Orbit size dependent return flow estimation for closed loop supply chains

In this thesis, we develop a return flow estimate based on the number of products in use (orbit) for both the terminal and mature phases of a product's life cycle in a partially observable hybrid production system with an unobservable product disposal process. The terminal phase has a transient structure as the product is no longer man- ufactured and the orbit size gradually decreases to zero. Conversely, the mature phase features a stationary demand and return process dependent on the orbit size, where the production control mechanism should also be considered. These structural differ- ences between the phases affect the behavior of the orbit size. Nevertheless, accurately estimating the orbit sizes is valuable in both phases for the collection estimates of re- turns. Therefore, we aim to dynamically estimate the orbit size in both phases. We use a simulation model of the hybrid production system in which we utilize the partial information obtained from product returns. We adapt Bayesian Estimation (BE) and Moving Average (MA) methods to our model and introduce a novel approach called the Two-State Dependent Filtering Algorithm (TSD-FA). This method extends the traditional Hidden Markov Model by allowing observations to depend on the last two hidden states. We also propose an approximation to TSD-FA, denoted as ATSD-FA, that limits the number of observable events in a review period. In the mature phase, we analyze the estimation methods under both orbit dependent and independent in- ventory control policies. We present the value of partial information by introducing another estimation method that ignores observations. The numerical results show that TSD-FA and ATSD-FA provide better estimates when there is limited information about the initial orbit size in the terminal phase and outperform BE and MA in terms of accuracy and robustness in the mature phase.