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This paper presents a multi-product, multi-period inventory problem in an uncertain environment where the main suppliers are prone to yield uncertainty. In order to overcome the arisen uncertainties, two basic approaches of emergency ordering and product substitutability are taken into consideration. In the proposed emergency ordering scheme, two sets of suppliers, i.e. cheap unreliable and expensive reliable (emergency) suppliers, are considered and a tradeo between the cheap price of the main suppliers and reliabilityof emergency supplier is attained. In product substitution scheme, the demand of each product is ful lled directly by the related product or other substitute products. A riskaverse decision maker is taken into consideration whose risk-averseness level is controlled by the portion of demand which should be de nitely satis ed and not backordered or lost. A robust optimization approach with two variability measures is proposed to minimize the variability of the model. The results reveal the value of emergency ordering and productsubstitution. In addition, the results suggest which measure should be selected according to the decision maker's attitude toward the desired pro t, variability, and service level.

scientia iranica

A robust optimization approach for an inventory problem with emergency ordering and product substitution in an uncertain environment: A case study in pharmaceutical industry