 are under study at the present time. We now classify the four situations in case I as follows.

Case I: Single toxic substance

a) single jobhingle worker; b) single job/multiple workers; c) multiple jobdsingle worker; d) multiple jobs/multiple workers.

Our basic approach uses a mathematical model to formulate and solve this problem. The following example illustrates how the most complex situation d) above is formulated.

Example: Two workers, two jobs (single shift = 8 working hours). We introduce the following notation:

i 1 , 2 , workers, j 1 , 2, jobs, X , ,

Lj

Ei

number of hours in a shift that worker i is to be assigned to job j , level of toxicity in the process at job j , in ppm or mg/m3, total weighted hourly exposure of worker i to the toxic substance, in ppm or mg/m3, where

IlXil +12xi2

8 E; =

L maximum permissible threshold limit level of the toxic substance, as specified by OSHA (TLV), where OSHA requires that Ei 5 L in ppm or mg/m3.

VILLEDA AND DEAN: SAFE ALLOCATION AND SCHEDULING OF A WORK FORCE 97

WORK STATION 1

3.64 (worker 1) 4.36 (worker 2)

Total - 8.0 hrs. Trichloroethane: 415 P.D.m.

The firm desires to determine an optimal safe allocation and schedule of worker assignments (X;;) so as to maximize work force utilization Win hours, and to comply with OSHA regulations L. This is achieved by formulating and solving the following mathematical model of this problem:

WORK STATION 2

4.36 (worker I) 3.64 (worker 2)

Total - 8.0 hrs.

Tri chl oroethane: 200 P . P .m.

max W = X I I +X12 +XD + X 2 2 cation problem as a case I d) problem:

where

l ixi i + 12Xi2 5 L (8), max w =XI1 +XI2 +x21 + x 2 2

where i = 1, 2 OSHA’s TLV for one 8-h shift ( 1 )

4 7 5 x 1 1 +200X12 5 350(8)

475x21 +2OOX22 5 350(8) XilXi2 5 8 ,

i = 1 , 2 availability of workers (2)

XI; +X2; 5 8 ,

j = 1, 2 job requirements for a shift (3)

xi; 2 0,

i, j = 1, 2 nonnegative constraints. (4)

The problem is a form of the general linear programming model [2] with four variables (X;;; i, j = 1 , 2) and ten con- straints given in (1)-(4) above. In summary, the approach has three components in organizing and processing the required information parameters, frame, and STORM [7]. Parameters are the OSHA TLV standards and specific manufacturing work force requirements. The frame is the mathematical model that allows the formulation of any single or multitoxic substance control problem (cases I or 11) as a linear programming model.

STORM is a user friendly commercially available software package for a microcomputer that solves the linear program- ming model [7]. There has been a phenomenal growth of mi- crocomputers, with the current linear programming software, including STORM, being quite good and getting better [16].

MODEL SOLUTION The following examples illustrate the use of the modeling

approach described above in realistic situations and the nature of the results obtained.

Example I Consider the workers to be assigned to staff two worksta-

tions in an instrument manufacturing plant, where they are assigned to clean printed circuit boards. The solvent used by the firm is trichloroethane, a commonly used chemical in this application [ 141. The concentrations of this toxic substance to which the workers are exposed are 475 ppm and 200 ppm in the first and second workstations, respectively. OSHA’s TLV for trichloroethane is 350 ppm for an 8-hour shift [18, p. 6551.

Our objective is to find the assignment of workers to sta- tions that maximizes the workers’ utilization, without violating OSHA specified regulations.

Using the mathematical model described in the previous section, a decision support system would formulate the allo-

XII +Xi2 L 8

X21 + X 2 2 5 8

Xi1 fX21 5 8

Xi2 + X 2 2 5 8

x 1 1 2 0

XI2 2 0

X2I 2 0

x 2 2 2 0.

The STORM package solves the linear programming model.

XII = 3.64 h (hours worker 1 should be assigned to work-

X12 = 4.36 h (hours worker 1 should be assigned to WS 2), X21 = 4.36 h (hours worker 2 should be assigned to WS l), X 2 2 = 3.64 h (hours worker 2 should be assigned to WS 2).

This assignment allows the firm to staff both workstations fully during the shift, using the workers efficiently and si- multaneously does not violate the OSHA TLV. The workers’ schedule is tabulated in Table I.

The total weighted hourly exposures (E;) for each worker are

The following is a summary of the computer printout:

station (WS) l),

475 (3.64) + 200 (4.36) = 325 8

El =

475 (4.36) + 200 (3.64) = 350 8

E2 =

El and E2 5 L (350 in this example).

Alternate Optimal Solutions A linear program with two or more optimal solutions is said

to have alternate optima, which is the case in this particular problem. When using the simplex method of solving a linear programming problem, it is possible to recognize that there are alternate optima by inspecting the final tableau. If there are alternate optima, the Cj - Zj will equal zero for one or more of the variables not in the solution [21.

~

98 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 37, NO. 2. MAY 1990

It is possible to show that this problem has more than one optimal safe solution using a two-dimensional graph. We in- troduce the following relationships:

X I I = the number of hours worker 1 should be assigned to

Xi2 = 8 - X I I , ws 1,

X2l =Xi2 = 8 - X I I , X 2 2 = 8 - (8 - X I ] ) = X11.

If we are able to achieve this schedule, without violating the OSHA TLV constraints, we will have full utilization of the work force

W =Xi1 + ( 8 - X I I ) + ( 8 - X I I ) +Xi1 = 16. Therefore El may be formulated as

I 350

475x11 + 1600 - 200x11 I 350

275x11 + 1600 ~ 350

8

8 34.375Xll + 200 I 350

34.375Xll 5 150

XI ] 2 4.36 and E2 may be formulated as

475 (8 - X I I ) + 200x11 8

350

3800 -475x11 f200X11 <_ 350 8

3800 - 275x11 5 350 8

475 - 34.375 X I I 5 350

-34.375X11 5 -125

XI1 2 3.64.

Therefore 3.64 5 Xjj I 4.36. This inequality implies some degree of flexibility in the optimal assignment and scheduling of workers, without violating OSHA constraints. The range of optimal solutions is r3.64, 4.361 (e.g., if we schedule X I 1 = 3.8 h; thenX12 = 8-Xl1 = 8-3.8 =4.2h, XZl = 8-X11 = 8 -3.8 = 4.2 h, and X 2 2 = X I I = 3.8 h). Fig. 1 presents the following relationships:

475x11 +200(8 XI^) P

E1 =

475(8 -Xl1) + 2 0 0 X 1 1 E2 =

8

34.375Xll.

I '

1 : , ! . I . 0

w 7 8 1 2 3 4 5 6 3 .64 4.36

Schedule of Worker. X,l, in Hours Per Shif t

Fig. 1 . Flexibility in work force scheduling in a toxic substance environ- ment.

In Fig. 1, the interval (3.64, 4.36) is shown as the fea- sible region where it is possible to achieve full work force utilization without violating OSHA constraints. It should also be noted that assigning additional workers to these jobs would yield increased scheduling flexibility and reduced toxic expo- sure to the original workers.

Minimizing Worker Exposure

It is also possible to minimize worker exposure. If there is a management (or union) policy requiring all workers to receive the same total weighted hourly exposure (Ei), it is possible to accomplish this by adding a constraint, in the form of

475x11 +200X12 -475x21 -200x22 =o . This constraint will force the model to provide a value of El = E2, where XI] = X I * = X21 = X22 = 4 (See Fig. 1 at the intersection of the El and E2 lines).

Another safe alternative would be to rotate schedules every day without exceeding the daily assignments given by the op- timal region in Fig. 1, so as to equalize worker exposure to the toxic chemical.

The dual formulation of the linear programming problem seeks to minimize worker exposure as given by

min (8)350Y1 +(8)350Y2 +8Y3 +8Y4 +8Y5 +8Y6

475Y2 + Y 3 + Y 5 2 1

The solution to this problem is

y3 = 1; Y4 = 1; YI, Yz, Y5, Y6 = 0.

VILLEDA AND DEAN: SAFE ALLOCATION AND SCHEDULING OF A WORK FORCE

WORK STATION 1 Acetone: 675 p.p.m.

2.07 (worker 1 ) 5 .93 (worker 2 )

99

WORK STATION 2 Acetone: 800 p.p.m.

3.25 (worker 1) 4.75 (worker 3 )

Example II This case discusses the situation where the number of work-

ers is greater than the number of workstations, and therefore workers may be assigned to other tasks to achieve full utiliza- tion. Suppose that three workers are to be assigned to staff two workstations, where they will be exposed to extremely high concentrations of the industrial solvent acetone (TLV = 500 ppm). Acetone is another solvent used by electronics and de- fense companies. The concentrations are 675 pprn and 800 ppm for the first and second workstations, respectively.

The linear programming model, incorporating six variables and fourteen constraints, is as follows:

max W = X I I +X12 +X21 + X 2 2 +x31 + x 3 2

where

675x11 +8OOX12 5 500(8)

675x21 + 800x22 5 500 (8)

675x31 + 800x32 5 5 0 0 ( 8 )

X I I +Xi2 5 8

x21 + x 2 2 I8

x31 +X32 5 8

X I I +X21 + X ~ I 2 8

Xi2 +X22 +X32 5 8

all X;, 2 0.

The STORM package solves the linear programming model.

X12 = 2.07 h (hours worker 1 should be assigned to WS I), X12 = 3.25 h (hours worker 1 should be assigned to WS 2), X21 = 5.93 h (hours worker 2 should be assigned to WS l ) , X22 = 0 X31 = 0 X 3 2 = 4.75 h (hours worker 3 should be assigned to WS 2).

This assignment allows the firm to staff fully both work- stations, although the concentrations of acetone at both work stations are above the OSHA’s TLV. Table I1 shows the work schedule for workstations 1 and 2.

The following are the total weighted hourly exposures (Ei) for each worker:

The following is a summary of the computer printout.

(worker 2 is not assigned to WS 2), (worker 3 is not assigned to WS l ) ,

675(2.0741) + 800(3.25) = 500 8 El =

E2 = 675 (5.9259)

E3 =

8

800 (4.75) 8

= 500

= 475

E l , E2, E3 5 L (500 in this example).

Since the three workers are assigned less than the full 8 hours to workstations 1 andlor 2, they are available to be

TABLE 11 SCHEDULE FOR WORK STATIONS I AND 2

I I T o t a l = 8.0 hrs . T o t a l - 8 .0 hrs . 1

reassigned for the remainder of the shift to work in an envi- ronment free of the acetone contaminant.

It is very likely that this problem has alternate optimum solutions. Unfortunately, STORM’S linear programming pro- gram provides only one optimal solution. Other software pack- ages, such as LINDO are able to provide alternate optima [161.

Also, as in example I, if there is a need to have all workers to have the same exposure, El = E2 = E3, this is accom- plished by adding the following linear constraints and finding the linear programming solution:

Example III This case analyses the situation where three workers will

staff three workstations. The manufacturing process involves an exposure to formaldehyde. Formaldehyde, a potential cancer-causing chemical, is widely used in the foundry, ap- parel, funeral, and furniture industries. The U.S. Department of Labor, acting under a court order, was expected to reduce formaldehyde’s TLV from the current 3 ppm to 1 ppm by late 1988. The new standard will cover about 2.2 million workers exposed to this chemical [ 121. In this example, the concentra- tions of formaldehyde are 0.5, 1 . 1 , and 1.3 ppm at the first, second, and third workstations, respectively.

The linear programming model, incorporating nine vari- ables and 18 constraints, is as follows:

max W = X I I +xI2 +xI3 +x2, +x22 + x ~ ~

where

all X;j 2 0,

100 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT. VOL. 31, NO. 2. MAY 1990

WORK STATION 1 Formaldehyde: 0 . 5 ppm

YORK STATION 2 YORK STATION 3 Formaldehyde: 1.1 DDm Formaldehvde: 1.3 oom

2.67 (worker I ) 1.33 (worker 2) 4.00 (worker 3)

Total - 8.00 hrs. The STORM package solves the linear programming model.

X I I = 2.67 h (hours worker 1 should be assigned to WS l), X12 = 1.33 h (hours worker 1 should be assigned to WS 2), Xi3 = 4.00 h (hours worker 1 should be assigned to WS 3), X21 = 1.33 h(hours worker 2 should be assigned to WS l), X22 = 6.67 h (hours worker 2 should be assigned to WS 2), X23 = 0 X31 = 4.00 h (hours worker 3 should be assigned to WS I), X32 = 0 X33 = 4.00 h (hours worker 3 should be assigned to WS 3).

The work schedules for workstations 1, 2, and 3 are shown

The total weighted hourly exposures (E;) for each worker

OS(2.67) + 1.1 (1.33) + 1.3(4.00) 8

The following is a summary of the computer printout:

(worker 2 is not assigned to WS 3),

(worker 3 is not assigned to WS 2),

in Table 111.

are

= 1 El =

~ ~~

1.33 (worker 1) 6.67 (worker 2)

4.00 (worker 1) 4.00 (worker 3)

Total - 8.00 hrs. Total - 8.00 hrs.

0.5 (1.33) $- 1.1 (6.67) 8

= 1 E2 =

0.5 (4.0) + 1.3 (4.0) = 0.90

8 E3 =

E l , E2, E3 5 L

(in this example we are using the 1988 OSHA TLV standard for formaldehyde, 1 ppm).

SUMMARY AND CONCLUSIONS This paper develops an approach to model and solve the

allocation and scheduling of a work force in a toxic substance environment, as a linear programming problem. The objective is to maximize utilization of the work force without violating any OSHA constraints or specifications.

The paper’s basic assumption is that engineering controls are either not practical or too costly, and that only manage- rial controls, in this case, the reduction or minimization of exposure time, was possible.

The approach has three components to organize and pro- cess information. These are 1) parameters (OSHA standards and specific manufacturing staffing requirements, 2) frame (the mathematical model that allows the formulation of any problem as a linear programming model), and 3) STORM (a microcomputer software package that solves the linear pro- gramming model). Similar linear programming models have been used by Dean and Salkin [SI, and others, to solve indus- trial operations management problems.

A variety of operational situations are analyzed to illustrate the use of the modeling approach, the use of a standard user

friendly software package and sample results. The illustrative examples demonstrate the feasibility of modifying standard work scheduling models to include toxic substance control constraints so as to yield optimal safe policies in this case.

The approach developed in this paper provides manufac- turing managers, human resource managers, engineers, and industrial hygienists with optimal safe schedules for the allo- cation and scheduling of a work force in a toxic substance en- vironment. It is important to point out that all problems tested have alternate optima, that is, there is more than one opti- mal solution. This characteristic facilitates the implementation of the solution obtained with our approach, by providing in- creased manufacturing management flexibility in safe worker assignments. In addition, our approach also may be used to 1) minimize worker exposure and 2) balance exposure among all involved workers.

Finally, the approach developed in this study demonstrates that some industry-government conflicts in the areas of work force safety management and risk management may be appro- priately resolved by means of an effective analytic method- ology and a low cost computer software application to the satisfaction of all concerned parties.

ACKNOWLEDGMENT The authors wish to thank the two anonymous referees for

their comments on an earlier draft of the paper. They also wish to thank firms who must remain anonymous for provid- ing them with data and information concerning products and processes involving toxic substances. For the opportunity to review preliminary results of this paper, they thank attendees at the 30th Annual Safety Conference, School of Business, San Jose State University, San Jose, CA, January 21, 1988 W I .

REFERENCES I. Bailey, “Integrated days off and shift personnel scheduling,” Com- put . f n d . Eng., vol. 9, no. 4, pp. 395-404, 1985. M. J . Best, Linear Programming: Active Set Analysis and Com- puter Programs. I . I . Browne and R. K. Tibrewala, “Manpower scheduling,” Ind. Eng., vol. 7, no. 8, pp. 22-23, 1975. N. Cherry, I . D. Johnston, H. Venables, and H. A. Waldron, “The effects of toluene and alcohol on psychomotor performance,” Er- gonomics, vol. 26, no. 1 1 , pp. 1081-1087, 1983. B. V. Dean and H. M. Salkin, “On minimizing workmen’s compen- sation schedules by linear programming,” in Studies in Linear Pro- gmmming. L. Ede and M. T. Barnard, “A report on state occupations health leg- islation,” U.S. Dept. of Health, Education and Welfare, Public Health Service, Bureau of Occupational Safety and Health, 1014 Broadway, Cincinatti, OH 45202, 1971. H. Emmons, A. D . Flowers, and K . Mathur, STORM-Quantitative Modeling for Decision Support. Oakland, CA: Holden-Day, 1986,

W. Hammer, Occupational Safety Management and Engineering. Englewood Cliffs, NJ: Prentice-Hall, 1985, p. 1. “Industry to give vast new data on toxic perils,” The New York Times, Feb. 14, 1988, p. 1 . S. Konz, Work Design. Columbus, OH: Grid Publishing, 1979, p. 418. R. M. Nelson, “Prevention-a government perspective,” Er- gonomics, vol. 30, no. 2 , pp. 221-226, 1987. “OSHA, under court order, will tighten guideline on exposure to formaldehyde,” The Wall Street Journal, Nov. 23, 1987, p. 14. R. M. Rank and T. H. Seymour, Directory and Index of Safety and Health Laws and Codes. Washington, DC: Supt. of Documents,

Englewood Cliffs, NJ: Prentice-Hall, 1985.

Amsterdam, Holland: North-Holland, 1971, ch. 6.

pp. 59-68.

VILLEDA AND DEAN: SAFE ALLOCATION AND SCHEDULING OF A WORK FORCE

U.S. Government Printing Office, U.S. Dept. of Labor, Bureau of Labor Standards, 1969. “Solvents detected in water. H-P spill travels to canal in Palo Alto,” San Jose Mercury News, Dec. 14, 1986, Sec. 2, p. 4B. Proc. 30th Annual Occupational Safety and Health Conference, San Jose State University, San Jose, CA, Jan. 21, 1988. R. Sharda, “The state of the art of linear programming on personal computers,” Interfaces, vol. 18, no. 4, pp. 49-58, 1988. V. M. Trasko, Occupational Health and Safety Legislation: A Com- pilation of State Laws and Regulations. Washington, DC: Supt. of Documents, U.S. Government Printing Office, Public Health Service Bulletin 357, 1954. US. Department of Health and Human Services, Code of Federal Regulations, Title 29-Lubor Chapter XVII. Washington, DC: Occupational Safety and Health Administration 1910.1000, Govern- ment Printing Office, July 1, 1985, pp. 654-658. R. Villeda, “Work shifts designed to limit exposure to toxic and haz- ardous substances,” Ind. Eng., vol. 19, no. 9, pp. 58-67, 1987. D. Warner and 3. Prawda, “A mathematical programming model for scheduling nursing personnel in a hospital,” Manag. Sci., vol. 19, no. 4, pp. 411-422, 1972. “Putting pizzazz into the circuit board,” Bus. Week, Sept. 19, 1988, p. 88.

* Ramiro Villeda received the B.S.I.E. degree from Instituto Tecnologico de Queretaro (Mexico), the M.S.I.E. degree from the University of Texas at El Paso, and the Ph.D. degree in production systems from Texas Tech University.

He is an Assistant Professor of Industrial Engi- neering at the University of Texas at El Paso. He has worked in manufacturing and industrial engi- neering for GTE Sylvania, and he was Quality Con- trol Manager for ESSEX. He has published articles in such journals as Industrial Engineering and the

International Journal of Production Research. His research areas include implementation of JIT production systems, group technology, simplified in- tegrated manufacturing, and computer simulation.

Dr. Villeda is a senior member of the IIE, APICS, and ORSAITIMS, and he is a certified practitioner of production and inventory management (CPIM) and a Professional Engineer in Mexico.

101

Burton V. Dean was born in Chicago, IL, on June 3, 1924. He received the B.S. degree from North- western University in 1947, the M.S. degree from Columbia University in 1948, and the Ph.D. degree from the University of Illinois in 1952.

He was a mathematics instructor at Columbia University from 1947 to 1949, and at Hunter Col- lege from 1949 to 1950. He was a mathematics Re- search kllow at the University of Illinois from 1950 to 1952 and a mathematician with the National Se- curity Agency from 1952 to 1955. He was then a

Research Mathematician with Operations Research, Inc., from 1957 to 1965. He then became Associate Professor Operations Research at Case Western Research University, Cleveland, OH (1957-1965). becoming Professor Op- erations Research and then Chairman of the Department. At San Jose State University he was Professor Operations Management, and then Chairman of the Department, from 1985 to the present. He was a Visiting Professor of in- dmtrial and management engineering at the Technion-Israel Institute of Tech- nology from 1962 to 1963. He was an Associate with the Institute of Public Administration Washington, DC, from 1972 to 1976, and with Booz, Allen, and Hamilton from 1980 to 1982. He was a Consultant with U.S. government and industry from 1957 to the present, and with TAHAL Water Planning for Israel from 1962 to 1964, the Greek Productivity Center (1980-1981), and the US.-Egyptian Economic Assistance Program (1984-1987). He was a Visit- ing Professor at the University of Louvain, Belgium, Ben Gurion University, the University of Tel Aviv (1978), and with Zero-Base Budgeting Seminars in Belgium, Egypt, Israel, Greece, and Spain in 1978; Greece, Spain, and Japan in 1979; Greece and Spain in 1980. He was a lecturer at U.S. CSC from 1977 to 1980. He was Advertising Director for Sourcenet Inc. from 1986 to the present, and Applied Imaging Corporation from 1987 to the present. He was then Visiting Professor of Industrial Engineering, and Management Engineer- ing at Stanford University in 1985. He is the author of Operutions Resemch in Research and Development (1963, reprinted 1978). He is a coauthor of Mathematics of Modern Management (1963, reprinted 1978) and Evalua- tion, Selection, and Control of R&D Projects (1968). He is also coauthor of Industria[ Inventory Control (1974), Management of Research and In- novation (1980), and Project Management (1985). He has also submitled articles and chapters in professional journals, books, and the Encyclopedia of Professional Management. He has been Editor of Management Science (1962 to the present); Associate Editor of OPSEARCH (1968-1974); North Holland Studies in Management Science and Systems (1974 to the present); the Journal of Business Venturing (1985 to the present); and Department Editor ofManagement of Technology Systems (1985-1988). He is also De- partment Editor of the IEEE WNSACTIONS ON ENGINEERING MANAGEMENT. Dr. Dean received the Centennial Medal of the IEEE Engineering Management Society in 1984, and the Centennial Scholar Medal from Case Institute of Technology in 1981. He is a Fellow of the AAAS, the American Production and Inventory Control Society, the Academy of Management, the Operations Research Society, the Institute of Management Sciences, the American Math- ematics Society, and Omega Rho.