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This paper considers system waiting time minimization of a customer-group processed sequentially on a mostly manual service system whose work servers have different learning slopes. The situation of processing customer groups in line configuration can typically be found in international tourist services for organized groups and in treating organized groups of students, or dealing with organized groups within passport security and customs control. Practical instances of this setting are presented in many papers (e.g., (Borkman, 1976; Menor, Roth, & Mason, 2001; Whitt, 1999). In addition, similar situation is well known in the production arena (Arditi, Tokdemir, & Suh, 2001; Cohen & Dar-El, 1998, 1998; Cohen, Vitner, & Sarin, 2006; Dar-El, 2013).
Although there is a bounty of literature on system balancing, and on the learning phenomenon, the literature on the intersection of both subjects is scarce. Especially, the literature on optimizing work allocation in service lines with learning effect is very limited. Since we will show that balancing policy is not optimal the introduction will concentrate on presenting the setting and assumptions of the model, the importance of industrial learning to the model and presenting relevant background in learning calculations.
Setting and Assumptions of the Model
The service process is composed of many tasks, each with estimated standard time, learning slope and precedence constraints. Each server is assigned a combination of these tasks. A study (Cohen & Dar-El, 1998) presented a specific instance of line balancing in the production arena where all the servers have the same learning slope. Another study (Cohen et al., 2006) showed that even under homogeneous learning, allocating the same amount of work to each server is not optimal. In this paper the service operators may have different learning slopes based on their work content. We also assume that the number of servers, L, is known a priori. A method to compute optimal L is given in (Cohen & Dar-El, 1998).
Since maximizing the simultaneous workload of all operators minimizes the system waiting time, and since simultaneous work is best achieved when the learning slopes of all servers are the same, it would be ideal to have the same learning slope at all servers (Cohen & Dar-El, 1998). In reality, however, learning slopes may vary considerably between servers. This may be due to highly constrained networks, or segregated tasks with very dissimilar learning slopes. In this paper, we show that the optimal workload assignment to servers is considerably affected by the learning phenomenon that induces variability between servers.