Production Chain Analysis Using Markov Chains

Many businesses maintain inventories of items, both virtual and material, to be sold directly to the end user or to be used in the production of manufactured items. Maintaining an inventory incurs cost to the business due to a variety of factors that include procurement of a storage facility, wages, and energy usage. In addition, the longer an item is idling in a storage facility, the more cost it incurs. Therefore, an effective inventory management scheme is essential to maintaining the profit margin of any business that runs an inventory. In this presentation, we discuss the steady-state analysis of a mathematical model of inventory originally developed by J. Artalejo (2006). Using matrix analytic queueing theory, the performance measures (average number of demands for inventory in system and the average time spend by demands in the system) are collected for systems undergoing the regimes of light, normal, and heavy traffic. The study will demonstrate that the average number of demands and the average time in system will increase in proportion to the severity of traffic experienced by the system.https://ecommons.udayton.edu/stander_posters/2812/thumbnail.jp