@article{MAKHILLJMMS20115328173,
    title = {Probabilistic Periodic Review (Q<SUB>m</SUB>, N) Backorders and Lost Sales Inventory Models under Constraint and Varying Holding Cost and Normally Distributed Protection Interval Demand},
    journal = {Journal of Modern Mathematics and Statistics},
    volume = {5},
    number = {3},
    pages = {71-79},
    year = {2011},
    issn = {1994-5388},
    doi = {jmmstat.2011.71.79},
    url = {https://makhillpublications.co/view-article.php?issn=1994-5388&doi=jmmstat.2011.71.79},
    author = {Hala and},
    keywords = {Probabilistic periodic review inventory system,varying holding cost,review cost,protection interval demand,Backorders inventory model,Egypt,Lost sales inventory model,Lagrangian multiplier technique},
    abstract = {This study derives the probabilistic periodic review Backorders and Lost sales inventory models when the holding cost is a function of the inventory cycle. The expected total cost is composed of four components; the expected purchase cost, the expected ordering cost, the expected reviewing cost, the expected holding cost and the expected shortage cost. The objective is to minimize the expected annual total cost under a restriction on the expected annual reviewing cost when the protection interval demand follows the normal distribution. The Lagrangian multipliers are used to solve this constrained model in a closed form. Finally, some special cases are deduced and an illustrative numerical example is added with some graphs.}
    }