Examples involve cutting smaller rolls from a large roll of film or paper, cutting patterns from a sheet of metal or glass, and manufacturing different kinds of semiconductor chips from a wafer. The problem involves the selection of the optimal number of each nest to minimize setup, holding, scrap, and overage costs. The problem is to determine the number and location of such stores to maximize return on investment subject to budgetary restrictions. The problem is modeled as an integer program. We can currently solve problems with 500 customer locations and 500 sites exactly.
Work is underway to refine the exact solution method and develop heuristics for larger problems.
We address job scheduling problems for partitionable massively parallel processor systems for the case in which the scheduler decides both when each job is run and how many processors are assigned to it. Linear, superlinear, and sublinear speedup functions are considered. However, by approximating the processors as continuous, we obtain a solution for the superlinear case also. This leads to several heuristics for the original discrete-processor problem. Scheduling on mesh-connected systems is also considered.