Duration and optimal number of shifts in the labour market U. Spiegela, L.D. Gonenb,* and M. Weberc a

Department of Management, Bar-Ilan University, Israel and Visiting Professor, Department of Economics, University of Pennsylvania, USA b Department of Economics and Business Administration, Ariel University, Israel c Department of Management, Bar-Ilan University and Faculty of Business Administration, Ono Academic College, Israel *Corresponding author. E-mail: [email protected] Significant conflicts impacting production costs and efficient use of labor are associated with shift work. We examine the relationship between the

number of

shifts and their duration in order to maximize efficient use of labor. We focus on the debate between two basic elements: (a) a greater number of shifts of shorter duration which require more idle time between shifts, and may lead to increased expenses and inefficient use of resources; and (b) shifts of shorter duration that generate higher productivity. We develop a formula for achieving a balance between the two elements and determining the optimal number of shifts and their duration. We present several applications that can be derived from our formula.

Keywords: shifts; work flexibility; idle time; labor efficiency

JEL Classification: D24; J2; J3; J7

I. Introduction In our model we raise the question of the optimal number and length of shifts in the labour market. In many industries, shifts with fewer hours are associated with higher output rates per hour (Holman et al., 2008), enhanced individual productivity improved employee health and well-being, and job or life satisfaction. However, shift work can increase the firm's hiring costs of recruitment and adaptation. Recruitment costs reflect the firm's effort to find suitable workers. Adaptation costs are associated with the training expenses for newly hired workers and with their reduced productivity. Moreover, employing more workers may increase the need for extra training in order to reach full productivity. It may also increase the costs of employee 1

benefits such as pensions and health insurance. Shift work has many inherent risks: decreased performance, poor concentration, absenteeism, accidents, errors, injuries, and fatalities. The issue becomes more alarming when shifts are associated with long hours of work. In addition, shift workers are often employed in dangerous jobs such as firefighting and the delivery of emergency medical and security services that require skilled nurses and doctors as well as drivers and transportation. The most crucial disadvantage of more shifts of shorter duration is the mandatory idle time between shifts. In their paper, Calmfors and HoelSource (1989) state that the reduction of working time is caused by employees who seek flexible work arrangements and by inevitable labour shortages. Companies therefore have no choice but to engage different types of employees in nonconventional work schedules and to accept flexible work patterns. A reduction of working time "is not a problem of dividing a given number of working hours between workers." Rather, they suggest that shift work should be considered in order to maintain or even increase operating time, preserve output and increase employment. In response to economic, technological, and social pressures, a 24-hour organization of the workplace is common and requires the workforce to adapt to many different forms of shift work schedules. However, the adverse effects of shift work are well chronicled. They include biological concerns as well as interference with social and domestic life (Smith et al., 1998). Research studies concerning the effects of shift duration on fatigue and job performance have produced ambiguous results. Long shifts compress the working week, increase motivation and stimulate greater effort, thereby reducing any detrimental effects of increased fatigue. In contrast, they also negatively impact the quality of job performance (Rogers et al., 2004). Regarding the quality of job performance, research findings have emphasized that labor productivity per hour may decrease for the entire shift because of the proportion of "nonproductive" time devoted to starting up and finishing work, overlapping between shifts, and other inevitable idle time (e.g., Hanna et al.,2008).

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The general shift scheduling problem involves determining the number of employees assigned to each shift (Aykin, 1996), while ensuring efficiency, labor scheduling efficient operations, on-time task execution, and consistent levels of customer service. The literature (i.e. Bechtold and Jacobs, 1990; Thompson, 1995; Aykin, 1996) suggests programming models for optimal shift scheduling with multiple rest and lunch breaks, allowing extensive flexibility in shift starting times, shift lengths, and break placement. Our paper proposes a basic and simple method for determining the assignment of workers to each shift, We generate a "formula" that determines the optimal number of workers and the duration of each shift while also taking into consideration issues such as diminishing productivity and idle time between shifts.

II. The Model We start our analysis by assuming the value of marginal productivity

of the

worker diminishes at a constant rate throughout the shift. We assume a simple function of

as follows:

(1) Where t is the actual working time from the starting point of the shift along the cycle of

of each shift.

defines the duration of each shift.

We define (further) that n represents the number of shifts that are resumed along the given period . We distinguish between two different periods at each cycle of each shift: the actual time of productive activity , and the time between shifts, namely idle time,

that is required for transitioning from one shift to the next. Idle time does not

contribute directly to actual production. It includes several necessary activities during the time when workers are present at their place of employment but do not generate any production. This is due to setup time between shifts, bureaucratic procedures that may be required, etc. Accordingly, when more shifts occur during a given period, more idle time is required. Therefore: (2) is the total amount of hours devoted to a given job and each cycle of each shift. 3

is the total time of

We assume further that the employer has to pay workers for the total hours per given job,

The workers are paid regardless of their contribution to the real productive

output. For example, medical doctors and nurses in between shifts deliver information and transfer records concerning the conditions and treatment of patients. The workers at a factory have to adjust the machines to a new position for each individual worker and to prepare the whole line for each new shift. In computer services, idle time includes opening and entry into the computer by using a code number etc. Again, the wage compensation is for any time they are present at work, whether they are at period

and contributing during the shift or at idle times,

, when they are not

productive workers. Employers pay not only the individuals who are already working on an earlier shift but also those who will begin work on a subsequent shift. The employer’s cost for each worker is comprised of two factors: 1. Payment per hour,

that each worker receives for being present at the

workplace regardless of whether he is productive or idle. 2. Payment to each working employee,

who holds a job, whether or not he is

productive and regardless of whether he works many or few hours. Based on the above, we can determine the total revenue each employer gains upon hiring

workers as:

(3) The total cost that each employer pays for hiring the n workers is: (4) The first term

represents the total salary payments for all working hours, since

the wage per hour is paid regardless of whether the worker is actually contributing to productivity during the overlapping idle time of . Both the worker who concludes the earlier shift and the one who begins the new shift are paid for their mutual time. The employer’s total profit diminishing of

that maximizes with respect to in the case of linear

is:

(5)

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Solving F.O.C. with respect to we get:

(6) From (6) we get (7) Or (7') The solution of that is the optimal productive time of each shift (8) And therefore we get the optimal number of shifts at each period . (9) While S.O.C are

Using equations (8) and (9) we can derive a comparative static analysis with respect to several independent variables as follows:

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, due to an exogenous change in the idle time between shifts, there is an increase in the optimal time duration of the shift, thus, period

, i.e., at a given time

the number of shifts decreases. an increase in the payment per hour work,

the optimal time of each shift

also increases, and again the number of shifts decrease,

.

, the optimal

productive time of each shift increases when the payment to each employee, increases. Therefore again

, for a given time period

the number of longer

shifts decreases. higher productivity of each given level of working hour leads to an increase in the optimal duration of each shift while the number of shifts decreases,

.

III. Conclusion and Implications The implications of our model might be of interest to employers and employees in different areas such as those described below: a. People in the transportation industry face some of the most serious challenges. Due to their irregular sleep schedules, they battle fatigue and endure long, tedious hours at the controls or behind the wheel. Our model predicts the need for a greater number of shifts of shorter duration. This creates the balance between productive (driving) activity and idle time (rest) activities. b. Hospital nurses often work shifts of 12 hours or longer, either by choice or out of necessity. Consideration should be given to the effects of long shifts on job satisfaction, patient discontent and the quality of patient care. In addition, the idle time between shifts also requires a longer period for information delivery between shifts. c. Some fire departments in the US, Canada and Europe have adopted 24-hour shifts, while other fire departments still use 10-14 hour shifts or other variations. Generally, firefighters tend to favour the 24-hour shifts because then they work only 7 days a month allowing for more free time. However, there are additional factors to consider: the impact of sleep deprivation on cognitive abilities in potentially life-threatening situations, the need to amend training schedules since firefighters cannot train for an 6

entire 24-hour shift and the incorporation of the required amount of training within 7 shifts. d. Shift workers are particularly vulnerable to increased sleepiness, chronic fatigue, and decreased performance, which can adversely impact productivity and safety in military operations. 12 hour shifts often become 13-14 hour shifts because of the idle turnover time between shifts. Reducing shift hours can also be physically difficult if the hours are constantly changing, and if there is not enough time between shifts. Today’s computerized work environment reduces and sometimes may even eliminate the idle time required between shifts for information delivery.

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REFERENCES Aykin, T. (1996) Optimal Shift Scheduling with Multiple Break Windows, Management Science, 42, 591-602. Bechtold, S.L. and Jacobs, L.W. (1990) Implicit optimal modeling of flexible break assignments in labor staffing decisions for service operations, Management Science, 36, 1339-1351. Calmfors, L. and HoelSource, M. (1989) Work Sharing, Employment and Shift work, Oxford Economic Papers, 41, 758-773. Fryf, T.D. and Blackstone, J.H. (1988) Planning for idle time: A rationale for underutilization of capacity, INT. J. PROD. RES, 26, 1853-1859. Hanna, A., Chang, C., Sullivan, K., and Lackney, J. (2008) Impact of shift work on labour productivity for labour intensive contractor, Journal of Construction Engineering and Management, 134(3), 197-204. Holman, C., Joyeux, B. and Kask, C. (2008) Labor productivity trends since 2000, by sector and industry, Monthly Labor Review, 131, 64-82. Rogers, A.E., Hwang, W-T., Scott L.D., Aiken L.H. and Dinges, F.D. (2004) The Working Hours of Hospital Staff Nurses and Patient Safety, Health Affairs, 23, 202212. Smith, L., Folkard, S., Tucke, p. and Macdonald, I. (1998) Work shift duration: a review comparing eight hour and 12 hour shift systems, Occup Environ Med 55, 217229. Thompson, G.M. (1995) Improved Implicit Optimal Modeling of the Labor Shift Scheduling Problem, Management Science, 41, 595-607.

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