Models for national energy policy analysis and planning

Two energy models have been developed that represent the national energy system. One of these is a ‘fuel model’ that includes only the major conversions and investments in the energy sector, covers a time span of 15 years and uses linear programming (LP) techniques. The other is an ‘energy model’ that includes the activities in the energy sector in considerable detail, covers a time span of 24 years, and uses mixed integer programming (MIP) formulation. The Fuel Model has been applied to Turkey for the years 1960–1975, while the ‘Energy Model’ has been used to analyze possible development for the years 1976–2000. Some of the results pertaining to the validation and analysis runs have been presented along with experiences in implementation of the models.     

Linear Programming Models for the User and System Optimal Dynamic Network Design Problem: Formulations,Comparisons and Extensions

In this paper we formulate a network design model in which the traffic flows satisfy dynamic user equilibrium conditions for a single destination. The model presented here incorporates the Cell Transmission Model (CTM); a traffic flow model capable of capturing shockwaves and link spillovers. Comparisons are made between the properties of the Dynamic User equilibrium Network Design Problem (DUE NDP) and an existing Dynamic System Optimal (DSO) NDP formulation. Both network design models have different objective functions with similar constraint sets which are linear and convex. Numerical demonstrations are made on multiple networks to demonstrate the efficacy of the model and demonstrate important differences between the DUE and DSO NDP approaches. In addition, the flexibility of the approach is demonstrated by extending the formulation to account for demand uncertainty. This is formulated as a stochastic programming problem and initial test results are demonstrated on test networks. It is observed that not accounting for demand uncertainty explicitly, provides sub-optimal solution to the DUE NDP problem.     

Hybrid-LP: Finding advanced starting points for simplex,and pivoting LP methods

The simplex method has proven its efficiency in practice for linear programming (LP) problems of various types and sizes. However, its theoretical worst-case complexity in addition to its poor performance for very large-scale LP problems has driven researchers to develop alternative methods for LP problems. In this paper, we develop the hybrid-LP; a two-phase approach for solving LP problems. Rather than following a path of extreme points on the boundary of the feasible region as in the simplex method, the first phase of the hybrid-LP moves through the interior of the feasible region to obtain an improved and advanced initial basic feasible solution (BFS). Then, in the second phase simplex or other LP methods can be used to find the optimal solution.