Abstract
In this paper new modeling techniques of (S-1,S) inventory systems (continuous review base-stock inventory systems) with state dependent demand rates are proposed. Examples of single-location (S-1,S) inventory systems where the demand, experienced by the system, varies due to the state of the system are, e.g., inventory models with partial backorders, inventory models with lost sales, inventory models with perishable items, inventory models with emergency replenishments etc. Models of such inventory systems are in general hard to solve due to the fact that the Markov property is often lost, and the prevalent tool used in the literature for providing exact solutions of such models is the theory of partial differential equations. Instead of using partial differential equations with rather complicated analysis of boundary conditions, we suggest considerably simpler techniques which are based on elementary theory of queueing and renewal processes. First, we show that it is possible to use Markov theory in order to prove certain statistical properties of the limiting distribution of the ages of the items in the system. Secondly, we develop a corresponding procedure based on renewal theory, which forms a basis for more complicated models assuming non-Poisson customer demand processes.
Highlights
In many supply chain systems it is common that the customer demand streams, experienced by the system, vary as a function of the state of the system
Instead of using the heavy mathematical machinery of partial differential equations (PDEs) we develop two simple modeling techniques which are based on some important characteristics of the model
To the best of our knowledge, most subsequent papers dealing with continuous review base-stock inventory systems with state dependent demand rates use variants of the method developed in Schmidt and Nahmias (1985) as a building block
Summary
In many supply chain systems it is common that the customer demand streams, experienced by the system, vary as a function of the state of the system. To the best of our knowledge, most subsequent papers dealing with continuous review base-stock inventory systems with state dependent demand rates use variants of the method developed in Schmidt and Nahmias (1985) as a building block. Olsson and Turova (2016) generalize the model studied in Schmidt and Nahmias (1985) by considering a more general demand structure by using the method of PDEs. For more detailed literature reviews concerning perishable items in inventory systems see, e.g., Karaesmen et al (2011) or Nahmias (2011). As mentioned before, by using our approach it is possible to consider more general non-Poisson demand processes As already mentioned, another line of research connected to our model concerns inventory models with partial backorders, where some arriving customers are backordered and others are lost depending on the state of the system upon arrival.
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