Selecting a Portfolio of Suppliers Under Demand and Supply Risks

We analyze a planning model for a firm or public organization that needs to cover uncertain demand for a given item by procuring supplies from multiple sources. Each source faces a random yield factor with a general probability distribution. The model considers a single demand season. All supplies need to be ordered before the start of the season. The planning problem amounts to selecting which of the given set of suppliers to retain, and how much to order from each, so as to minimize total procurement costs while ensuring that the uncertain demand is met with a given probability. The total procurement costs consist of variable costs that are proportional to the total quantity delivered by the suppliers, and a fixed cost for each participating supplier, incurred irrespective of his supply level. Each potential supplier is characterized by a given fixed cost and a given distribution of his random yield factor. The yield factors at different suppliers are assumed to be independent of the season's demand, which is described by a general probability distribution.