“…This problem also has been addressed in the scientific literature ( Singh et al., 2020 ). For example, San-José et al., 2009 , San-José et al., 2015 have been working with this problem for years. They proposed solutions in which shortages are allowed and, during the stock out period, only a fraction of demand is partially backordered.…”
Section: Literature Review and Problem Backgroundmentioning
“…This problem also has been addressed in the scientific literature ( Singh et al., 2020 ). For example, San-José et al., 2009 , San-José et al., 2015 have been working with this problem for years. They proposed solutions in which shortages are allowed and, during the stock out period, only a fraction of demand is partially backordered.…”
Section: Literature Review and Problem Backgroundmentioning
“…They proposed a decision support system so that the best solution can be obtained by a practitioner without mathematical complexities of the model. San-José, et al [11] studied a single-item inventory model where the shortages are allowed. They developed a new approach where backlogging unit cost is continuous, positive and non-decreasing with time.…”
“…Montgomery [11] considered one of those behaviors and extended the EOQ pattern through partial backordering (EOQ-PBO). The EOQ-PBO problem was studied by many investigators [6,8,14,15,18,19,21,22,25,26,27,28,31]. Mak [10] developed an EPQ-PBO model with time dependent-backorder cost and constant unit lost sale cost.…”
We consider a three-level distribution network involving a raw material supplier with imperfect quality, a manufacturer and several retailers. A production-inventory model accompanied by a partial backlogging approach is developed by considering random disruptions. Any batch received from the supplier is inspected by the manufacturer and if any flaw is visited, all the goods in the inspected batch are rejected. The aim is to minimize the total cost. A heuristic algorithm is presented to compute the optimal policy.
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