Production to order and off-line inspection when the production process is partially observable

Abraham Grosfeld-Nir*, Eyal Cohen, Yigal Gerchak

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This study combines inspection and lot-sizing decisions. The issue is whether to INSPECT another unit or PRODUCE a new lot. A unit produced is either conforming or defective. Demand need to be satisfied in full, by conforming units only. The production process may switch from a "good" state to a "bad" state, at constant rate. The proportion of conforming units in the good state is higher than in the bad state. The true state is unobservable and can only be inferred from the quality of units inspected. We thus update, after each inspection, the probability that the unit, next candidate for inspection, was produced while the production process was in the good state. That "good-state-probability" is the basis for our decision to INSPECT or PRODUCE. We prove that the optimal policy has a simple form: INSPECT only if the good-state-probability exceeds a control limit. We provide a methodology to calculate the optimal lot size and the expected costs associated with INSPECT and PRODUCE. Surprisingly, we find that the control limit, as a function of the demand (and other problem parameters) is not necessarily monotone. Also, counter to intuition, it is possible that the optimal action is PRODUCE, after revealing a conforming unit.

Original languageEnglish
Pages (from-to)845-858
Number of pages14
JournalNaval Research Logistics
Volume54
Issue number8
DOIs
StatePublished - Dec 2007

Keywords

  • Binomial yield
  • MLPO
  • Off-line inspection
  • POMDP
  • Production
  • Rigid demand

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