Optimization and Customer Utilities under Dynamic Lead Time Quotation in an M/M Type Base Stock System

Koichi Nakade,Hiroki Niwa

doi:10.1155/2017/5805404

Abstract

In a manufacturing and inventory system, information on production and order lead time helps consumers’ decision whether they receive finished products or not by considering their own impatience on waiting time. In Savaşaneril et al. (2010), the optimal dynamic lead time quotation policy in a one-stage production and inventory system with a base stock policy for maximizing the system’s profit and its properties are discussed. In this system, each arriving customer decides whether he/she enters the system based on the quoted lead time informed by the system. On the other hand, the customer’s utility may be small under the optimal quoted lead time policy because the actual lead time may be longer than the quoted lead time. We use a utility function with respect to benefit of receiving products and waiting time and propose several kinds of heuristic lead time quotation policies. These are compared with optimal policies with respect to both profits and customer’s utilities. Through numerical examples some kinds of heuristic policies have better expected utilities of customers than the optimal quoted lead time policy maximizing system’s profits.

Highlights

In manufacturing systems the production and inventory control must be appropriate to reduce the production cost
For large c the delay probability needs to be decreased, and as a result the higher quoted lead time is set under the optimal policy, and customer’s utility increases the fraction that customers enter the system decreases
The optimal policy gives the smaller utilities, and in particular if the number of base stocks is not appropriate, the other better policy exists on both profits and utilities than the optimal policy

Summary

Introduction

In manufacturing systems the production and inventory control must be appropriate to reduce the production cost. Ata and Olsen [2] consider a make-to-order system where customers are dynamically quoted lead times They recommend quotation policies for convex, concave, and convex-concave delay cost functions. In Savasaneril et al [14], the optimal lead time quotation in an M/M/1 base stock inventory queue for maximizing the system’s profit is discussed In this system, if the lead time quoted to the arriving customer is long, the probability that the customer enters the system and receives service becomes small. The effect by the lead time quotation in an M/M/1 base stock manufacturing-inventory queue into the customer’s utility function is discussed.

Lead Time Quotation Model

Profit and Utility

Numerical Experiments

Conclusions