Flexibly Serving A Finite Number of Heterogeneous Jobs in A Tandem System

Many manufacturing and service systems require a finite number of heterogeneous jobs to be processed by two stations in tandem. Each station serves at most one job at a time and there is a finite buffer between the two stations. We consider two flexible servers that are cross-trained to work at both stations. The duration for a server to finish a job at a station is exponentially distributed with a rate that depends on the server, the station, and the job. Our goal is to identify an efficient policy to dynamically assign the servers to the stations such that the expected makespan (duration to complete all the jobs) is minimized. Given that an optimal policy is non-idling, we focus on non-idling policies. We first derive the expected makespan of a general non-idling policy. We then analyze three simple non-idling policies: the summation-myopic, the product-myopic, and the teamwork policies. We prove that (i) the product-myopic policy is optimal if the servers maintain the same service-rate ratio at each station for all the jobs, (ii) the teamwork policy is optimal if the servers maintain the same service-rate ratio at different stations for jobs that are sequenced near each other, and (iii) the summation-myopic policy is no worse than the teamwork policy. Our numerical study based on general service rates suggests that the summation-myopic policy can be better or worse than the product-myopic policy. We also extend the model to incorporate moving costs and service defects.