Queueing Theory 2

6Inventory with Positive Service Time: a Survey

Achyutha KRISHNA MOORTHY¹, Dhanya SHAJIN² and Viswanath C. NARAYANAN³

¹Department of Mathematics, CMS College, Kottayam, India.

²Department of Mathematics, S. N. College, Chempazhanthy, Thiruvananthapuram, India.

³Department of Mathematics, Government Engineering College, Thrissur, India

In classical inventory, a customer is served the demanded item immediately on his arrival, provided at least one item is available. However, in inventory with positive service time, it takes a certain amount of time to serve the item. As a result, a queue of demands builds up. We intent to overview the work so far done in mathematical inventory models involving positive service time. These include perishable items, stock supplied through production or through various control policies such as (s, S), (r, Q), random reorder quantity, etc. Stochastic decomposition results are also discussed. A brief account of the work done in queues with requirement of additional items for service is also provided.

6.1. Introduction

In classical inventory model, it is assumed that the item demanded is served instantly, provided it is available. This is the case of negligible service time. If the item is not available, the following possibilities arise: (i) no backlog of demands, (ii) finite backlog and (iii) infinite backlog. In case (i), demands arising are lost to the system forever when inventory level is zero (unless such customers keep retrying). In case (ii), ...