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Comprehensive quantity discount model for dynamic green supplier selection and order allocation

Hamdan, Sadeque, Cheaitou, Ali, Shikhli, Amir, Alsyouf, Imad (2023) Comprehensive quantity discount model for dynamic green supplier selection and order allocation. Computers & Operations Research, 160 . Article Number 106372. ISSN 0305-0548. E-ISSN 1873-765X. (doi:10.1016/j.cor.2023.106372) (KAR id:102413)


We model and solve a deterministic multi-period single-product green supplier selection and order allocation problem in which the considered suppliers’ availability, cost, and green performance change from one period to another in the planning horizon. Moreover, the available suppliers may offer an all-unit or an incremental quantity discount (QD) scheme, resulting in three problem configurations. In one configuration, all suppliers offer all-unit QD. In the second, all suppliers offer incremental QD. In the third, some suppliers offer all-unit QD, and others offer incremental QD. The problem is modelled using a bi-objective integer linear programming formulation that maximizes the total green value of the purchased items from all the suppliers and minimizes their total corresponding cost, including the fixed cost, variable cost, inventory holding cost, and shortage cost. The proposed bi-objective model is scalarized and solved using the branch-and-cut algorithm and a population-based heuristic. A numerical analysis is conducted, which allows first to validate the heuristic approach using small-size instances by comparing its results with those of the exact approach. Moreover, an extensive comparison between the exact and heuristic solution approaches is carried out. The results reveal different findings. First, the economic and environmental solutions of an instance are different, and the environmental solution is independent of the suppliers’ pricing schemes. Second, the maximum difference between the heuristic approach and the exact approach in terms of the bi-objective function value is 4.72%, which makes the proposed heuristic recommended for large-size instances due to its short computation time and good accuracy. Third, there is no difference in terms of the heuristic performance between the combined model and the models with a single type of discount. Fourth, the all-unit discount scheme seems to be generally better in terms of the trade-off between the green value of purchasing and cost.

Item Type: Article
DOI/Identification number: 10.1016/j.cor.2023.106372
Uncontrolled keywords: green supplier selection; order allocation; quantity discounts; supplier availability; bi-objective optimization; multi-criteria decision-making (MCDM)
Subjects: H Social Sciences
Divisions: Divisions > Kent Business School - Division > Department of Analytics, Operations and Systems
Funders: University of Kent (
Depositing User: Sadeque Hamdan
Date Deposited: 11 Aug 2023 13:27 UTC
Last Modified: 10 Jan 2024 05:07 UTC
Resource URI: (The current URI for this page, for reference purposes)

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