ISYE SEMINAR SERIES – Optimal Design Problems in Production Systems Modeled by Fork/Join Queueing Networks
In this talk, we introduce some basic optimal design problems in production systems presenting some numerical examples and future research topics.
1) Buffer space allocation problem for assembly/disassembly production systems;
2) Kanban and initial inventory allocation problem for extended kanban control systems;
3) Service capacity allocation problem for assembly/disassembly production systems;
4) Release time determination problem for tandem line production systems;
All production systems considered here are modeled by Fork/Join type queueing network systems with blocking, and the performance measures to be optimized are manufacturing efficiencies such as throughput, lead time and work-in-process.
In general, in order to optimize queueing network systems with blocking, we have to resolve two difficult tasks: one is to evaluate the values of the performance measures, and the other is to search the optimal design parameters. For the first task (calculating values of performance measures), we could devise approximate Markov analysis or run simulations. Here, we put focus on the simulation-based approaches. Having an approximation scheme for calculating the performance measure established, we could use conventional optimization methods to optimize it. We apply total enumeration or meta-heuristics such as Genetic Algorithm for discrete optimal design problems, and non-linear optimization methods for continuous problems. In particular, the service capacity allocation problem is formulated as a Second Order Cone Programming problem (SOCP), which can be solved effectively. While, the release time determination problem results in a global minimization of difference piecewise linear convex functions which seems to be difficult to solve.