Performance Evaluation of a Lost Sales, Push-Pull, Production-Inventory System Under Supply and Demand Uncertainty

A three stages, linear, push-pull, production-inventory system is investigated. The system consists of a production station, a finished goods buffer, and a retailer following continuous review (s, Q) policy. Exponentially distributed production and transportation times are assumed. External demand is modeled as a compound Poisson process, and a lost sales regime is assumed. The system is modeled as a continuous time—discreet space Markov process using Matrix Analytic methods. An algorithm is developed in MatLab to construct the transition matrix that describes the system for different parameters. The resulting system of linear equations provides the vector of the stationary probabilities, and then key performance measures such as customer service levels, average inventories etc. are computed. The proposed model can be used as a descriptive model to explore the dynamics of the system via different scenarios concerning structural characteristics. Also, it may be used as an optimization tool in the context of a prescriptive model.