Bilevel Multi-follower Programming Research Articles

On solving uncooperative linear bilevel multi-follower programming problems

The relationship between the reference-uncooperative linear bilevel two-follower decision making and the multi-objective decision making has been recently considered (Sadeghi and Moslemi, 2019). In this paper, we address the foregoing relation for the
 uncooperative linear bilevel multi-follower programming (ULBMFP) model with followers. Furthermore, we consider some geometric properties of the feasible solutions set of the ULBMFP problem. Moreover an algorithm to find an optimal solution for the ULBMFP problem was proposed. Ultimately, some numerical examples to illustrate the proposed algorithm were provided.

Optimization Problem of Pricing and Seat Allocation Based on Bilevel Multifollower Programming in High-Speed Railway

This paper studies the multistage pricing and seat allocation problems for multiple train services in a high-speed railway (HSR) with multiple origins and destinations (ODs). Taking the maximum total revenue of all trains as the objective function, a joint optimization model of multistage pricing and seat allocation is established. The actual operation constraints, including train seat capacity constraints, price time constraints in each period, and price space constraints among products, are fully considered. We reformulate the optimization model as a bilevel multifollower programming model in which the upper-level model solves the seat allocation problem for all trains serving multiple ODs in the whole booking horizon and the lower optimizes the pricing decisions for each train serving each OD in different decision periods. The upper and lower are a large-scale static seat allocation programming and many small-scale multistage dynamic pricing programming which can be solved independently, respectively. The solving difficulty can be significantly reduced by decomposing. Then, we design an effective solution method based on divide-and-conquer strategy. A real instance of the China’s Wuhan-Guangzhou high-speed railway is employed to validate the advantages of the proposed model and the solution method.

Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. In this paper, we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

Cloud manufacturing service composition and optimal selection with sustainability considerations: a multi-objective integer bi-level multi-follower programming approach

The process of service composition and optimal selection (SCOS) is an important issue in cloud manufacturing (CMfg). However, the current studies on CMfg and SCOS have generally focused on optimising the allocation of resources against quality of service (QoS), in terms of e.g. cost, quality, and time. They have seldom taken the perspective of sustainability into discussion, although sustainability is indispensable in the CMfg environment. Addressing this gap, we aim to (1) propose a comprehensive method to assess the sustainability of cloud manufacturing (SoM) in terms of the economic, environmental, and social aspects; (2) establish a multi-objective integer bi-level multi-follower programming (MOIBMFP) model to simultaneously maximise SoM and QoS from the perspectives of both platform operator and multiple service demanders; and (3) design a hybrid particle swarm optimisation algorithm to solve the proposed MOIBMFP model. The experimental results show that the proposed algorithm is more feasible and effective than the typical multi-objective particle swarm optimisation algorithm when solving the proposed model. In other words, the proposed model and algorithm suggest better alternatives to meet the needs of the platform operator and service demanders in the CMfg environment.

A multiple objective programming approach to linear bilevel multi-follower programming

In this paper, we investigate the relationship between a certain class of linear bilevel multifollower programming problems and multiple objective programming. We introduce two multiple objective linear programming problems with different objective functions and the same constraint region. We show that the extreme points of the set of efficient solutions for both problems are the same as those of the set of feasible solutions to the linear bilevel multi-follower programming problem. Based on this relationship, a new algorithm to find an optimal solution for the linear bilevel multifollower programming problem is developed. Some numerical examples are presented to show the feasibility of the proposed algorithm.

A multi-follower bilevel stochastic programming approach for energy management of combined heat and power micro-grids

This paper presents a multi-follower bilevel programming approach to solve the 24-h decision-making problem faced by a combined heat and power (CHP) based micro-grid (MG). The framework contains the interests of two different agents: the MG operator/owner (MGO), who procures the maximization of total profit incurred in attending the forecasted demand of consumers via demand response program (DRP) as well as day-ahead (DA) and real-time (RT) markets participation, and the various CHP owners (CHPOs) who procure the maximization of the profits obtained from the thermal and electrical energy sales. The interaction between the entities is determined in a bilateral contract. Further, to deal with various uncertainties, each level is formulated as a stochastic two-stage problem, where the volatility nature of consumers' loads, RT market price and wind speed uncertainties are modeled using autoregressive moving average (ARMA) technique. In this paper, in order to consider realistic model of the problem, on the contrary to the most CHP-based MG scheduling literature, the network operation constraints such as voltage magnitude of buses and line flow limits are taken into account.

On solving multi-objective linear bi-level multi-follower programming problem

Multi-objective linear bi-level multi-follower programming problem (MOBLMFPP) is a special case of two level hierarchical programming problems in which the second level hierarchy includes multiple followers. This paper presents an alternate method based on fuzzy goal programming approach for the solution of multi-objective linear bi-level multi-follower programming (MOLBMFP) problem in which there is no sharing of information among followers. In the proposed FGP model formulation, each of objective functions of each level (leader and follower's level of MOLBMFPP) as well as decision variables at each level are characterised into fuzzy goals. Suitable linear membership functions are defined for each objective function and decision variables. Then minimising the sum of the negative deviational variables of both levels, the highest membership value of each of fuzzy goals is obtained. Existence of compromise optimal solution for MOLBMFPP is established in context of proposed approach. A numerical example is illustrated in support of proposed methodology. A comparative analysis is also carried out in order to show efficiency of proposed method over earlier method for the solution of MOLBMFPP.

On solving multi-objective linear bi-level multi-follower programming problem

Multi-objective linear bi-level multi-follower programming problem (MOBLMFPP) is a special case of two level hierarchical programming problems in which the second level hierarchy includes multiple followers. This paper presents an alternate method based on fuzzy goal programming approach for the solution of multi-objective linear bi-level multi-follower programming (MOLBMFP) problem in which there is no sharing of information among followers. In the proposed FGP model formulation, each of objective functions of each level (leader and follower's level of MOLBMFPP) as well as decision variables at each level are characterised into fuzzy goals. Suitable linear membership functions are defined for each objective function and decision variables. Then minimising the sum of the negative deviational variables of both levels, the highest membership value of each of fuzzy goals is obtained. Existence of compromise optimal solution for MOLBMFPP is established in context of proposed approach. A numerical example is illustrated in support of proposed methodology. A comparative analysis is also carried out in order to show efficiency of proposed method over earlier method for the solution of MOLBMFPP.

Pricing and advertising decisions in a dominant-retailer supply chain: A multi-follower bi-level programming approach

Pricing and advertising is one of the most important decisions in each supply chain especially in the competitive environment. In the previous studies, this is as a centralized decision. However, if each channel member makes its decision independently, the utility of all members is optimized. In such decentralized situations, the channel members may have different market power that they influence on the other members’ decisions. These issues can modeled through leader-follower Stackelberg game or bi-level programming. This study investigates coordination of pricing and cooperative advertising in a two-stage supply chain consisting of one dominant-retailer and multiple competitive manufactures which produce several perishable and substitutable products. This paper aims to determine pricing and cooperative advertising decisions expenditure as well as the amount of manufacturers’ production or retailer’s purchase such that utility of all members is met. Hence, the problem is modeled as a multi-follower bi-level programming problem. Since it is proved that the model is NP-hard, the proposed model is solved through simulated annealing. A numerical example is used to show the impact of demand’s variations on the members’ decisions.

Strategic decision-making of distribution network operator with multi-microgrids considering demand response program

In this paper, the operation scheduling of future distribution network is discussed under assumption of multi-microgrids. The economic operation scheduling of distribution network operator in the presence of autonomous microgrids is formulated as a game problem. Due to participation of multiple players with different objective functions, the multi follower bi-level programming is intended in the energy management scheme. From the distribution network operator's perspective, the decision-making strategy seeks to minimize the operation costs of distribution network operator. Distribution network operator interconnecting with upstream grid and interaction with microgrids, schedules distributed energy resources and loads in economical matter to operate in optimal operation point. On the other hand, microgrid owners fed electrical loads interacting with the other microgrids and distribution network operator implementing demand response program during the scheduling horizon to acquire maximum profit. Therefore, the key focus of this approach is decision-making of distribution network operator which will be affected, not only by the reactions of microgrids, but also by the exchanging power between the microgrids. The paper discusses the theoretical background, architecture and algorithms of the proposed multi follower bi-level programming, and demonstrates the performance of distribution network operator and microgrids by means of simulation on the radial distribution test system.

Partially-shared pessimistic bilevel multi-follower programming: concept, algorithm, and application

When multiple followers are involved in a bilevel programming problem, the leader’s decision will be affected by the reactions of these followers. For actual problems, the leader in general cannot obtain complete information from the followers so that he may be risk-averse. Then he would need a safety margin to bound the damage resulting from the undesirable selections of the followers. This situation is called a pessimistic bilevel multi-follower (PBLMF) programming problem. This research considers a partially-shared linear PBLMF programming in which there is a partially-shared variable among the followers. The concept and solution algorithm of such a problem are developed. As an illustration, the partially-shared linear PBLMF programming model is applied to a company making venture investments.

FUZZY BILEVEL PROGRAMMING: MULTI-OBJECTIVE AND MULTI-FOLLOWER WITH SHARED VARIABLES

Bilevel programming deals with hierarchical optimization problems in which the leader at the upper level attempts to optimize his or her objectives, but subject to a set of constraints and the follower's reactions. Typical bilevel programming considers one leader one follower situation and supposes each of them has only one objective. In real world situations, multiple followers may be involved and they may be with different relationships such as sharing decision variables or not, sharing objectives or not. Therefore, the leader's decision will be affected not only by those followers' reactions but also by their relationships. In addition, any of the leader and/or these followers may have multiple conflict objectives that should be optimized simultaneously. Furthermore, the parameters of a bilevel programming model may be described by uncertain values. This paper addresses all these three issues as a whole by particularly focusing on the situation of sharing decision variables among followers. It first proposes a set of fuzzy multi-objective multi-follower bilevel programming (FMMBP) models to describe the complex issue. It then presents an approximation branch-and-bound algorithm to solve the FMMBP problems. Finally, two examples illustrate the proposed models and algorithm.

Linear bilevel multi-follower programming with independent followers

This paper considers a particular case of linear bilevel programming problems with one leader and multiple followers. In this model, the followers are independent, meaning that the objective function and the set of constraints of each follower only include the leader's variables and his own variables. We prove that this problem can be reformulated into a linear bilevel problem with one leader and one follower by defining an adequate second level objective function and constraint region. In the second part of the paper we show that the results on the optimality of the linear bilevel problem with multiple independent followers presented in Shi et al. [The kth-best approach for linear bilevel multi-follower programming, J. Global Optim. 33, 563---578 (2005)] are based on a misconstruction of the inducible region.

The Kth-best approach for linear bilevel multifollower programming with partial shared variables among followers

In a real world bilevel decision-making, the lower level of a bilevel decision usually involves multiple decision units. This paper proposes the Kth-best approach for linear bilevel multifollower programming problems with shared variables among followers. Finally a numeric example is given to show how the Kth-best approach works.

The Kth-Best Approach for Linear Bilevel Multi-follower Programming

The majority of research on bilevel programming has centered on the linear version of the problem in which only one leader and one follower are involved. This paper addresses linear bilevel multi-f...