A branch-and-bound algorithm for the concave cost supply problem

Effective supplier selection and allocation of order quantity among multiple suppliers are indispensable to the success of a manufacturing company. While companies have begun to turn into a comprehensive multi-criteria approach, most buyers still consider purchasing cost to be their primary concern in selecting their suppliers. In this paper, we consider the concave cost supply problem where a manufacturer seeks to select the suppliers and simultaneously procure the quantity of material/component required for production at the minimum total cost during a standard production period. We provide and validate an effective and efficient branch-and-bound algorithm that is finite and that finds the global optimal solution of the problem without any restrictions on the cost functions or on the set of input parameters used in the problem. Numerical experiments are conducted to evaluate the performance of the proposed algorithm.