Heuristics for capacity planning problems with congestion

• Published in: Computers & operations research Vol. 36; no. 6; pp. 1924 - 1934
• Main Authors: Kim, Sukgon, Uzsoy, Reha
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.06.2009; Elsevier; Pergamon Press Inc
• Subjects: Applied sciences; Capacity expansion; Clearing functions; Exact sciences and technology; Heuristic; Heuristics; Inventory control, production control. Distribution; Lagrangian relaxation; Operational research and scientific management; Operational research. Management science; Production planning; Queueing; Queuing theory. Traffic theory; Semiconductors; Studies; Work in process; Queueing; Capacity expansion; Lagrangian relaxation; Heuristics; Clearing functions; Lower bound; Lagrangian; Shortest path; In-process inventory; Location problem; Production management; Computation time; Microelectronic fabrication; Lagrange multiplier; Production planning; Heuristic method; Greedy algorithm; Relaxation method; Production capacity; Queue
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2008.06.006

Motivated by a problem in the semiconductor industry, we develop improved formulations for the problem of planning capacity acquisition and deletion over time when resources are subject to congestion, motivated by a problem in the semiconductor industry. We use nonlinear clearing functions to relate the expected output of a production resource in a planning period to the expected work in process (WIP) inventory level. Exploiting the properties of the clearing function allows us to formulate the single workcenter problem as a shortest path problem. This forms the basis for two greedy constructive heuristics and a Lagrangian heuristic for the multistage problem. The latter procedure also provides lower bounds on the optimal value. We present computational experiments showing that the proposed heuristics obtain high-quality solutions in modest CPU times.