Stochastic dynamic Bi-level model of procurement for nickel raw material in supply chain

In the stainless steel supply chain, the manufacturers pay much attention to procurement for nickel raw material, in that its cost holds a large percentage of the stainless steel production cost, while the increasing demand of stainless steel pulls up the demand and price of nickel raw material synchronously, and the nickel futures speculation makes the nickel raw material market more fluctuant. Practically, in order to keep uniform supply of nickel raw material, most quantities of procurement contracts for nickel raw material have long term rather than short term or spot procurement, and then the key decision is to determine the quantity of long term procurement. For solving this problem optimally under uncertainties of the demand and price of nickel raw material, there is no effective method so far. This paper gives a stochastic dynamic bi-level model for this problem, where the upper level minimizes the total cost, and given the quantity of long term procurement by the upper level, the lower level takes the quantities of monthly short term procurement for a given supply service level, to minimize the related procurement cost and inventory cost. Finally, a simulation analysis is presented that proposes a satisfying solution for decision making on both of long term procurement and spot procurement.