...overloaded workers whereas underutilized specialized workers cannot offer help. However, because of the time and cost needed to cross-train workers to perform more than one type of task, it is important to cross-train with a view to long-term efficiency. In this paper, we analyze a cross-training strategy known as chaining, in which some workers are trained to perform a second task type so that all task types are linked in a chain. We show, for maintenance operations at an automotive assembly plant, that cross-training configured in what we call complete chains is very efficient and robust to changing or uncertain conditions.

This paper is organized as follows. In the remainder of the Introduction, we define our cross-training problem and what we mean by chaining. We also review the literature on the modeling of cross-training and discuss cross-training costs and implementation issues. In Section 2, we present a queueing and simulation model for studying cross-training, and consider a simple example of homogeneous workloads and service rates to highlight the basic value and robustness of chaining. In Section 3 we model a realistic example of maintenance and repair tasks with heterogeneous workloads and rates, and demonstrate chaining's robustness in an industrial setting. We simulate different chaining configurations, and analyze the sensitivity to changes in plant data. In Section 4 we discuss the implications of chaining as a strategy for workforce agility and the importance of robust chaining configurations.

Figure 1 illustrates the cross-training pattern. There are pools of workers that are primarily assigned to independent task types. The notation in Fig. 1 uses squares for task types, circles for worker pools, and diamonds for individual workers. Workers can be individually cross-trained to do other task types; Fig. 1 shows one worker cross-trained for one task, i.e., a single cross-training "link." In Fig. 1 and throughout this paper, a solid line represents a worker's primary training and a dashed line represents cross-training. Since showing individual workers is cumbersome, the right hand side of Fig. 1 is a simplified representation showing only worker pools. The heavy solid line indicates that all the workers in the pool are trained for the linked primary task; each dashed line indicates that one worker (with standard workers it doesn't matter which one) is cross-trained for the linked task. A key question is what should be the cross-training pattern?

Figure 2(a-c) compares chaining, no cross-training, and total cross-training. In the no cross-training case, each worker is trained to perform only one task type. In total cross-training, all workers can perform all task types. In chaining, some workers are cross-trained to perform a second task type, and the assignments of task types to workers are linked in a complete chain, as shown.

[FIGURE 1 OMITTED]

We refer to the chaining solution of Fig. 2(b) as a minimal complete chain. We say that a chain is complete if the following three properties hold:

1. Every task type has a backup worker.

2. One worker from each worker pool is cross-trained.

3. All tasks are interconnected.

In other words, a chain is complete if one can start at any node and traverse the entire graph and return to the starting node without traversing any arc more than once. We say that a complete chain is minimal if it has the minimal number of cross-train links needed to be a complete chain. A minimal complete chain does not specify a unique cross-training arrangement, i.e., the specific task type for which a worker from a specific worker pool will be cross-trained. If there are n task types and worker pools, there are (n - 1)! different minimal complete chains.

[FIGURE 2 OMITTED]

Jordan and Graves (1995) introduced the principle of chaining for achieving production flexibility for a group of plants manufacturing a portfolio of products. Two plants are considered linked if they share a product. If one of these plants shares another product with a third plant, then these three plants form a chain (although not necessarily a complete chain). Jordan and Graves showed that limited flexibility has the greatest benefits when all the plants are linked forming a complete chain. Although most plants will only need to produce two different products, if the plants form a chain the benefits are almost the same as total flexibility (where every plant can produce every product). In this context, chaining reduces lost sales because the system of plants can shift production of linked products to make room for high demand products.

Chaining has only recently been applied to cross-training. Brusco and Johns (1998) present an integer linear programming model to minimize staffing costs subject to labor requirements for a specified cross-training structure. Based on a realistic model of the maintenance service operations at a paper mill, they observe that cross-training structures that permit chaining perform well. Hopp et al. (2002) apply the concept of chaining to worker cross-training in production systems with a CONWIP release policy. They provide guidance for deciding which skill(s) should be cross-trained, and how to coordinate cross-trained workers dynamically. Gurumurthi and Benjaafar (2001) provide a framework for analyzing queueing systems with routing and server flexibility. They show that chaining yields most of the benefits of total cross-training for symmetric systems, but that better asymmetric solutions can usually be found for asymmetric systems. Iravani et al. (2002) explore manufacturing and service operations' structural flexibility enabled by flexible resources including cross-trained workers. All these analyses in the literature show that chaining provides efficient cross-training in a variety of situations of workforce flexibility. The focus in our paper is on chaining's robustness to changes in the system where it is applied.

Cross-training has clear flexibility benefits; however, it also has drawbacks. As we will show later, careless control policies can result in cross-training being counterproductive for reducing mean in-system times. Nembhard (2001) shows that workers can only learn so many tasks before they forget how to perform some of the previous tasks. Pinker and Shumsky (2000) argue that the quality of a worker's output can degrade with increasing cross-training. Schultz et al. (2003) show that behavioral effects of cross-training can reduce or even eliminate the theoretical benefits and recommend using real-time feedback systems to mitigate the negative side effects. Additionally, Spear and Bowen (1999) identify rules of the Toyota Production System (TPS) that challenge the value of unlimited cross-training. They argue that the TPS rule: "The pathway for every product and service must be simple and direct" warns against labor pooling, because it can lead to ambiguity about who will perform a task. Moreover, limiting the workers who perform a task reduces variation and enables quicker diagnosis of production and quality problems. Cross-training can also be expensive and takes time to implement. These drawbacks suggest that cross-training needs to be done judiciously.

There are also questions about how to implement cross-training. For instance, should cross-training be left up to individual worker responsibility or should management control cross-training decisions? If management wants to exert central control over cross-training, how specific should be this control? Should management mandate specific tasks to be cross-trained or is control through incentives that encourage, but does not mandate, specific cross-training sufficient? Certain tasks may be more compatible for cross-training than others. Should we only cross-train a worker on tasks that are similar to those the worker...

NOTE: All illustrations and photos have been removed from this article.



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