Markov chain modeling and forecasting of product returns in remanufacturing based on stock mean-age

A method is presented for real-time forecasting of product returns in remanufacturing. It determines the quantity of imminent returns and quality features such as age distribution and number of past cycles. Required data in real-time include the mean age of stock, a scaled quantity (population average) reliably monitored, even from small-size or decentralized stock samples, the maximum and minimum age in return samples and past volumes of net demand or sales. The characteristic parameters of the return distribution (center axis and spread) are updated in real-time. The method sequentially determines the retention probability in each time period, a key random variable that unties the dynamic closed-loop-supply chain knot. The retention probability sequence is used in explicit expressions for the product return flow and age distribution (a quality index), based on Markov representation of stock and flows. The model allows for arbitrarily random early loss and non-stationarities, uncertain demand and varying utilization of reusable returns. Markov-chain Monte-Carlo simulation enables assessment of the efficacy of the forecasting method. Exploiting reliable, current information, the method may provide improved estimates of product returns compared to linear models that relate returns to past levels of sales and/or returns, and utilize conventional regression, recursive least squares, or adaptive identification methods. Forecasting efficiency is higher as measured by mean or integral absolute error, and particularly so, regarding peaks and lows of the return flow. The results may be useful for enhanced acquisition of returns with reduced stock inventories and efficient planning of remanufacturing operations.