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A positive linear discrete-time model of capacity planning and its controllability properties. (English) Zbl 1112.93009
Summary: One of the most important concepts in production planning is that of the establishment of an overall or aggregate production plan. In this paper, the problem of establishing an aggregate production plan for a manufacturing plant is considered. A new dynamic discrete-time model of capacity planning utilizing concepts arising in positive linear systems (PLS) theory is proposed and its controllability property is analyzed. Controllability is a fundamental property of the system with direct implications not only in dynamic optimization problems (such as those arising in inventory and production control) but also in feedback control problems. Some new open problems regarding controllability of stationary and nonstationary PLS with linear constraints are posed in the paper. An optimal control problem for capacity planning is formulated and discussed.

90B30Production models
93C55Discrete-time control systems
Full Text: DOI
[1] Berry, W. L.; Vollman, T. E.; Whybark, D. C.: Manufacturing planning and control systems. (1992)
[2] Ozdamar, L.; Bozyel, M. A.; Birbil, S. L.: A hierarchical decision support system for production planning. European journal of operations research 104, 403-422 (1998) · Zbl 0960.90505
[3] Van Hilten, O.; Kort, P. M.; Van Loon, P. J. M.: Dynamic policies of the firm: an optimal control approach. (1993)
[4] Berman, A.; Plemmons, R. J.: Nonnegative matrices in mathematical sciences. (1994) · Zbl 0815.15016
[5] Luenberger, D. G.: Introduction to dynamic systems: theory, models & applications. (1979) · Zbl 0458.93001
[6] Rumchev, V. G.; James, D. J. G.: Controllability of positive linear systems. International journal of control 50, No. 3, 845-857 (1989) · Zbl 0695.93009
[7] Sontag, E. D.: Mathematical control theory: deterministic finite dimensional systems. (1998) · Zbl 0945.93001
[8] Caccetta, L.; Rumchev, V. G.: A survey of reachability and controllability of positive linear systems. Annals of operations research 98, 101-122 (1998) · Zbl 0972.93003
[9] Jennings, L. S.; Fisher, M. E.; Teo, K. L.; Goh, C. J.: MISERS: optimal control software (Theory and user manual). (1990)