Stationary Analysis of a Continuous-Review Inventory System with Demand Dynamics Governed by Product Innovation Diffusion
Keywords:
Inventory Control, Continuous-Review (s, S) Policy, Continuous-Time Markov Chain, Stationary DistributionAbstract
In this paper, we develop an infinite-horizon mathematical model for stationary study of a continuous review (s, S) inventory system for a product whose demand is strongly influenced by its market adoption rate. The system state is defined by the joint stochastic process of inventory level and cumulative adopters. The classical Bass Diffusion Model is non-stationary, which is solved for the system by introducing a modification that includes a long-run replacement demand to ensure that the joint system is ergodic. The coupled dynamics are described by a Continuous-Time Markov Chain (CTMC) over a discretized state space. We derived the steady-state global balance equations and then solved for the stationary probability distribution π (I, A) and use this distribution to calculate the long-run average cost rate, Cs, S, and the optimal inventory parameters. A thorough numerical and sensitivity assessment on the innovation (p) and imitation (q) coefficients will be crucial in understanding how the market diffusion influences the optimal stocking and system costs.
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References
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