Bekleme süresine duyarlı heterojen müşterileri içeren sürekli izlenen sınırlı stok geri siparişli (r,q) envanter modeli

The motivation of this study is to characterize the equilibrium behavior of a continuous review, limited-backorder (r,Q) inventory model that accommodates heterogeneous, waiting-time-sensitive customers. We assume that arriving customers may be presented with one of three information levels upon arrival: no information, stockout information, or complete stock-availability information. The cumulative potential arrival process is modeled as a homogeneous Poisson process; however, the interaction of heterogeneous waiting sensitivities and varying information availability results in a state-dependent Poisson process in equilibrium. Both deterministic and exponential procurement lead-time settings are investigated. First, we derive the conditional waiting-time distribution for a continuous review, unlimited-backorder (r,Q) policy with homogeneous Poisson arrivals and deterministic procurement lead times, an analysis that, to the best of our knowledge, does not currently exist in the literature. Second, for any continuous review (r,Q) model, we introduce an analogous bulk queueing representation. Using the supplementary variable technique, we formulate the Forward Kolmogorov equations corresponding to this bulk queueing system, which features a state-dependent Poisson arrival process, an infinite number of servers, fixed batch service of size Q, and deterministic service times. We obtain closed-form solutions to these equations in the case where at most one server is operational. For cases involving multiple operational servers, we develop a finite-difference-based numerical technique to solve the equations and approximate steady-state behavior. We note that the proposed analogy, the derived Forward Kolmogorov equations, the analytical solutions for the single-server case, and the numerical technique are all novel contributions to the literature. Next, we focus on the continuous review, limited-backorder (r,Q) model with deterministic procurement lead times. Arriving customers are assumed to be presented with one of the three information levels: no information, stock-out information, or complete stock availability. Customers are heterogeneous with respect to their waiting-time sensitivity and upon arrival, decide strategically whether to purchase or balk based on the available information and the state of the system. For the case with at most one outstanding order, we provide exact equilibrium behavior at arrival, departure, and arbitrary epochs, as well as exact characterizations of inventory metrics and conditional or unconditional waiting-time distributions. For cases with multiple outstanding orders, we employ our finite-difference-based technique to obtain satisfactory numerical approximations for the equilibrium behavior, inventory metrics, and waiting-time characterizations. Finally, for the exponential lead-time case with at most one outstanding order, we derive the exact equilibrium behavior, inventory metrics, and conditional or unconditional waiting-time characterizations. For cases with multiple outstanding orders, we propose a combinatorial method to determine the exact equilibrium behavior and waiting-time distributions. We note that the equilibrium behaviors and waiting-time characterizations developed in this study do not appear to exist in the existing literature.