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

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...

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Published in:	Computers & operations research Vol. 160; p. 106372
Main Authors:	Hamdan, Sadeque, Cheaitou, Ali, Shikhli, Amir, Alsyouf, Imad
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.12.2023
Subjects:	Bi-objective optimization Green supplier selection Multi-criteria decision-making (MCDM) Order allocation Quantity discounts Supplier availability Supplier availability Green supplier selection Multi-criteria decision-making (MCDM) Bi-objective optimization Order allocation Quantity discounts
ISSN:	0305-0548
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Abstract	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 modeled 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. •We study a supplier selection and order allocation problem with green criteria.•Three quantity discount configurations are considered: all-unit, incremental and combined.•A bi-objective model is solved using both exact and population-based approaches.•An extensive numerical study shows the effectiveness of the approach.•A software is developed to guide procurement managers in making decisions.
AbstractList	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 modeled 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. •We study a supplier selection and order allocation problem with green criteria.•Three quantity discount configurations are considered: all-unit, incremental and combined.•A bi-objective model is solved using both exact and population-based approaches.•An extensive numerical study shows the effectiveness of the approach.•A software is developed to guide procurement managers in making decisions.
ArticleNumber	106372
Author	Shikhli, Amir Hamdan, Sadeque Cheaitou, Ali Alsyouf, Imad
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Keywords	Supplier availability Green supplier selection Multi-criteria decision-making (MCDM) Bi-objective optimization Order allocation Quantity discounts
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Snippet	We model and solve a deterministic multi-period single-product green supplier selection and order allocation problem in which the considered suppliers’...
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SubjectTerms	Bi-objective optimization Green supplier selection Multi-criteria decision-making (MCDM) Order allocation Quantity discounts Supplier availability
Title	Comprehensive quantity discount model for dynamic green supplier selection and order allocation
URI	https://dx.doi.org/10.1016/j.cor.2023.106372
Volume	160
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