Batch production systems are very common and popular in
advanced manufacturing environments. In these production systems,
the products are produced and delivered in batches, because
that helps to reduce costs and increase profitability. However, in
real life cases, the production process may not be perfect and they
may face production interruptions, such as: machine breakdown,
raw material shortage or any other type of system failure. In an
imperfect production system, it is expected that a certain percentage
of products will be defective. As a result, process reliability is
considered as an important factor in real production environments.
Hence, the consideration of production interruption with process
reliability, in any production inventory system, will make the
research problem closer to those in the real-world.
Over the last half a century, one of the most commonly studied
research topics, in applied operations research and industrial engineering,
is the analysis of production inventory system. A few
examples of such studies include: a single item inventory system
with a non-stationary demand process in a single stage production
inventory system (Graves, 1999), a periodic review stochastic
inventory system (Chan & Song, 2003), determination of lot size