A closed-form approximation solution for an inventory model with supply disruptions and non-ZIO reorder policy

In supply chains, domestic and global, a producer must decide on an optimal quantify of items to order from suppliers and at what inventory level to place this order (the EOQ problem). A very practical inventory management issue is how to modify the EOQ in the face of failures and recoveries by the supplier. In this situation, called the EOQ with disruption problem (EOQD). the supplier will make transitions between being capable and not being capable of filling at? order from the producer. following a Markov failure and recovery process. In this case, the producer must adjust the reorder point to provide a margin of safety in it? the face of this unreliability while keeping the extra inventory costs to no more than necessary. Numerical solutions to the FOOD problem have been developed. In addition, a closed form approximate solution hits been developed for the zero inventory option ZIO, where the inventory level on reordering is set to be zero. This paper develops a closed form approximate solution for the EOQD problem when the reorder point can be non-zero, obtaining for that situation an optimal reorder quantity and optimal reorder point that represents an improvement on the optimal ZIO solution. The paper also supplies numerical examples demonstrating the cost savings against the ZIO situation, as well as the accuracy: of the approximation technique.