Interval-Valued Optimal Control for Imperfect Production Systems: An Improved Centre-Radius Approach with Budget Constraints and Sensitivity Analysis
Main article
Abstract
Manufacturing decision-making under real-world conditions is inherently characterized by parameter imprecision arising from demand fluctuations, production variability, and measurement uncertainty. Classical optimal control and inventory models assume exact parameter knowledge—an assumption that frequently fails in practice, leading to suboptimal policies and inflated operational costs. This paper introduces the concept of the Interval-Valued Isoperimetric Control Problem (IVICP) and develops a comprehensive theoretical framework for its solution. Extending classical calculus of variations and Pontryagin Maximum Principle results to the interval arithmetic setting, we derive necessary and sufficient optimality conditions for IVICPs under interval-valued parameter flexibility. The theoretical framework is applied to an imperfect Economic Production Quantity (EPQ) model subject to a fixed manufacturing budget constraint, formulated as an isoperimetric control problem in an interval environment. An Improved Centre-Radius Optimization Technique (ICROT) translates the interval problem into a pair of deterministic subproblems for the centre and radius components of the optimal policy, enabling efficient numerical solution without the computational overhead of stochastic simulation. Two numerical examples with distinct structural configurations demonstrate the framework's applicability across different parameter regimes. Comprehensive sensitivity analysis with respect to production rate, holding cost, setup cost, demand rate, and budget constraint reveals counterintuitive trade-offs between cost minimization and budget utilization that would be obscured by crisp-parameter models. The resulting interval-valued optimal policies [T*L, T*U] and [Q*L, Q*U] provide decision-makers with actionable bounds that explicitly quantify the impact of parameter uncertainty on production planning. The IVICP framework extends naturally to ecological, biomedical, and financial optimization problems characterized by inherent imprecision.
