On Markovian approximations for virtual-build-to-order systems

The Virtual Build-to-Order (VBTO) approach strives to allow a producer to fulfil customers with the specific product variants they seek more efficiently than a conventional order fulfilment system. It does so by opening the planning pipeline. Here the feasibility of modelling the VBTO system as a Markov process is investigated. Two system configurations are considered—a random pipeline feed policy that assumes only knowledge of the overall demand pattern and an informed policy that ensures a mix of different variants in the system. First-order Markov models, which assume stationarity requirements are satisfied, are developed for small VBTO systems. The model for the informed feed policy has excellent agreement with simulation results and confirms the superiority of this policy over the random policy. The model for the random policy is more accurate at high variety than at low variety levels. Accuracy is improved with a second-order Markov model. Although impractical for modelling large scale VBTO systems for either configuration, the Markov approach is valuable in providing insights, theoretical foundations and validation for simulation models. It aids the interpretation of observations from simulations of large scale systems and explains the mechanism by which an unrepresentative stock mix develops over time for the random policy.