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A Warning Zone Method for the Multiperiod Cost Variance Investigation Problem
Author(s) -
Finley David R.,
Liao Woody M.
Publication year - 1989
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1989.tb01395.x
Subject(s) - variance (accounting) , computer science , control limits , mathematical optimization , process (computing) , markov decision process , limit (mathematics) , markov chain , bayesian probability , computation , markov process , control (management) , operations research , control chart , mathematics , statistics , algorithm , economics , artificial intelligence , accounting , mathematical analysis , machine learning , operating system
This paper develops a warning zone approach to make variance investigation decisions for a multiperiod process. The assumed cost generation process varies between an in‐control and out‐of‐control state. These states cannot be directly observed, but must be inferred from the reported cost variances. Using the warning zone method of inference, the manager investigates the process whenever an upper threshold is exceeded or a lower threshold is exceeded for two consecutive periods. A four‐state Markov chain models the resulting decision process. Steady state probabilities are derived for this chain and are used to obtain explicit formulas for the effectiveness and efficiency of the decision process. These formulas permit computation of the cost savings attainable by the warning zone method. Compared to other decision rules, the warning zone method is much simpler than the theoretically optimal Bayesian revision method, but uses more information than the Markovian control limit method. Numerical comparison of results shows that the warning zone method usually captures most of the available cost savings, even in cases where the Markovian control limit method does not perform well.