Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
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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.