An  $(s,S)$ inventory model with level-dependent $G/M/1$-Type structure

Sung-Seok  Ko; Jangha  Kang; E-Yeon  Kwon

doi:10.3934/jimo.2016.12.609

Article Contents

2016, Volume 12, Issue 2: 609-624. Doi: 10.3934/jimo.2016.12.609

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An $(s,S)$ inventory model with level-dependent $G/M/1$-Type structure

1.
Department of Industrial Engineering, Konkuk University, 120 Neungdong-ro, Gwangjin-gu, Seoul, 143-701
2.
Department of Industrial Engineering, Chosun University, 309 Pilmun-daero, Dong-gu, Gwangju, 501-759

Received: July 2014

Revised: March 2015

Published: April 2016

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Abstract

Inventory models are widely used in a variety of real-world applications. In particular, inventory systems with perishable items have received a significant amount of attention. We consider an $(s,S)$ continuous inventory model with perishable items, impatient customers, and random lead times. Two characteristic behaviors of impatient customers are balking and reneging. Balking is when a customer departs the system if the item they desire is unavailable. Reneging occurs when a waiting customer leaves the system if their demand is not met within a set period of time. The proposed system is modeled as a two-dimensional Markov process with level-dependent $G/M/1$-type structure. We also consider independent and identically distributed replenishment lead times that follow a phase-type distribution. We find an efficient approximation method for the joint stationary distribution of the number of items in the system, and provide formulas for several performance measures. Moreover, to minimize system costs, we find the optimal values of $s$ and $S$ numerically and perform a sensitivity analysis on key parameters.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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