Computing robust basestock levels

In this paper we develop procedures for setting the basestock levels for a buffer in a supply chain subject to uncertainty in the demands. Our work is motivated by experience with an industrial partner in the electronics industry who was subject to the following difficulties: short product cycles, a complex supply chain with multiple suppliers and long production leadtimes, and a very competitive environment. The combination of these factors produced a paucity of demand data and a significant exposure to risk, in the form of either excessive inventory or shortages. We consider a buffer evolving over a finite time horizon. For t = 1, 2, . . . , T , the quantity xt denotes the inventory at the start of period t (possibly negative to indicate a shortage) with x1 given. We also have a (per unit) inventory holding cost ht, a backlogging cost bt, and a production cost ct. The dynamics during period t work out as follows: