A general quantity discount and supplier selection mixed integer programming model

Operations Research-Spektrum (Impact Factor: 0.99). 07/2007; 29(4):723-744. DOI: 10.1007/s00291-006-0066-z


Recently, new models and heuristics for exploiting quantity discounts have been proposed that are applicable in classical
purchasing as well as in an e-business environment and can be implemented as part of an advanced planning system. These models
can now handle both the single- and multi-item case with fixed cost to be shared among several products ordered at the same
point in time from a single supplier. Furthermore, the supplier selection problem is addressed, i.e., how to best exploit
quantity discounts over time offered by several suppliers. Last but not least, additional constraints on the buyer’s or on
the supplier’s side may be included. While so far only purpose-built heuristics have been proposed for this generalized problem,
we present a linear mixed integer programming (MIP) model, which not only represents the all-units discount but also the incremental discount
case. Furthermore, the objective function chosen resolves (former) conflicts among proponents of a purely cost oriented and
a cash flow oriented modeling approach. Computational tests show that our model yields near optimal solutions within a given
CPU time limit by making use of a standard MIP solver.

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    • "There are several supplier selection and benchmarking methods available in the literature such as analytical hierarchical process (AHP) (Ghodsypour and O'Brien, 1998; Chan et al., 2007; Ng, 2008), fuzzy programming model (Sanayei et al., 2010; Wu et al., 2010), artificial intelligence (AI) (Hong et al., 2005; Lau et al., 2006), multiple attribute utility approach (MAUT) (Min, 1994). Also there are other methods for supplier selection problem such as fuzzy logic approaches (Bevilacqua and Petroni, 2002; Lee, 2008; Goal-directed benchmarking Noorul Haq and Kannan, 2006), case-based reasoning (de Boer et al., 2001; Choy et al., 2005), multi-objective programming (MOP) (Arunkumar et al., 2006), mixed integer programming (Hartmut, 2007), DEA (Narasimhan et al., 2001; Azadi and Farzipoor Saen, 2012a, b, c; Azadi et al., 2012; Hosseinzadeh Zoroufchi et al., 2012), analytic network process (ANP) (Bayazit, 2006; Gencer and Gürpinar, 2007), real options approach (Costantino and Pellegrino, 2010), supply base (Choi and Krause, 2006), simulated annealing (Chen and Zhang, 2010), integrated approach (Ting and Cho, 2008), total cost of ownership approach (Bhutta and Huq, 2002), hybrid AHP (Sevkli et al., 2008), etc. "
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    ABSTRACT: Purpose ‐ In this paper, the authors extend the goal-directed benchmarking theory proposed by Stewart for benchmarking and selecting suppliers. This extension is in recognition of the fact that benchmarking for suppliers is more than a pure monitoring process and includes a component of future planning. The paper aims to discuss these issues. Design/methodology/approach ‐ In this paper, the proposed model utilizes a goal programming structure to find points on the efficient frontier which are realistically attainable by suppliers in the presence of undesirable outputs, but at the same time achieving a closer method to long-term organizational goals (as distinct from the local performance of individual suppliers). Findings ‐ The contributions of the current paper are as follows: the proposed model considers undesirable outputs in the context of goal-directed benchmarking. The proposed model does not demand weights from the decision maker. The proposed model can be easily computerized, enabling it to serve as a decision making tool to assist decision makers. For the first time, the proposed model is applied for the supplier selection and benchmarking. Originality/value ‐ To the best of knowledge of the authors, there is not any reference that discusses supplier selection problem and benchmarking in the presence of undesirable outputs in the context of goal-directed benchmarking.
    Full-text · Article · Apr 2014 · Benchmarking An International Journal
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    • "Varios autores se han ocupado de casos relacionados a descuentos de precio [2], [3], [32], [35]. Stadler [32] considera el problema de un descuento para todas las unidades y el caso de un descuento incremental, presenta un modelo de programación lineal entera mixta para resolver ambos casos. Xia y Wu [3] consideran el caso donde el descuento está basado en el volumen de la compra total asignada al proveedor, y proponen un enfoque compuesto por PAJ mejorado a través de la teoría de conjuntos aproximados y programación lineal entera mixta multi-objetivo. "
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    ABSTRACT: The globalization of production systems has led organizations to consider the supplier management function as a strategic decision. There is signifcant research work addressing decision making and supplier management. However, there is a lack of research in the case of multiple suppliers with different characteristics and attributes and able to satisfy a product demand defined by a fixed lot size. This kind of demand arises in production environments organized by processes such as the pharmaceutical and food industry. This research aims at fulfilling this lack of research in supplier management. The proposed methodology is based on the formulation of a Mixed Integer Linear Programming model for optimizing the decisions of supplier selection and order quantity allocation in the case of fixed lot size. A numerical example shows the applicability and usefulness of the proposed model. Furthermore, a sensitivity analysis shows that the model is sensitive to changes in parameters. Finally, the results also show that the model is practical and can be easily adapted by organizations that purchase products in fixed-size lots.
    Full-text · Article · Jul 2013
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    • "Xia and Wu [24] formulated the procurement problem as a multi-objective MIP model and utilized the optimization toolbox in MATLAB to solve the problem. Stadtler [25] presented a general model that is applicable to both all-units and incremental discount policies, and solved the model using the standard MIP solver Xpress-MP optimizer. Goossens et al. [7] proposed a mincost network flow based branch-and-bound algorithm that uses the commercial MIP solver CPLEX 8.1 to solve the procurement problem under a total quantity discount structure optimally. "
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    ABSTRACT: This paper studies a problem encountered by a buying office for one of the largest retail distributors in the world. An important task for the buying office is to plan the distribution of goods from Asia to various destinations across Europe. The goods are transported along shipping lanes by shipping companies, which offer different discount rates depending on the freight quantity. To increase the reliability of transportation, the shipper imposes a quantity limit on each shipping company on each shipping lane. To guarantee a minimum business volume, each shipping company requests a minimum total freight quantity over all lanes if it is contracted. The task involves allocating projected demand of each shipping lane to shipping companies subject to the above conditions such that the total cost is minimized.
    Full-text · Article · Aug 2012 · Omega
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