Stochastic Multilevel Programming with a Hybrid Intelligent Algorithm

A framework of stochastic multilevel programming is proposed for modelling decentralized decision-making problem in stochastic environment. According to different decision criteria, the stochastic decentralized decision-making problem is formulated as expected value multilevel programming, and chanceconstrained multilevel programming. In order to solve the proposed stochastic multilevel programming models for the Stackelberg-Nash equilibriums, genetic algorithms, neural networks and stochastic simulation are integrated to produce a hybrid intelligent algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the hybrid intelligent algorithm

Multi-parametric programming : novel theory and algorithmic developments

Imperial Users onl

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

An algorithm for the global resolution of linear stochastic bilevel programs

The aim of this thesis is to find a technique that allows for the use of decomposition methods known from stochastic programming in the framework of linear stochastic bilevel problems. The uncertainty is modeled as a discrete, finite distribution on some probability space. Two approaches are made, one using the optimal value function of the lower level, whereas the second technique uses the Karush-Kuhn-Tucker conditions of the lower level. Using the latter approach, an integer-programming based algorithm for the global resolution of these problems is presented and evaluated

Hierarchical decision making with supply chain applications

Hierarchical decision making is a decision system, where multiple decision makers are involved and the process has a structure on the order of levels. It gains interest not only from a theoretical point of view but also from real practice. Its wide applications in supply chain management are the main focus of this dissertation.The first part of the work discusses an application of continuous bilevel programming in a remanufacturing system. Under intense competitive pressures to lower production costs, coupled with increasing environmental concerns, used products can often be collected via customer returns to retailers in supply chains and remanufactured by producers, in orderto bring them back into “as-new” condition for resale. In this part, hierarchical models are developed to determine optimal decisions involving inventory replenishment, retail pricingand collection price for returns. Based on the simplified assumption of a single manufacturer and a single retailer dealing with a single recoverable item under deterministic conditions,all of these decisions are examined in an integrated manner. Models depicting decentralized, as well as centralized policies are explored. Analytical results are derived and detailed sensitivity analysis is performed via an extensive set of numerical computations.In the second part of this dissertation, a discrete bilevel problem is illustrated by investigating a biofuel production problem. The issues of governmental incentives, industry decisions of price, and farm management of land are incorporated. While fixed costs are natural components of decision making in operations management, such discrete phenomena have not received sufficient research attention in the current literature on bilevel programming, due to a variety of theoretical and algorithmic difficulties. When such costs are taken into account, it is not easy to derive optimality conditions and explore convergence properties due to discontinuities and the combinatorial nature of this problem, which is NP-hard. In order to solve this problem, a derivative-free search technique is used to arrive at a solution to this bilevel problem. A new heuristic methodology is developed, which integrates sensitivity analysis and warm-starts to improve the efficiency of the algorithm.Ph.D., Decision Sciences -- Drexel University, 201

Bilevel linear programs: generalized models for the lower-level reaction set and related problems

Bilevel programming forms a class of optimization problems that model hierarchical relation between two independent decision-makers, namely, the leader and the follower, in a collaborative or conflicting setting. Decisions in this hierarchical structure are made sequentially where the leader decides first and then the follower responds by solving an optimization problem, which is parameterized by the leader's decisions. The follower's reaction, in return, affects the leader's decision, usually through shaping the leader's objective function. Thus, the leader should take into account the follower's response in the decision-making process. A key assumption in bilevel optimization is that both participants, the leader and the follower, solve their problems optimally. However, this assumption does not hold in many important application areas because: (i) there is no known efficient method to solve the lower-level formulation to optimality; (ii) the follower either is not sufficiently sophisticated or does not have the required computational resources to find an optimal solution to the lower-level problem in a timely manner; or (iii) the follower might be willing to give up a portion of his/her optimal objective function value in order to inflict more damage to the leader. This dissertation mainly focuses on developing approaches to model such situations in which the follower does not necessarily return an optimal solution of the lower-level problem as a response to the leader's action. That is, we assume that the follower's reaction set may include both exact and inexact solutions of the lower-level problem. Therefore, we study a generalized class of the follower's reaction sets. This is arguably the case in many application areas in practice, thus our approach contributes to closing the gap between the theory and practice in the bilevel optimization area. In addition, we develop a method to solve bilevel problems through single-level reformulations under the assumption that the lower-level problem is a linear program. The most common technique for such transformations is to replace the lower-level linear optimization problem by its KKT optimality conditions. We propose an alternative technique for a broad class of bilevel linear integer problems, based on the strong duality property of linear programs and compare its performance against the current methods. Finally, we explore bilevel models in an application setting of the pediatric vaccine pricing problem