Performance optimization of event graphs modeling manufacturing systems

Abstract

The objective of the paper is to show that relatively complex manufacturing systems can be modeled as time event graphs and that significant optimization problems can be stated and solved using this representation. Particular attention is focused on the multi-objective optimization of the system throughput, and of a function weighting the work-in-progress along with the buffer space in finite buffers, with respect to: 1) the lot-sizes of the components flowing through the system; 2) the service sequences at the various machines; and 3) the work-in-progress and the (finite) buffer sizes. A two-step optimization procedure has been set up, in which the first step corresponds to the maximization of the system throughput, under the assumption of unlimited work-in-progress and buffer sizes. As a second step, the minimization of the remaining objective is carried out taking into account the constraint of achieving the optimum throughput provided by the solution of the higher level problem. Both the above problems are intrinsically combinatorial. In particular, for the higher level problem, a branch-and-bound approach is proposed, where at each node a relaxed problem having a linear fractional structure is solved. Despite the limited modeling capability of timed event graphs, it is possible, through the determination of the lot-sizes, to optimize the material flow in the system. Of course, the application of dynamic material flow policies is prevented in this framework. However, the optimization of the lot-sizes turns out to be equivalent to that of static routing coefficients. Further research activity is being devoted to the extension of the proposed approach to open (that is, non-cyclic) manufacturing systems and to the optimization of different performance objectives (for instance, the product flow times). In this case, analytic tools based on max-plus algebra are to be used, in order to obtain the expressions of the quantities of interest as functions of the decision variables.