TY - JOUR

T1 - Production to order and off-line inspection when the production process is partially observable

AU - Grosfeld-Nir, Abraham

AU - Cohen, Eyal

AU - Gerchak, Yigal

PY - 2007/12

Y1 - 2007/12

N2 - 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.

AB - 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.

KW - Binomial yield

KW - MLPO

KW - Off-line inspection

KW - POMDP

KW - Production

KW - Rigid demand

UR - http://www.scopus.com/inward/record.url?scp=36549081475&partnerID=8YFLogxK

U2 - 10.1002/nav.20256

DO - 10.1002/nav.20256

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AN - SCOPUS:36549081475

SN - 0894-069X

VL - 54

SP - 845

EP - 858

JO - Naval Research Logistics

JF - Naval Research Logistics

IS - 8

ER -