This paper presents a fuzzy multiple-objective mixed-integer programming model that tackles some different features of order assignment problems by considering vague aspects of such decision-making problems, the model reflects realities encountered in practice. In particular, the model considers three main parties of the supply chain: the purchasing organisation, suppliers, and third-party logistics providers (3PL) and in doing so, considers the three main aspects of order assignment, namely purchasing, holding, and ordering. By applying the theory of fuzzy sets, and through some operations on objective function and constraints, this research achieves a mixed-integer programming model with less complexity and more performance in a group of order assignment problems.
The first intention of this paper is to model and analyse the order assignment problem with a wider view by considering buyer, supplier, and 3PL parties. This modelling reflects the multiple-objective nature of the problem by including the contribution of each party to total cost and overall performance of the supply chain. The second intention is to model existing uncertainties in decision criteria of the order assignment problem. Finally, the paper tries to develop a solution for the multiple-objective decision-making problem under uncertainty.
Competitive price, on time delivery, flexibility, innovation, pro-activity, quality, and high serviceability are key operations objectives demanded by today’s fast changing markets. To meet those objectives, clusters of suppliers, retailers, and logistics providers shape supply chains and compete with each other rather than single companies or brands (Christopher, 2000). To be competitive, a supply chain should be based on qualified associates, such as manufacturers, suppliers, distributors, wholesalers, retailers, and so on. In the supply chain, at the upstream or supply side, it is mainly the responsibility of the purchasing or procurement organisation or department to create a reliable, competitive supply base. In that respect, managing suppliers and assigning the right product to the right suppliers is of great importance.
This study concentrates on the order assignment problem where multiple-product orders are to be allocated to different suppliers and a 3PL. The selection of the right supplier and the assignment of the right quantity are tackled in the modelling process developed by this paper. The ordering, holding inventory and purchasing costs are considered in three main engaged parties—the buyer company, the 3PL, and the suppliers. The research avoids single perspective approaches, which looks at the order assignment problem only from the viewpoint of the buyer or supplier. On the other hand, the contributions of different parties are taken into account, and are aggregated in a broader model. Taking numerous perspectives into consideration leads to a multiple-objective type of decision making. To deal with real-life practical issues of the order assignment problems in the supply chain management, this study considers some aspects of uncertainties in the associated decision-making process. The uncertainties are discussed in setting the objective function level. Fuzzy systems in mathematical programming are employed to find a solution for the developed model. To have a better understanding of different aspects of the study, the next section provides a review of the literature on order assignment and related bodies of knowledge.
This paper developed an enhanced order assignment model considering multiple parties (the buyer, the supplier, and the 3PL) in the supply chain and considering multiple products, where each product could be assigned to various available suppliers. This model assumes a purchasing plan of a supply chain of one buyer company, one 3PL, and multiple suppliers with limited capacity for different required products. As suppliers generally offer some advantages and disadvantages in terms of cost, quality, services level, amongst others, the order assignment decision is made based on various criteria. For this purpose, first, a crisp multi-objective model with three objective functions was developed. The three objectives attempt to reflect ordering costs, inventory costs, and purchasing cost in 3PL, suppliers, and buyer, respectively. In real-world conditions, it is not easy, and usually not possible, to satisfy all objectives jointly. Therefore, each objective is met to some extent. How to manage and model this approximation and moderation between three parties of an order assignment system is the core contribution of this research.
In addition to the multi-dimension nature of the developed order assignment model, existing uncertainties in objective functions have been tackled by applying fuzzy sets theory. Through operations on objective functions and constraints, the multi-objective fuzzy mixed-integer model was transferred to the single-objective model with less complexity, while it still reflects all aspects of the multi-objective model. In view of that, this paper has shown different aspects of modelling order assignment in real-world situations, where decision makers face various uncertainties in decision parameters. As shown in by the case study, the model is particularly useful to buyer companies who want to solve the problem, but in theory, any party, which leads the supply chain may come find the model useful. With reference to the very few researches on fuzzy modelling of order assignment problems, this research has attempted to present a sensible supply chain model from the order assignment point of view. However, different parts of this article suggest potential future research. In fuzzification of LP model, an algorithmic approach can be developed for fast resolution of such models. Furthermore, the development of models in other real-world problems with several tiers of suppliers is another potential area for future work.
