Optimizing Group Waiting Time in Service System with Learning Effect

This paper deals with service lines that serve groups of customers that differ in their service processes, but have similarities regarding the service capabilities of the specific servers. This paper optimizes the problem of allocating work elements with various learning slopes to servers to minimize the system waiting time of customers in such a line. The customer groups have a large variety of service needs. The service is organized in tandem, and the service repetitions in each group causes learning effect, but due to the nature of work, server's learning slopes can vary. The authors propose a two stage optimization methodology: the first stage is an optimization based on a non-linear formulation for work allocation with some constraints relaxation; the second stage drops the relaxations and finds a solution that is the closest to the unconstrained solution found in the first stage. The authors show that in the presence of learning, the optimal system waiting time requires assigning different workloads to different servers. This difference depends on the number of cycles of a customer group, the server's learning slope, and the server's location along the line. The savings in the optimal system waiting time due to the imbalanced loading of work over the balanced load case are demonstrated.