## Building Stable Matchings Between Suppliers and Consumers

**MAGAZINE №4 (93) August 2019**

**AUTHORS**** **MIRONOV V. L.

**CATEGORY **Logistic integration and coordination Optimization and mathematical modelling

**ABSTRACT**

The article considers one of logistics problems such as building of stable matchings between suppliers and consumers. In contrast to the standard approach, when stability refers to different degrees of matching between counterparties, we will examine how to assign several suppliers to several consumers so that suppliers and consumers did not have a mutual intention to modify initial assignment. If such a matching is found, it is called stable.

The main result of the article consists in the implementation of the Gale–Shapley algorithm to the solution of the problem of the building of stable matching between suppliers and consumers. To achieve that suppliers and consumers are considered as elements of certain sets and their mutual preferences are specified by inequations. Thus, a stable matching is a matching between sets of suppliers and consumers that satisfies certain criteria.

The introduction presents basic definitions in order to determine the term of stability. Further two chapters show how to build stable matchings when suppliers and consumers interact in “one-to-one” and “one-to-many” ways. In the first case each supplier cooperates only with one consumer, though in the second case one consumer can cooperate with many suppliers, meanwhile such “polygamy” is forbidden to suppliers. *The last chapter* describes a case when suppliers and consumers have several stable matchings the optimality of which can be compared using the Pareto optimality method. *In the conclusion* it is said that the Gale-Shapley algorithm can also be applied in cases when suppliers and consumers interact in a “many-to-many” way, which means that suppliers as well as consumers can cooperate with several counterparties at the same time.

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