Inventory Queuing System Study Using Simulation and Birth–Death Process

Abstract

Inventory problem and queuing problems are two of the most widely studied domains in operation research. But when we are applying these ideas in real systems, we are facing some issues related to their form as such in the system which usually is a combination of more than one model under the operations research category of models. So, a combinational study of models becomes an essential part of implementation and Inventory queuing system is one such combinational model where we combine ideas of a queuing model and an inventory model to suit the necessities of real life implementation. This is a more realistic one for study and in this paper we are using a well-established line of a Birth–Death process to study which both is interesting and a fruitful line of study. To add another dimension to the study we have added simulation, a relatively easy and most sought-after avenue of studying practical implementation of models which is usually used when we have no compact analytical solutions is available by theoretical modeling. We first study an inventory queuing system as a two-dimensional Birth–Death process and derive stationary probabilities analytically. As the solutions obtained have not turned out to be as compact as we usually have in an inventory set up, we moved into the simulation domain and employed two lines of simulation, one using the usual newsboy type and the other inspired by the BD type study and we have obtained a reasonable set measures to make some nice conclusions.