bi-level programming

The purpose of this research is to design and plan the production and distribution supply chain in an integrated manner.

By using the bi-level programing approach, it is possible to maintain the integrity of decision-making while managing the conflict between the goals and interests of the decision-makers. In the proposed model, supply chain design decisions are considered at the leader level and production and distribution planning decisions are jointly considered at the follower level. At the leader level, the three goals of minimizing the costs of the entire supply chain, maximizing reliability and minimizing adverse environmental effects, and at the follower level, minimizing production costs and minimizing distribution costs are pursued. Therefore, the proposed bi-level programing model is multi-objective and multi-follower. To calculate the credibility of SCOR12 model parameters, hierarchical data analysis technique and fault tree analysis were used. The carbon dioxide emission factor was used to measure the adverse environmental effects. Finally, meta-heuristic technique has been used to solve the proposed model.

The findings indicate that due to the high accuracy of the MOEA/D algorithm, the findings of this algorithm can be trusted for the supply chain problem.

This research is considered a new approach in terms of leveling the problem and choosing the problem of leader and follower. If the decisions related to the design and planning of the supply chain are made with the cooperation of the supply chain links and in an integrated manner, the probability of achieving more favorable results increases

The management of production and distribution of electricity is one of the most important issues in developing countries and it is the framework for development. Because of limitations and different technologies and existence of so many factors on electricity management, consideration such problem as a single level approach is not reasonable. So, in this paper a bi-level follower leader approach is considered in which the follower is the company of Iran management network electricity and the leaders are some operation companies. Based on the accomplished researches, this paper is the first bi level attempt in the field of production and transmission management of electricity and it is localized with the special specifications in Iran. The objective function is minimizing the emission cost of greenhouse effect and distribution costs and consumed fuels and startup for follower and leader respectively. Because of high complexity of presented model, a Simulated Annealing is used for solving the problem. The results of current study could be used for improvement of Iran management network.

This paper aims to propose a knowledge sharing optimization model based on the game theory that optimizes both employer and employee(s) decisions simultaneously. This model is a bi-level programming model. The upper-level problem includes employer decision about the reward, and the lower-level problem contains employee(s) decisions about time and effort allocation to knowledge sharing activity. Mathematical formulation of the model designed based on previous literature and in the framework of Motivation-Opportunity-Ability. The proposed bi-level programming model provides a foundation to investigate more different parameters comparing with previous models introduced in the literature. This model considers opportunity and ability factors in addition to the motivation. Also, payoff functions in this model are non-linear and therefore is more consistent with real cases relative to previous linear models. Additionally, this model analyzes the effects of available time as a key factor. The bi-level model coded in GAMS using EMP syntax and solved for a set of randomly generated data using BARON algorithm. Results indicated that the increase of applicability of codified knowledge and impact coefficient of social comparison could improve organizational performance and also save the cost of reward system. Therefore, neglecting these two parameters in designing a reward system could lead to under optimized decision making. This research provides a basis to consider more parameters simultaneously and help to improve organizational decisions. However, based on the results, BARON algorithm is not efficient to solve big problems, so developing a more efficient algorithm is needed.

Providing a bi-level programming model to solve the simultaneous problem of supplier selection and order allocation in multi-echelon supply chain is sought. The model will be proposed so that at the leader level, the supplier selection problem with the objective of increasing system reliability and at the follower level, the order allocation problem with the objective of reducing cost of system are formulated and customers’ demand at the last echelon of the supply chain is considered as an uncertain parameter.

Modeling the supplier selection and order allocation problem is based on the bi-level programming model, so the robust optimization technique was used to deal with the problem of uncertainty and a bi-level genetic algorithm was used to obtain the optimal solutions.

The results obtained from solving a real problem in the steel industry under various scenarios indicated that there is an opposing relationship between reliability and cost objectives, and increasing the number of chain members can lead to an increase in system reliability and cost. On the other hand, as increased reliability can lead to higher system costs, reliability reduction, which is mainly due to lack of quality and deficiency issues, can also lead to an increase in customers' dissatisfaction and, ultimately, an increase in aggregate system costs. Moreover, the results obtained in uncertain conditions, in comparison with definite conditions, indicated an unfavorable situation.

In order to improve the reliability of supply chain, the average reliability of the echelons in supply chain, which are at the lowest (highest) level in comparison to other echelons, should increase (decrease) in order to avoid additional costs. Besides, the interactive approach in proposed methodology provides a suitable solution for maximizing the interests of leader and follower levels.

In this study, the design of a network for municipal solid waste management has been studied from the viewpoint of an organization (e.g. Municipality) which collects different types of waste from all over the city and pays waste generation points in exchange for waste. Determining purchase price for waste and forming outsourcing policies are matters to be decided upon. In case of outsourcing, auction will be held and the private company who their business is recycling and composting can participate by bidding, which results in the selection of an organization or non-outsourcing. The problem is modelled as a bi-level model, in the first level, Municipality decides as the leader on outsourcing, and if outsourcing is agreed upon, a company is selected. In the second level, bidders compete as followers in the auction for receiving more waste from the organization and offer prices.

Bi-level programming (BLP), is one of the important problems in the decision-making theory, is multilevel programming with two levels. It involves two optimization problems where the constraint region of the first level problem is implicitly determined by another optimization problem. Since the BLP problem is NP-hard, it is impossible solving it by traditional methods. This paper reviews the BLP problem and applies enumeration techniques for finding extreme points. It uses the genetic algorithm for the searching region and finding the optimum solution. Also, the search region is controlled by a parameter in order to avoid the increased time. The results show that the solutions are acceptable in comparison with previous studies.