Server Assignment Policy for Minimizing the Output Variability of a Pull Serial Line

Server Assignment Policy for Minimizing the Output Variability of a Pull Serial Line

  Variability and unevenness in processing times create a problem of imbalance in the production system. So in a pull serial line, even though the product is expected to come out of the preceding cell "Just In Time", yet this imbalance creates different problems of unequal utilization of server, fluctuation of production rate, creation of temporary inventory, blocking and starvation in the line. The prior knowledge of these consequential results of different configurations of imbalance in a pull serial line will help the operations manager to control the production in more efficient ways such as the optimal ordering(assigning) of servers.   Relatively much attention has being given by the research community to the assignment of servers in a push serial line. But little effort has been put toward such work in a pull serial line. In this study, we consider a pull serial line as tandem queueing networks with finite buffer capacities and address the issue of assigning the servers so that the variation of the output is minimized.   For simplicity, we assume that each server can work on only one job at a time, that several servers can not work together on one job and that the number of cells equals the number of servers. Furthermore, assume that the service rates depend only on the servers. Without loss of generality, each server is cross-trained to work at all cells. Also, it is considered as given two boundary conditions that there is an infinite supply of raw materials to the cell (1) and external demands are permitted to be backlogged. Note that these boundary conditions are not required to support the theoretical results, but to help simplify the details.   We can gain much by analyzing pull systems and obtaining theoretical results in a general environment. Particularly, valuable is the variability propagation property gained from the analysis; it is this property that helps in developing efficient assignment policies of servers. Based on the variability propagation property, we propose a policy - (RULE 1) for assigning the servers. (RULE 1) refers to the assignment of servers obtained by unbalancing a pull serial line such that the mean or the variance of service times decreases progressively from cell (1) to cell (m). Numeric results illustrate that (RULE 1) always agrees with the optimal assignment of servers.