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...options increasing capacity flexibility which have shown promise past research. Cross training is one approach that is relatively common in practice and is widely discussed in the literature. Past research, for example, has lent insight into the operational benefits of workforce flexibility-benefits that can be weighed against the costs of training and a higher pay scale. A thorough discussion of the issues and research in this area is available in Hopp and Van Oyen (2004).
Another means of gaining flexible capacity is flexible workdays. The use of flexible workdays is governed differently, depending on the legal structures of different countries. In the US, the use of flexible workdays in the private sector is governed by the Fair Labor Standard Act (US Government, 1938). The Act requires all private sector employers to compensate workers for overtime with cash payments. It prohibits private sector employers from offering workers the option of time off as a compensation for overtime. To create this option of compensatory time off in lieu of cash payments for overtime, the Working Families Flexibility Act (US Government, 2001a) and the Workplace Flexibility Act (US Government, 2001b) have been proposed and are currently being debated in the US Legislature.
Yang et al. (2002, 2003) study flexible workdays in a job shop. Their results suggest that the use of flexible workdays can be effective in matching capacity with demand and improving key performance measures such as tardiness and work-in-process inventory. Furthermore, these studies suggest that a simple input/output control can be a viable approach to the scheduling of overtime and time off. However, these studies also assume that workers are not cross trained to work in more than one department and therefore they provide no insight into how these two forms of flexibility interact.
The presence of cross-trained workers has two possible and opposing effects on the use of flexible workdays. On the one hand, a cross-trained workforce may reduce or eliminate the need for scheduling overtime since workers can respond to variations in workload across machines. Overtime is expensive because it is compensated at time-and-a-half (as proposed by the pending bills), which means that any use of overtime compensated by time off translates into a reduction in overall capacity. On the other hand, the presence of cross-trained workers may allow managers to make more effective use of flexible workdays since time off can be granted more easily to a worker whose skills are possessed by other workers.
Flexible workday policies are unlikely to be viable if workers can be coerced into working more overtime with little control over when their earned time off can be used. This issue has been raised by House Representative Judith Conti (Conti, 2002). In this paper we examine flexible workdays in environments where workers have significant control over when time off is used and when overtime is scheduled. This control is exercised through two means.
First, compensatory time off is only scheduled upon a worker's request; however, the management retains some authority on whether to deny or grant a request. A worker's attitude towards compensatory time is a potentially important determinant of performance because there is an upper limit on accrued compensatory time (i.e., the pending bills in the US Legislature set this limit at 160 hours). This means that a worker who never requests compensatory time off will always work a fixed 8-hour schedule once his/her accrued compensatory time reaches 160 hours. An increasing willingness to take compensatory time off not only gives management greater latitude in scheduling overtime, but also increases unplanned reductions in capacity when the management's authority to deny time off requests is restricted. Second, no worker can be scheduled to work overtime unless he or she volunteers. Each of the two requirements restricts the options available to management for using flexible workdays.
The degree to which both of these factors impact the performance of flexible workdays will be influenced by cross training. However, the nature of this influence is not obvious. As employees are given more control in the use of flexible workdays we would expect performance to deteriorate as the number of unplanned shortages increases. However, as discussed above, redundancy in employee skills may blunt this effect somewhat.
Finally, the potential for performance improvement of both cross training and flexible workdays is dependent on the degree of capacity imbalance inherent in the job shop. We would expect an increase in workload variability to increase the value of flexible capacity in general though the precise impact on the two types of flexibility considered in this research is unclear. We examine the impact of workload variability in a separate experiment.
2. Simulation model
We evaluate cross training and flexible workdays in a simulated job shop using SLAM II (Pritsker, 1986). The job shop is modeled in a manner similar to that used in the studies of Fryer (1973, 1974, 1975), Weeks and Fryer (1976), Elvers and Treleven (1985), Treleven and Elvers (1985), Treleven (1987), and Bobrowski and Park (1989). The job shop consists of six workers and six departments with two identical machines in each department. The shop operates 5 days per week and 4 weeks per month. Modeling a small job shop gives a conservative stance for assessing the benefit of compensatory time off. The granting of time off, for instance, should affect a small shop more negatively than a larger shop with more workers to cover the duties of those who are granted time off.
When a job arrives, its routing is generated with the same method used in the past research cited above. Each department is given an equal probability of being the first department visited by a job. After a department is visited, it cannot be revisited by the same job. For each subsequent operation, a job is routed to any of the unselected departments including an exit with equal probability. This produces routings with an average of 3.5 departments per job.
The number of job arrivals per day is generated using a Poisson distribution with a mean of six jobs per day which corresponds to a Coefficient of Variation (CV) of 0.4. Upon arrival, the routing, processing times, and due date of each job are generated. The jobs are then released into the job shop every morning. A job is started immediately if the appropriate worker and machine are available in the first department visited. Otherwise, the job is directed to the job queue of the first department. The jobs are processed in the order of the smallest-to-largest due date (i.e., EDD rule). Whenever a worker finishes a job, he/she joins a queue of idle workers. The first worker in the queue is always activated first whenever jobs are available. He/she will search for jobs in the departments that he/she is trained in and choose the job with the earliest due date at an idle machine. If no such jobs are found, the next idle worker will be activated. This rule for scheduling jobs and workers has been found to be effective in past studies on labor flexibility (Treleven, 1989).
The processing time of each operation is generated from a gamma distribution with a CV value of 0.5 and truncated at 10 minutes and 16 hours to eliminate excessively short or long processing times. The mean processing time is chosen for a mean worker utilization of 90%. This level of utilization is similar to those used in other studies on labor and routing flexibility (e.g., Fryer (1973, 1974, 1975), Weeks and Fryer (1976), Elvers and Treleven (1985), Treleven and Elvers (1985), Treleven (1987, 1989), Bobrowski and Park (1989), and Yang et al. (2002, 2003)). Our use of Poisson and gamma distributions to generate the number of job arrivals and processing times follows the recommendation of Law and Kelton (1991). We also tested other levels of mean...
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