On the simultaneous optimization of server and work allocations in production line systems with variable processing times

The allocation of servers and the allocation of work are two important decision variables in designing production line systems. Previous studies of each variable in isolation have found that throughput is maximized by using an allocation that gives preferential treatment to interior stations (especially center stations) over the two end stations. In this paper we study the simultaneous optimization of server and work allocations and obtain some surprising results of a different nature. One key finding is the L-phenomenon, whereby the throughput is maximized by assigning all extra servers over one per station to just one of the end stations and then adjusting the work allocation so that this station has by far the greatest amount of work per server. Another key finding is the multiple-server phenomenon, whereby extra servers add far more throughput per server than the initial one-per-station servers. Both findings have important implications for the design of some production line systems in ways that will greatly improve their efficiency. Similar conclusions are drawn when lower and/or upper bounds are imposed on the number of servers per station and the number of stations is included as a decision variable.