CHING'S MARKOV CHAIN MODELS
INVENTORY CONTROL
U. Kocer (2013). Forecasting Intermittent Demand by Markov Chain Model. International Journal of Innovative Computing, Information and Control, 9:3307-3318.
In Kocer (2013), the author considered the problem of inventory control of products. The author seeks to model and estimate intermittent demand data. It is found that the demands of different products are influenced by each other. Therefore, multivariate Markov chain model is suggested to be used such that the interaction between different demand sequences can be modeled.
The categorical data sequences are the intermittent demand data sequence. For the data forecasting, she mainly followed the parsimonious higher-order multivariate Markov chain model along with the parameter estimation method in Ching et al. (2006, 2008). The major difference is that Kocer (2013) considered not only the state with the highest probability but also all the states in proportion to their probabilities when estimating the next state of the Markov chain. Although the models in Ching et al. (2006, 2008) is modified, the major advantage of it, the decrease in the number of parameters required is reserved.
Furthermore, with the help of the parameter estimation method in Ching et al. (2006, 2008), the parameter estimation problem can be reduced to a linear programming problem which is easier to handle.
The accuracy of the model in Kocer (2017) is estimated. The author obtained monthly demand data of 695 different products from a medium size enterprise which has been active in Turkey since 2000. Each data sequence is for 66 months and has different lead times. She calculated the r and mean absolute scaled error (MASE) values of the forecasting result of the multivariate Markov Chain model to these datum. The mean r value, which measures the agreement of the forecasts obtained by means of the modified Markov chain model with the original data set, is found as 0.503. Also, the highest and the lowest rate of the r value are found to be 0.64 and 0.40, respectively. This indicates that the agreement of forecast values with the real data is high; namely 50.3 percent on the average. In parallel with this, the MASE value to be smaller than 1 demonstrates that the forecasts are reliable.
W. Ching and M. Ng (2006) Markov chains models, algorithm and application. Springer.
https://www.springer.com/la/book/9781441939869
W. Ching, E. Fung, and M. Ng (2008) Higher-order Multivariate Markov Chains and Their Applications, Linear Algebra and its Applications, 15, 492-507.
https://www.sciencedirect.com/science/article/pii/S0024379507002169