Supply chain optimization with all-units discount policy under demand uncertainty

Quantity discount is the decision making of the tradeoff price between suppliers and manufacturers while the production is changeable due to the unknown demand in the real market. In this paper, supply chain optimization model under demand uncertainty with all-unit discount policy which considers the selection of the contracted suppliers, production quantity and inventory simultaneously is addressed. All-unit discount is the policy that the procurement cost is discounted based on the total quantity. The optimization problem including the integral function is reformulated with the expectation formulation. The mixed integer nonlinear programming problem is solved by an outer approximation algorithm combined with the sequential quadratic programming technique. The effectiveness of the proposed algorithm is demonstrated from computational experiments. The objective of this paper is to formulate the mathematical model by applying all-unit discount policy in order to help the decision making in the supply chain management.