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Regarding today’s business environment restrictions, one of significant concern of
inventory manager is to determine optimal policies of inventory/production systems under
some restrictions such as budget and storage space. Therefore here, a budget constraint on
total inventory investment and a maximum permissible storage space constraint are added
simultaneously to a stochastic continuous review mixed backorder and lost sales inventory
system. This study also assumes that the received lot may contain some defective units
with a beta-binomial random variable. Two lead time demand (LTD) distribution approach are
proposed in this paper, one with normally distributed demand and another with distribution
free demand. For each approach, a Lagrange multiplier method is applied in order to solve
the discussed constrained inventory models and a solution procedure is developed to find
optimal values. This study, also, shows that the respective budget and storage space
constrained inventory models to be minimized are jointly convex in the decision variables.
Numerical examples are also presented to illustrate the models
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