Necessary Optimality Conditions for Scheduling Problems
The purpose of this chapter is to study analytically the optimal behavior of different flexible manufacturing systems in different production environments. The instruments of the study are the maximum principle and variational analysis conducted for scheduling problems which are constructed from the modeling elements described in Chapter 5. Due to such a constructive approach, a great many models of different FMS can be investigated. As in the chapters of part II, analysis of the maximum principle leads to properties which the optimal solution must satisfy. Such properties provide a better understanding of the optimal behavior of a production system and facilitate construction of numerical methods for approximating the optimal solutions.
KeywordsSchedule Problem Maximum Principle Setup Time Planning Horizon Setup Condition
Unable to display preview. Download preview PDF.
- Bryson, A.E., and J.Y-C. Ho, 1975, Applied Optimal Control, Hemisphere Publishing Corporation, Washington.Google Scholar
- Epstein, R., S. Kaluczky, R. Waters and H. Fraser, 1995, “Periodic Proving of Tooling at Sikorsky Aircraft”,Capstone Report, Boston University.Google Scholar
- Hillier F.S. and G.J. Lieberman, 1995, Introduction to Operations Research, 6th ed. McGraw Hill, NY.Google Scholar
- Khmelnitsky, E., K. Kogan and O. Maimon, 1996, “Optimal Flow Control for Continuoustime Scheduling in Flexible Manufacturing Systems”, International Transactions in Operations Research, 2(4).Google Scholar
- Kolmogorov, A. N., 1957, Elements of the Theory ofFunctions and Functional Analysis, Graylock, Rochester N.Y.Google Scholar