Chance-constrained LQG production planning problem under partially observed forward-backward inventory systems.

Abstract The target system of our research is a reverse logistics system with imperfect information of inventory variables. This system is affected by two independents and uncorrelated random variables that represent demand and return fluctuations. A Discrete-time, chance-constrained, Linear Quadratic Gaussian Problem under imperfect information of inventory systems (DCLQG) is formulated in order to develop an aggregate manufacturing and remanufacturing plan. Technically, an optimal closed-loop solution for this stochastic problem is possible, but it is not easy to get it, particularly for large size problems. Thus, an open-loop updating approach that provides a quasi-optimal solution is investigated here. This approach considers an equivalent deterministic problem to the DCLQG problem. It is based on the conditional mean value and on variances of inventory variables, which are estimated from a Kalman filter procedure. Such an approach allows managers to build an aggregated production plan, periodically revised, that helps them to make decisions. An open-loop updating approach is compared to a no-updating approach, which depends only on the initial condition of states of the system. An example shows the importance of information gathering to provide sub-optimal solutions for stochastic problems with imperfect information of states. It is also shown that sub-optimal production policies can improve the company’s profitability.