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...multidimensional challenge, firms must develop operational systems that are both efficient and flexible.
Methods to improve efficiency have been collected under the heading of lean manufacturing and include a range of techniques for process simplification, quality management, and work flow control. A flow control method that is widely used to drive efficiency improvements is pull production, which works by placing constraints on the Work-In-Process (WIP) in the systems. Specific implementations of pull system, such as kanban (Monden, 1993), CONWIP (Hopp et al., 2005) and POLCA (Suri, 1998), differ with respect to how they constrain the WIP. However, all pull systems place an explicit limit on the amount of inventory that can be in the system in order to reduce costs, shorten cycle times and improve quality (e.g., by reducing the time between the creation and detection of defects). For a more detailed discussion of pull systems and the role they play in lean manufacturing, see Hopp and Spearman (2004).
However, while pull systems and other lean methods are very effective in improving efficiency, they are sometimes regarded as antithetical to the goal of increasing flexibility. For example, researchers have long recognized that the kanban approach is best suited to "repetitive manufacturing" environments, in which the product mix and volume stays relatively constant over time (see e.g., Schonberger (1982)). To cope with market fragmentation and customer demands for variety, firms have pursued another set of policies, collectively termed agile manufacturing, which include a variety of means to increase the flexibility of equipment, workforce and operating procedures. A widely used method to enhance flexibility is the cross-training of workers, which enables them to shift between tasks as needed in a dynamically changing environment.
In this paper we address cross-training in the context of WIP-constrained pull systems. In particular, we consider a specific type of cross-training, called hierarchical cross-training, in which worker skill sets can be represented as a series of nested subsets. This type of structure tends to arise when worker skills are largely a function of experience. For instance, new employees can perform basic tasks, while experienced employees can perform basic as well as advanced tasks. In a hierarchical cross-training environment, we can define a partial order based on worker skills, such that each worker is capable of performing all tasks that can be performed by a lower-ranked worker.
2. Literature review
Because of its growing importance in industry, academic researchers have begun studying labor flexibility and cross-training in recent years (see Hopp and Van Oyen (2004) for a survey). The simplest (from a modeling perspective) and most ambitious (from an implementation perspective) form of cross-training is full cross-training, in which all workers are trained to perform all required tasks in a given production system. Although Van Oyen et al. (2001) demonstrated that the performance improvement from full cross-training can be very large, considerations such as the cost of cross-training, differences in skill requirements among tasks, the need for additional equipment or tooling, union rules and safety concerns frequently make full cross-training impractical. As a result, a large variety of partial cross-training applications with different skill set patterns and worker organizational approaches have been implemented in various industrial settings. These applications range from relatively simple worksharing between neighboring stations to more complex task and worker allocations.
If less than full cross-training is used, the questions of who to cross-train for which tasks and how to share those tasks become important management considerations. For systems with less than full cross-training, Ostolaza et al. (1990) introduced the concept of dynamically controlling the buffer inventory quantities between two successive stages of production by allowing some work to be done at either of the two stations (i.e., worksharing). The authors demonstrated that "helping your neighbors" (upstream or downstream) improves throughput in multistage, serial production systems, by dynamically balancing the line. Ostolaza et al. (1990) proposed a threshold-type work-sharing policy in which a cross-trained worker selects the shortest job from his/her upstream buffer and processes the shared task on the job if and only if his/her downstream buffer has more than a certain number of jobs. Although myopic, their policy is highly effective and works best when the buffers are kept half-full. McClain et al. (1992) illustrated how the dynamic line balancing policy of Ostolaza et al. (1990) can increase efficiency even when buffers are very small, provided more information is used to decide who should do the shared task. Gel et al. (2002) extended the work on dynamic line balancing using an optimized control approach and showed that the granularity of the shared task, variability and preemptability strongly influence the effectiveness of dynamic line balancing. Askin and Chen (2003) and Chen and Askin (2003) explored the problem in further detail and studied effective dynamic decision rules to implement worksharing in longer lines under similar conditions. The authors showed that myopic strategies that only consider adjacent workstations, such as a simple rule based on a buffer threshold level, tend to perform well.
Zavadlav et al. (1996) examined U-shaped production lines where each task is carried out on only one machine and task sharing is possible because there are more machines than workers. They concluded that altering work assignments "on-the-fly" enables a production line to "balance itself by shifting the workloads continuously and automatically in response to changes in the state of the system." McClain et al. (2000) evaluated the use of various policies in a variety of situations, in a manner similar to Zavadlav et al. (1996). Hopp et al. (2005) examined work allocation policies for dynamically balancing a line of manual and automated machines staffed by a single cross-trained worker. In a study of two-station production lines with the hiring and firing of workers, Ahn et al. (2004) provided a partial characterization (including exhaustive service of at least one queue) of optimal policies in two-station lines with and without server collaboration in the case of two fully flexible servers. Ahn and Righter (2004) generalized earlier results on the optimality of pick-and-run, bucket brigade and expedite policies and in open and closed tandem manufacturing systems. They also showed that for exponential processing times, the optimal policy will tend to have several workers assigned to the same station. Other recent work inspired by the analysis of "chaining" as a capacity flexibility policy by Jordan and Graves (1995), such as Gurumurthi and Benjaafar (2004), Hopp et al. (2004) and Inman et al. (2004), has examined the surprising effectiveness of overlapping-zone-type (i.e., chained) patterns of cross-training.
This paper draws upon our earlier work in Gel (1999) to focus on systems with partial cross-training, particularly those in which there are both high and low-skilled workers. This situation is common in industry when certain tasks are easy to perform and train for while others are either hard to learn or require expensive equipment. Under these conditions it may be practical to train workers in a hierarchical manner, by which we mean that the skill sets of some workers are subsets of those of other workers in the system. To be precise, let us define a hierarchical skill pattern of cross-training as one in which there are at least two workers with different and overlapping skill sets such that the worker skill sets satisfy the following criteria. For any given pair of workers, W and W': (i) the skill sets of W and W' are disjoint and thus W and W' are unrelated; (ii) worker W is above W' in the sense of having a skill set that is a strict superset of the skill set of W' or vice versa (in which case W is below W'); or (iii) worker W is a peer of W' in the sense of having a skill set that is a identical to that of W'. Moreover, there is at least one worker who is above at least one other worker. Figure 1 shows an example of a hierarchical cross-training structure, where worker 2 is above all others, worker 4 is above worker 5 and worker 1 is above worker 3.
Some systems we have observed to share this particular structure include the following.
* Continental Plastic Containers Corp., a high-volume manufacturer of blow-molded containers, employed many single-skill machine operators to attend the automated equipment. In addition, one broadly experienced (cross-trained) worker was responsible for troubleshooting the line during breakdowns.
* A magazine publisher's call center received a large volume of order calls and a smaller volume of calls for support and problem solving. All customer service representatives trained for customer support were first given training and responsibility to handle order calls. Only experienced representatives handled support calls. This example shared the skill hierarchy we study in this paper, but had parallel instead of serial flow.
* An apparel manufacturing operation had predominantly specialized labor assigned to workstations. To achieve flexibility, two or three fully cross-trained workers were authorized to float dynamically to the workstation that most needed help, based on the observed congestion in the system. This example illustrates the use of cross-training to improve performance by dynamically balancing the line. It also illustrates the fairly common approach of using a fully cross-trained floater as the source of flexibility, one implementation of which we explore in the final model of this paper.
Although, to our knowledge, this paper is one of the first to consider hierarchical cross-training in serial CONWIP lines with a control-theoretic approach, the hierarchical pattern of skill assignment is not completely new to the literature. Emmons and Burns (1991), Billionnet (1999), and Narasimhan (2000) all addressed the optimal deterministic scheduling of workforces with hierarchical skill sets to satisfy various labor requirements in manufacturing and service operations. Costa and Ferria (1999) used simulation to analyze a flexible flowline producing footwear. High variability in the model mix and a large amount of manual labor led the particular operation they studied to install a system of two constant-speed conveyors traveling in opposite directions to allow any product mix and any sequence of operations on a given part. The workstations were designed for a primary operation and also a secondary one. This very naturally gave rise to a hierarchical structure of worker skill sets when newly hired workers first learned only a basic operation, so that their skill set was a subset of the more experienced workers' set. The authors mentioned in passing that when they allowed the less-utilized workstations to supplement the activities of the bottleneck stations, "the results become a lot better." The insights of our analysis clarify why such cross-training and agility offers a significant performance opportunity and suggests starting points for effective worksharing policies.
[FIGURE 1 OMITTED]
As summarized above, the bulk of the literature on work-sharing systems has assumed a specific environment and has focused on the effectiveness of a particular policy tailored to that environment. In contrast, we examine hierarchical approaches to cross-training and reveal basic insights and principles for the structure of optimal strategies. Since a basic unit of most agile workforce systems is worksharing between two workers, understanding the dynamics and underlying principles of two worker systems is crucial to developing a scientific framework for understanding more general and complex systems. Therefore, in this paper, we focus on effective strategies for controlling worksharing between two or three workers attending two or three tandem stations. More specifically, we limit our scope to the discussion of asynchronous (unpaced) flowlines with variability.
Our main contribution in this paper is to identify and analyze a fundamental principle in production environments with limited WIP such as pull systems; namely, that a flexible worker should give priority to processing the task(s) that he/she is uniquely qualified for before helping out other workers. We show that this "fixed-before-shared" principle describes the optimal policy in simple two-station and three-station systems, and we also discuss its applicability to several real-life systems. Ultimately, we expect that the insights provided in this paper will enable the development of better managerial principles and heuristics for the complex systems found in industry.
The remainder of this paper is organized as follows. Section 3 describes the basic two-station, two-worker problems we consider, characterizes optimal task allocation policies, and explores the performance improvement opportunity for exponential systems. In Section 4, we develop and analyze specific three-worker systems with a hierarchical floater structure to further validate and clarify the principles discovered. We discuss industrial applications and insights in Section 5 and then draw conclusions in Section 6. The Appendix includes rigorous arguments for the proofs of the theorems presented in the main body of the manuscript.
3. Optimal control of worksharing between adjacent stations
Much of this paper focuses on a two-station segment over which workers can share tasks. Specifically, we consider CONWIP lines in which a single type of job consisting of two sequential tasks (tasks A and B) is processed by two workers attending two stations. As discussed in Hopp and Spearman (2000), CONWIP is a proven pull production control mechanism that exhibits the control...
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