Random data generation.

This paper studies the flexible large-scale supplier selection and order allocation problem with various quantity discounts, i.e., no discount, all-unit discount, incremental discount, and carload discount. It fills a literature gap that models usually formulate one or seldom two types because of the modeling and solution difficulty. All suppliers offering the same discount are far from reality, especially when the number of suppliers is large. The proposed model is a variant of the NP-hard knapsack problem. The greedy algorithm, which solves the fractional knapsack problem optimally, is applied to cope with the challenge. Three greedy algorithms are developed using a problem property and two sorted lists. Simulations show the average optimality gaps are 0.1026%, 0.0547%, and 0.0234% and the model can be solved in centiseconds, densiseconds, and seconds for supplier numbers 1000, 10000, and 100000. This allows the full use of data in the big data era.