Minimizing task completion time with the execution set method

We consider a partial ordered set (POSET) of assembling operations, with known execution durations, that must be accomplished. The assembling operations can be executed on an acyclic network with an identical set of robots on each conveyer (arc). The number of depots (nodes) is a known integer. Between each pair of depots we can locate only one conveyer. We seek an arrangement of the network and a plan that divides the task operations among the conveyers, minimizing the overall task completion time. We use linear programming optimization, subject to reasonably general rules for distributing the operation-fragments among the conveyers.