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Dynamic Lead-Time Quotation for an M/M/1 Base-Stock Inventory Queue

Seçil Savaaneril, Paul M. Griffin, Pnar Keskinocak

Department of Industrial Engineering, Middle East Technical University, 06531, Ankara, Turkey
Harold and Inge Marcus Department of Industrial Engineering, Pennsylvania State University, University Park, Pennsylvania 16801
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
secil{at}ie.metu.edu.tr
pmg14{at}psu.edu
pinar{at}isye.gatech.edu

We study a dynamic lead-time quotation problem in a base-stock inventory system characterized by lead-time sensitive Poisson demand and exponentially distributed service times. We show that the optimal profit is unimodal in the base-stock level. We compare the base-stock system with a make-to-order (MTO) system and show that the lead-time quotes are lower in an MTO system and that increasing the base-stock level does not necessarily decrease the expected number of customers waiting. Numerical results show that when customers are less sensitive to lead-time quotes, the benefit of quoting lead times with a higher precision is significant, whereas when customers are more sensitive to lead-time quotes, the benefit of holding inventory is significant.

Subject classifications: inventory/production policies; stochastic production systems; optimal control; order acceptance; due-date quotation; benefits of flexibility.
History: Received May 2007; revision received November 2008; accepted February 2009.