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A solution procedure for mixed-integer nonlinear programming formulation of supply chain planning with quantity discounts under demand uncertainty

Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.

A game theoretic model for coordination of single manufacturer and multiple suppliers with quality variations under uncertain demands

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.

Column generation approach to ship scheduling problems for international crude oil transportation

Nowadays, the new trend of global economy has driven the business strategy from the local to the global supply chain optimization. The comprehensive logistics solutions are critical to integrate supply chain management in the global landscape. We propose a column generation algorithm to solve the ship scheduling problem for international crude oil distribution. The problem is to find an optimal assignment and sequence and loading volume of demand simultaneously in order to minimize the total distance satisfying the capacity of the tankers. The problem can be generalized as split delivery routing problem. In this paper, an efficient algorithm by using the column generation is developed to generate a feasible solution taking into account for several practical constraints. The performance of the proposed method is compared with a heuristic algorithm and that of human operators. Computational results demonstrate the effectiveness of the proposed algorithm for a real case study.

Column Generation for Split Pickup and Delivery Vehicle Routing Problem for Crude Oil Transportation

The pickup and delivery crude oil transportation scheduling problem is to find an optimal assignment of requests to a fleet of tankers, sequence of visiting places, and loading and unloading volume of demand simultaneously in order to minimize the total cost with the capacity of the tankers. The problem can be formulated as a split pickup and delivery vehicle routing problem. We apply a column generation algorithm to solve the problem efficiently. In order to obtain a feasible solution by column generation, we propose an effective algorithm to generate a feasible solution satisfying the set partitioning constraints. Computational results demonstrate the effectiveness of the proposed method.Copyright