| We first examine the problem of scheduling in a two-stage flow shop where parts are manufactured at the first stage and assembled at the second stage. The system addressed is characterized by deterministic processing and setup times. We develop a heuristic model that attempts to minimize the mean flow time of jobs through the system by first minimizing the mean flow time through the first stage and then, conditional on the first minimization, minimizing the second stage mean flow time. We consider two conditions, corresponding to the extreme cases of heavy and light traffic at the second stage, for which the model is shown to be optimal. The model's performance is evaluated by comparing its solutions, for ninety-six randomly generated problems, against a lower bound corresponding to statistical point estimates of the optimal solution. On the average, the heuristic solution was only 0.49% worse than the lower bound; in the worst case, the heuristic resulted in a mean flow time that is 4.3% above the value of the lower bound.;We then address the problem of scheduling in a Flexible Manufacturing System with the objective of maximizing production throughput. We assume exponentially distributed machine inter-failure and repair times, deterministic processing time, zero setup times, and uni-directional material flow.;We use a continuous flow approximation model to solve this problem. Specifically, we first develop a myopically optimal linear programming scheduling model under assumptions of continuous flow and processor sharing, and establish two optimality conditions. The model is then used as an approximation tool for scheduling discrete part manufacturing. The continuous flow problem is also formulated as an optimal dynamic program but is shown to be computationally intractable. The approximation model is then evaluated on three randomly generated test problems with five random seeds for breakdown generation for each problem. The model resulted in production throughputs that were, on the average, 2.17% (and in the worst-case 3.8%) less than those obtained from an infeasible upper bound. Finally, the model is extended to the general FMS problem with multiple part routings. |
