An open-loop solution for a stochastic problem with imperfect state information and chance-constraint adjusted by an optimal gain

Abstract

This study aims to develop an optimal aggregate production planning policy for a reverse logistics system with imperfect state information and chance constraints. The system consists of a forward channel for storing and distributing products and a backward channel for collecting, remanufacturing, or discarding products. The paper presents a chance-constrained linear-quadratic Gaussian optimization model that considers imperfect state information and formulates an equivalent deterministic problem. It also introduces a minimum variance problem to address the uncontrolled variance of the serviceable inventory variable, whose result is an optimal gain to balance the conditional variances of inventory and production over time, making the solution more cost-efficient. The open-loop solution with the minimum variance gain shows its efficiency through a simple example, reducing the total cost of production by controlling the growth of inventory and production variances. Furthermore, this approach offers a practical way for managers to create inventory-production scenarios for decision-making in a reverse logistics system with imperfect state information and chance constraints.