Optimal Profit Distribution in Supply Chain
MAGAZINE №5(88) October 2018
AUTHORS MIRONOV V. L.
CATEGORY Logistic integration and coordination Optimization and mathematical modelling
ABSTRACT
The paper features application of corporate game theory to logistics illustrated by a problem of optimal profit distribution in supply chain.
The supply chain is given as a direct graph with edges as chain units and state points as transshipment points. All graph edges are marked; each mark indicates a supplier which owns a chain unit of that edge and the edge capacity. Two state points are specified in graph: a source (from where the product comes) and a stock (where the product is delivered). By combining their chain units, the suppliers can transfer several (maximal) units of products from the source to the stock, whereby the volume that is transferred by common efforts is superior to individual suppliers' capacities.
In that context there naturally occurs a problem of optimal (fair) distribution of total profit among suppliers.
The main article result is a calculation of suppliers’ shares in the most optimal distribution of total profit. For this purpose suppliers are considered as players of a coalition game, and their shares are determined with Shapley value.
As an example, a chain with 3 suppliers is considered and then a general case is described – any supply chain with any number of suppliers.
In conclusion two problems are defined and resolved with practical examples. In the first problem a supplier invests funds in buying chain units of another supplier; in the second one – in increasing of carrying capacities of own chain units. It is also noted that application of Shapley method allows suppliers to optimize future investments in chain development, i.e. foresee their commercial activities.
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