Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands

Junmin Shi, Michael N. Katehakis, Benjamin Melamed

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

This paper addresses the problem of inventory penalty pricing under the risk-neutral valuation principle. The underlying production-inventory system has a constant replenishment rate and a compound renewal demand stream (i.e., iid demand interarrival times are independent of iid demand sizes), and is subject to underage and overage penalties. Our pricing approach treats the penalties as a series of perpetual American options, and constructs auxiliary martingale processes in term of the inventory process. We provide a necessary and sufficient martingale condition for general compound renewal demands. Explicit expressions of penalty functions for underage and overage are obtained for the case where demand arrivals follow a Poisson process.

Original languageEnglish (US)
Pages (from-to)593-612
Number of pages20
JournalAnnals of Operations Research
Volume208
Issue number1
DOIs
StatePublished - Sep 1 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research

Keywords

  • Inventory penalty functions
  • Martingale
  • Overage
  • Risk-neutral pricing
  • Underage

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