Cost Analysis of Fuzzy Discrete (s, S) Queueing Inventory System with Positive Lead Time and Optimization using Genetic Algorithm

Abstract

In this article, a queueing inventory model with discrete time (DQIM) FGEOM/FGEOM/1 with (s, S) replenishment policy incorporating fuzzy numbers as input parameters is considered. The system has a fuzzy pentagonal number arrival rate according to a Bernoulli process and a fuzzy pentagonal number service rate that follows a geometric distribution. Here, S represents the highest level of stock where the process of replenishment is stopped, and s represents the lowest level of stock at which replenishment is started again. Using matrix geometric method, the steady-state solution is obtained followed by derivation of various fuzzy performance measures. Further, the total cost function is defined as a two-variable function of the minimum and maximum stock level. Genetic algorithm is employed to optimize the total cost. Various examples are presented to highlight the dependence of cost on input parameters. The use of PFN in DQIS and genetic algorithm in the optimization of DQIS is introduced in this paper for the first time. JEL Codes: C44, C61, C62, D11, D12, L89 Received: 17/07/2024. Accepted: 29/09/2024. Published: 04/10/24.

Keywords

• Discrete Queueing inventory model
• Matrix geometric method
• Pentagonal fuzzy number
• Genetic algorithm