Optimal Requirement Allocation among Capacity Constrained Discount Quoting Suppliers

We consider a problem motivated by a central purchasing organization for a major office products distributor. This purchasing organization must source a quantity of a particular resale item from a set of capacitated suppliers. In our case each supplier offers an incremental quantity discount purchase price structure. The purchaser's objective is to obtain a quantity of a required item at minimum cost. The resulting problem is one of allocating order quantities among an approved supply base and involves minimizing the sum of separable piecewise linear concave cost functions. We develop a branch and bound algorithm that arrives at an optimal solution by generating linear knapsack subproblems with feasible solutions to the original problem.