TITLE:
Waiting Time Distribution of Demand Requiring Multiple Items under a Base Stock Policy
AUTHORS:
Naoaki Morita, Koichi Nakade
KEYWORDS:
Base Stock Policy; MX/M/1 Queue, Waiting Time Distribution
JOURNAL NAME:
Journal of Service Science and Management,
Vol.6 No.4,
October
29,
2013
ABSTRACT: In demanding for repair items or standard products, customers sometimes require multiple common items. In this study, the waiting time of demand which requires multiple items under base stock policy is analyzed theoretically and numerically. It is assumed that the production time has an exponential distribution and the demand is satisfied under a FCFS rule. Each demand waits until all of its requirements are satisfied. An arriving process of demand is assumed to follow a Poisson process and the numbers of required items are independent and generally distributed. A method for deriving waiting time distribution of demand is shown by using methods for computing MX/M/1 waiting time distribution and for deriving the distribution on the order corresponding to the last item the current customer requires. By using the analytical results, properties of waiting time distribution of demand and optimal numbers of base stocks are discussed through numerical experiments.