Multi-Item, Multi-Period Production Planning with Uncertain Demand

Abstract

We provide a formulation and solution algorithm for the finite-horizon capacitated production planning problem with random demand for multiple products. Using Lagrangian relaxation, we develop a subgradient optimization algorithm to solve this formulation. We also provide some computational results that indicate this approach works well for rolling-horizon planning compared with the rolling-horizon performance of the corresponding optimal finite-horizon solution. The advantage of our approach is that realistic problem instances can be solved quickly while optimal solutions to such instances are computationally intractable.

Additional information

Notes on contributors

Charles R. Sox

Charles R. Sox is currently an Assistant Professor in the Department of Industrial and Systems Engineering at Auburn University. Professor Sox completed his Ph.D. degree at Cornell University in the School of Operations Research and Industrial Engineering in 1992, where he also earned an M.S. degree in 1991. He finished the B.S. degree in mathematics at Furman University in 1988. His current area of research is on optimization-based heuristics for stochastic production planning and inventory control problems, supported by the National Science Foundation. Professor Sox is also working on applications of this research in the pulp and paper industry. That work is supported by the Auburn Pulp and Paper Research Center and involves collaboration with industry partners including International Paper, S. D. Warren, and James River. Professor Sox serves as an active reviewer for IIE Transactions, Management Science, Operations Research Letters, and Naval Research Logistics. He lives in Auburn, Alabama, with his wife and three children where, in addition to his professorial responsibilities, he manages a vegetable garden primarily enjoyed by his children.

John A. Muckstadt

John A. Muckstadt is director of the School of Operations Research and Industrial Engineering at Cornell University. He studied at the University of Rochester for an A.B. degree in mathematics and at the University of Michigan for an M.S. in industrial administration, an M.A. in mathematics, and a Ph.D., granted in 1966, in industrial engineering. He joined the Cornell faculty in 1974 after 12 years of active military service as a faculty member of the Air Force Institute of Technology and an operations research analyst at the Air Force Logistics Command Headquarters. Professor Muckstadt has served as a consultant to numerous industrial organizations, including Avon, Chicago Pneumatic Tool Company, IBM, Bell Atlantic, General Motors, RAND, TRINOVA, SAS Airlines, General Foods, Logistics Management Institute, US Navy, Unilever, General Electric, and Xerox, and he has been an associate editor of several professional journals. His teaching interests include applied operations research, production and inventory control, logistics, manufacturing control, and materials handling. Currently, he is conducting research related to manufacturing logistics and inventory control. He has written over 40 papers on these subjects. Professor Muckstadt served from 1982 to 1987 as the founding director of the Cornell Manufacturing Engineering and Productivity Program, which is now the Center for Manufacturing Enterprise. Currently, Professor Muckstadt is also growing Riesling grapes, which are primarily enjoyed by the local deer population.