Lot-sizing problem with supplier selection considering safety stock

The Supplier selection problem is one of the most critical activities of purchasing management. Safety-stock has to be maintained to mitigate risk of stock-outs due to uncertainties in supply and demand. It is an objective to reach for organization. In this paper, we develop a new mixed integer programming model for a mono-item multi period inventory lot-sizing problem with supplier selection including safety stock. We consider a situation where the demand is known over a finite planning horizon. The buyer needs to decide what quantities to order, with which suppliers, and in which periods. The complexity of this problem is known to be NP-hard. We used a genetic algorithm (GA) to solve our problem.