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In this paper, a game theoretic model for supply chain coordination problem is studied. The supply chain coordination problem involves one manufacturer and multi-suppliers with quality variations under demand uncertainty. The number of defective parts purchased from suppliers is unknown to the manufacturer while each supplier can determine the standard deviation of defective items. The relationship between the manufacturer and the suppliers is modelled by a non-cooperative game. The non-cooperative game model is analysed by the Stackelberg equilibrium where the manufacturer is regarded as a leader and the suppliers as followers. By deriving suppliers' best response functions, the Stackelberg equilibrium under uncertainties is established. Sensitivity analysis is conducted to investigate the features of the proposed models with cost parameters. The results validate the derived managerial insights derived for the proposed model.

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In this paper, we propose a heuristic algorithm to solve a practical ship scheduling problem for international crude oil transportation. The problem is considered as a vehicle routing problem with split deliveries. The objective of this paper is to find an optimal assignment of tankers, a sequence of visiting and loading volume simultaneously in order to minimize the total distance satisfying the capacity of tankers. A savings-based meta-heuristic algorithm with lot sizing parameters and volume assignment heuristic is developed. The proposed method is applied to solve a case study with real data. Computational results demonstrate the effectiveness of the heuristic algorithm compared with that of human operators.