A Characterization of the SSD-Efficient Frontier of Portfolio Weights by Means of a Set of Mixed-Integer Linear Constraints

2016 ◽  
Vol 62 (12) ◽  
pp. 3549-3554 ◽  
Author(s):  
Iñaki R. Longarela
Keyword(s):  
Efficient Frontier ◽  
Linear Constraints ◽  
Mixed Integer

scholarly journals A game-theoretic optimisation approach to fair customer allocation in oligopolies

2020 ◽  
Vol 21 (4) ◽  
pp. 1459-1486
Author(s):  
Vassilis M. Charitopoulos ◽  
Vivek Dua ◽  
Jose M. Pinto ◽  
Lazaros G. Papageorgiou
Keyword(s):  
Integer Program ◽  
Linear Constraints ◽  
Nash Bargaining ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Programming Approach ◽  
Theoretic Approach ◽  
Separable Programming ◽  
Process Industries ◽  
Game Theoretic

Abstract Under the ever-increasing capital intensive environment that contemporary process industries face, oligopolies begin to form in mature markets where a small number of companies regulate and serve the customer base. Strategic and operational decisions are highly dependent on the firms’ customer portfolio and conventional modelling approaches neglect the rational behaviour of the decision makers, with regards to the problem of customer allocation, by assuming either static competition or a leader-follower structure. In this article, we address the fair customer allocation within oligopolies by employing the Nash bargaining approach. The overall problem is formulated as mixed integer program with linear constraints and a nonlinear objective function which is further linearised following a separable programming approach. Case studies from the industrial liquid market highlight the importance and benefits of the proposed game theoretic approach.

Mixed Integer Linear Programming for UAV Trajectory Planning Problem

2014 ◽  
Vol 541-542 ◽  
pp. 1473-1477 ◽  
Author(s):  
Lei Zhang ◽  
Zhou Zhou ◽  
Fu Ming Zhang
Keyword(s):  
Real Time ◽  
Predictive Control ◽  
Trajectory Planning ◽  
Arrival Time ◽  
Linear Constraints ◽  
Mixed Integer ◽  
Planning Problem ◽  
Convex Constraints ◽  
3D Environments ◽  
On Line

This paper describes a method for vehicles flying Trajectory Planning Problem in 3D environments. These requirements lead to non-convex constraints and difficult optimizations. It is shown that this problem can be rewritten as a linear program with mixed integer linear constraints that account for the collision avoidance used in model predictive control, running in real-time to incorporate feedback and compensate for uncertainty. An example is worked out in a real-time scheme, solved on-line to compensate for the effect of uncertainty as the maneuver progresses. In particular, we compare receding horizon control with arrival time approaches.

scholarly journals A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints

2019 ◽  
Vol 44 (3) ◽  
pp. 793-820 ◽  
Author(s):  
Joey Huchette ◽  
Juan Pablo Vielma
Keyword(s):  
Piecewise Linear ◽  
Expressive Power ◽  
Complete Characterization ◽  
Linear Functions ◽  
Mixed Integer ◽  
Ordered Sets ◽  
Special Ordered Sets ◽  
Disjunctive Constraints

A framework is presented for constructing strong mixed-integer programming formulations for logical disjunctive constraints. This approach is a generalization of the logarithmically sized formulations of Vielma and Nemhauser for special ordered sets of type 2 (SOS2) constraints, and a complete characterization of its expressive power is offered. The framework is applied to a variety of disjunctive constraints, producing novel small and strong formulations for outer approximations of multilinear terms, generalizations of special ordered sets, piecewise linear functions over a variety of domains, and obstacle avoidance constraints.

HYBRID SEARCH STRATEGIES FOR HETEROGENEOUS SEARCH SPACES

2000 ◽  
Vol 09 (01) ◽  
pp. 45-57 ◽  
Author(s):  
CARLA GOMES ◽  
BART SELMAN
Keyword(s):  
Operations Research ◽  
Resource Constraints ◽  
Optimization Problems ◽  
Search Strategies ◽  
Mixed Integer ◽  
Hybrid Search ◽  
Search Spaces ◽  
Probabilistic Information ◽  
Numeric Information

Recently, there has been much interest in enhancing purely combinatorial formalisms with numerical information. For example, planning formalisms can be enriched by taking resource constraints and probabilistic information into account. The Mixed Integer Programming (MIP) paradigm from operations research provides a natural tool for solving optimization problems that combine such numeric and non-numeric information. The MIP approach relies heavily on linear program relaxations and branch-and-bound search. This is in contrast with depth-first or iterative deepening strategies generally used in artificial intelligence. We provide a detailed characterization of the structure of the underlying search spaces as explored by these search strategies. Our analysis shows that much can be gained by combining different search strategies for solving hard MIP problems, thereby leveraging each strategy's strength in terms of the combinatorial and numeric information.

Characterization of efficient frontier for mean–variance model with a drawdown constraint

2013 ◽  
Vol 220 ◽  
pp. 770-782 ◽  
Author(s):  
Haixiang Yao ◽  
Yongzeng Lai ◽  
Qinghua Ma ◽  
Huabao Zheng
Keyword(s):  
Efficient Frontier ◽  
Variance Model ◽  
Drawdown Constraint ◽  
Mean Variance

scholarly journals Dynamic Programming and Heuristic for Stochastic Uncapacitated Lot-Sizing Problems with Incremental Quantity Discount

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yuli Zhang ◽  
Shiji Song ◽  
Cheng Wu ◽  
Wenjun Yin
Keyword(s):  
Dynamic Programming ◽  
Lot Sizing ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Programming Algorithm ◽  
Quantity Discount ◽  
Path Property ◽  
Commercial Solver

The stochastic uncapacitated lot-sizing problems with incremental quantity discount have been studied in this paper. First, a multistage stochastic mixed integer model is established by the scenario analysis approach and an equivalent reformulation is obtained through proper relaxation under the decreasing unit order price assumption. The proposed reformulation allows us to extend the production-path property to this framework, and furthermore we provide a more accurate characterization of the optimal solution. Then, a backward dynamic programming algorithm is developed to obtain the optimal solution and considering its exponential computation complexity in term of time stages, we design a new rolling horizon heuristic based on the proposed property. Comparisons with the commercial solver CPLEX and other heuristics indicate better performance of our proposed algorithms in both quality of solution and run time.

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