bi-level programming

In this paper, a mathematical negotiation mechanism is designed to minimize the negotiators’ costs in a distributed procurement problem at two echelons of an automotive supply chain. The buyer’s costs are procurement cost and shortage penalty in a one-period contract. On the other hand, the suppliers intend to solve a multi-period, multi-product production planning to minimize their costs. Such a mechanism provides an alignment among suppliers’ production planning and order allocation, also supports the partnership with the valued suppliers by taking suppliers’ capacities into account. Such a circumstance has been modeled via bi-level programming, in which the buyer acts as a leader, and the suppliers individually appear as followers in the lower level. To solve this nonlinear bi-level programming model, a hybrid algorithm by combining the particle swarm optimization (PSO) algorithm with a heuristic algorithm based on A* search is proposed. The heuristic A* algorithm is embedded to solve the mixed-integer nonlinear programming (MINLP) sub-problems for each supplier according to the received variable values determined by PSO system particles (buyer’s request for quotations (RFQs)). The computational analyses have shown that the proposed hybrid algorithm called PSO-A* outperforms PSO-SA and PSO-Greedy algorithms.

The integration of the distributed energy resources into a single entity can do with virtual power plants. VPP is a cluster of dispatchable and non- dispatchable resource with flexible loads which distributed in allover the grid that aggregated and acts as a unique power plant. Flexible load is able to change the consumption so demand response program is applied to use them to improvement of the power system performance. Virtual power plant generation has uncertainty and it make hard to schedule the VPP. To deal this matter Information gap decision theory hint us to optimal schedule of the VPP. To show the effects of VPP and DRP on power system operation cost a bi-level unit commitment with regard the VPPs and DRP is solved in modified IEEE 24 bus reliability test system. Results in presence of VPP and DRP in both IGDT strategies are compared with disregard VPP and DRP and effectiveness of the proposed model is reflected.

In this paper, we focus on solving the integrated energy and flexiramp procurement problem in the day-ahead market. The problem of energy and ramp procurement could be perfectly analyzed through Stackelberg concept, because of its hierarchical nature of the decision-making process. Such a circumstance is modeled via a bi-level programming, in which suppliers act as leaders and the ISO appear as the follower. The ISO intends to minimize the energy and spinning reserve procurement cost, and the suppliers aim to maximize their profit. To solve the proposed model, a fuzzy max-min approach is applied to maximize the players’ utilities. The objectives and suppliers’ dynamic offers, determined regarding the market clearing prices, are reformulated through fuzzy utility functions. The proposed approach is an effective and simple alternative to the KKT method, especially for problems with non-convex lower-level.

This study aims in providing a new approach regarding design of a closed loop supply chain network through emphasizing on the impact of the environmental government policies based on a bi-level mixed integer linear programming model. Government is considered as a leader in the first level and tends to set a collection rate policy which leads to collect more used products in order to ensure a minimum distribution ratio to satisfy a minimum demands. In the second level, private sector is considered as a follower and tries to maximize its profit by designing its own closed loop supply chain network according to the government used products collection policy. A heuristic algorithm and an adaptive genetic algorithm based on enumeration method are proposed and their performances are evaluated through computational experiences. The comparison among numerical examples reveals that there is an obvious conflict between the government and CLSC goals. Moreover, it shows that this conflict should be considered and elaborated in uncertain environment by applying Min-Max regret scenario based robust optimization approach. The results show the necessity of using robust bi-level programming in closed loop supply chain network design under the governmental legislative decisions as a leader-follower configuration.

The present study aimed to design a bi-objective bi-level mathematical model for multi-dimensional cellular manufacturing system. Minimizing the total number of voids and balancing the assigned workloads to cells are regarded as two objectives of the upper level of the model. However, the lower level attempts to maximize the workers' interest to work together in a special cell. To this aim, two nested bi-level metaheuristics including particle swarm optimization (NBL-PSO) and a population-based simulated annealing algorithm (NBL-PBSA) were implemented to solve the model. In addition, the goal programming approach was utilized in the upper level procedure of these algorithms. Further, nine numerical examples were applied to verify the suggested framework and the TOPSIS method was used to find the better algorithm. Furthermore, the best weights for upper level objectives were tuned by using a weight sensitivity analysis. Based on computational results, all three objectives were different from their ideal goals when decisions about inter and intra-cell layouts, and cell formation to balance the assigned workloads by considering voids and workers' interest were simultaneously madeby considering a wide assumption-made problem closer to the real world. Finally, NBL-PBSA could perform better than NBL-PSO, which confirmed the efficiency of the proposed framework.

This paper proposes two models to formulate a Supplier Selection Problem (SSP) in a single-buyer, multi-supplier two-echelon supply chain network. The model coordinates order allocation and supplier selection problems under all-unit quantity discount policy. In this way, bi-level programming is employed to obtain two models: 1) The model with buyer as a leader; 2) The model with vendor as a leader. The resulted nonlinear bi-level programming problems are hard to solve. Therefore, Particle Swarm Optimization (PSO) algorithm is used to deal with the complexity of the model and makes it solvable. Numerical results show that the proposed model is ecient for SSP in compliance with order allocation decision making.

Globalization, increased governmental regulations, and customer demands regarding environmental issues has led organizations to review measures necessary for implementation of supply chain management, in order to improve environmental and economic performance. In this study, a competitive market is considered consisting of product producers and raw material suppliers with a focus on automotive industry. This research also utilizes the rules of Oligopoly and Cournot games to compete with each other and to achieve greater profits. In other words, price of a product is a function of market demand. In this regard, a nonlinear bi-level model is proposed at its first level of which, the government controls environmental pollution to maximize its net income. In the second level, the main objective is to maximize the profit of each Green Supply Chain member’s. The bi-level model is converted to a single level model by replacing the second level with its Karush Kuhn Tucker conditions and linearization techniques. Subsequently, a Genetic Algorithm is utilized to solve the single level model using MATLAB software. Afterwards, the obtained results are compared with optimal solutions acquired by Enumerative method (EM) to evaluate validity and feasibility of the proposed Genetic Algorithm. A sensitivity analysis of this model indicates that fiscal policy of the government heavily impacts reduction of environmental pollution costs caused by industrial activities such as automobile production in a competitive market. Therefore, the amount of taxes for non-green products is directly related to reduction of the environmental pollution.