This paper presents an inventory model for deteriorating items with variable demand when shortage is permitted and quantity discount in purchase cost, and rework on deteriorating products are also allowed. The main idea of this research is to study the effects of the discount and the rework on the inventory costs. In this paper, it is assumed that for a certain quantity of purchased items, the seller would offer a discount and the manager would have the choice to either accept the discount or dismiss. On the other hand, there is also a similar decision-making scenario, where the manager makes a decision to reduce the total costs by using the rework and reducing the shortage periods or reducing the total costs by ignoring the rework cost and increasing the shortage periods. The implementation of the mathematical model is illustrated with a numerical example and sensitivity analysis describes the effects of the parameters on the total costs. The results show that the rework will decrease the total costs of the inventory system, significantly.

This research presents a new bi-level bi-objective production-routing-inventory model for a medicine supply chain. In this case, the production is executed by multi-separated producers in a multiproduction line for different kinds of medicines which will be saved in stores for delivering to customers. The capacitated vehicle routing problem is considered in designing a distribution system from stores to customers. The goal of this model is to make a suitable trade-off between the customer satisfaction and the budget cost. This problem has been formulated in a bi-level form where the first objective function is the minimization of the budget during the scheduled time and the second one is the minimization of the shortage amount associated with the lost sale of medicine demands delivering to drug stores. Uncertainty is considered as a nature of the main parameters of the problem. Then the robust approach was used to handle the associated uncertainty of related parameters and the resulted problem is solved by Benders decomposition algorithm. The results indicate that the model make an improvement in medicine supply chain.