On a Newton-Like Method for Solving Algebraic Riccati Equations
SIAM Journal on Matrix Analysis and Applications
Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches
SIAM Journal on Matrix Analysis and Applications
A Hybrid Approach to Designing Inbound-Resupply Strategies
IEEE Intelligent Systems
Automatica (Journal of IFAC)
A Numerical Method for a Generalized Algebraic Riccati Equation
SIAM Journal on Control and Optimization
Dynamic modeling and control of supply chain systems: A review
Computers and Operations Research
Improved Newton's method with exact line searches to solve quadratic matrix equation
Journal of Computational and Applied Mathematics
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The paper addresses the problem of efficient inventory management in production-inventory systems focusing on the dynamical nature of goods flow process. In the considered systems, the stock used to satisfy an unknown, time-varying demand is replenished either from a single or from multiple supply sources. The replenishment orders issued in each review period are realized with a delay, which differs among the suppliers and transport alternatives. For the analyzed setting, modeled as a discrete-time nth-order deterministic system, a new inventory policy is developed using a strict control-theoretic methodology. In contrast to the classical, stochastic approaches, the proposed control law is obtained by minimizing a quadratic cost functional, which guarantees the optimal dynamical performance of production-inventory systems with (possibly) different lead-time delays in the supply path. The designed policy ensures that the demand is always entirely satisfied from the on-hand stock (yielding zero lost-sales cost) and the warehouse capacity is not exceeded (which eliminates the risk of high-cost emergency storage). The closed-form solution of the linear-quadratic (LQ) optimization problem allows for a straightforward implementation of the developed control strategy in real systems.