Efficient Algorithms for a Large-Scale Supplier Selection and Order Allocation Problem Considering Carbon Emissions and Quantity Discounts

This paper considers a multi-period supplier selection and order allocation problem for a green supply chain system that consists of a single buyer and multiple heterogeneous suppliers. The buyer sells multiple products to end customers and periodically replenishes each item's inventory using a periodic inventory control policy. The periodic inventory control policy used by the buyer starts every period with an order size determination of each item and the subsequent supplier selection to fulfill the orders. Because each supplier in the system is different from other suppliers in the types of carrying items, delivery distance, item price, and quantity discount schedule, the buyer's problem becomes a complicated optimization problem. For the described order size and supplier selection problem of the buyer, we propose a nonlinear integer programming model and develop two different algorithms to enhance the usability of the model in a real business environment with a large amount of data. The algorithms are developed to considerably cut computational time and at the same time to generate a good feasible solution to a given supplier selection and order allocation problem. Computational experiments that were conducted to test the efficiency of the algorithms showed that they can cut as much as 99% of the computational time and successfully find feasible solutions, deviating not more than 3.4% from the optimal solutions.