A Closed-Form Approximation Solution for an Inventory Model with Supply Disruptions and Non-ZIO Reorder Policy

David Heimann, Frenck Waage

In supply chains, domestic and global, a producer must decide on an optimal quantity of items to order from suppliers and at what inventory level to place this order (the EOQ problem). We discuss how to modify the EOQ in the face of failures and recoveries by the supplier. This is the EOQ with disruption problem (EOQD). The supplier makes transitions between being capable and not being capable of filling an order in a Markov failure and recovery process. The producer adjusts the reorder point and the inventories to provide a margin of safety. Numerical solutions to the EOQD problem have been developed. In addition, a closed-form approximate solution has 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.

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