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It is a well-known fact that inventory research has its roots in the monetary theory. In this note we sketch the interaction between inventory theory and finance today. We consider the development from a simple deterministic model to continuous-time stochastic models in modern finance. Hereby we restrict our study to consumption--investment problems incurring transaction costs which closely resembled decision problems in inventory control but differ in the modelling of uncertainty. Finally, we support the application of mathematical methods in finance to improve inventory models. Keywords: Consumption-investment problems; Transaction costs; Inventory models; Diffusion approximation

A study was conducted to analyze a static urban transportation system from problems associated with the routing of a garbage-collecting fleet. In line with this, ecological data were considered. A straightforward approach was then utilized to obtain optimal routes depicted by a novel stock point. In addition, the method was utilized in a transshipment problem supporting various ecological restrictions.

A functional normal approximation for stochastic internal demand process is described to address problems in solving multi-echelon inventory systems with a large-scale external demand and an internal demand that is a function of the system's structure, the control policy and the external demand. The approximation, which is applicable to multi-product demand processes, is applied to modified single-product single-location whose demand function is modeled as a Wiener process with drift.

An inventory model with impulse control and a resetting rule and in which the dynamic system needs to be maintained around a specific standard level and within a particular tolerance region is presented. In situations involving spherical tolerance regions and a dynamic system characterized by an n-dimensional vector, average cost in a special two-product inventory system was derived by combining the expected process cost and an integral with respect to the von Mises distribution.

A continuous review stochastic system controlled by interventions and changes in the parameters is applied to a production-inventory model. The method utilizes a unified approach for covering impulse control and the switching of the control mode. The method solves a coupled control problem under uncertainty where control alters the state and rules of the underlying stochastic process.