George Kozanidis

A mixed integer knapsack model for allocating funds to highway safety improvements

This paper presents a methodology for allocating funds to highway safety improvements. Besides the commonly used binary variables that represent discrete interventions at specific points of a highway, continuous variables are introduced to represent the lengths of a highway over which continuous improvements, such as pavement resurfacing or lighting, are implemented. The problem is formulated as a mixed integer knapsack model with linear multiple choice constraints. Some insight into its solution properties is provided and an efficient branch and bound algorithm is proposed for its solution. A case study that illustrates the application of the model is also presented.

Performance Evaluation of an Automatic Transfer Line with WIP Scrapping During Long Failures

We develop a model of a failure-prone, bufferless, paced, automatic transfer line in which material flows through a number of workstations in series, receiving continuous processing along each workstation. When a workstation fails, it stops operating, and so do all the other workstations upstream of it. The quality of the material trapped in the stopped workstations deteriorates with time. If this material remains immobilized beyond a certain critical time, its quality becomes unacceptable and it must be scrapped. We develop analytical expressions for important system performance measures for two cases. In the first case, the in-process material has no memory of the quality deterioration that it experienced during previous stoppages, whereas in the second case it has. In both cases, we assume that the workstation uptimes and downtimes follow memoryless distributions. We use the analytical expressions to numerically study the effect of system parameters on system performance. To evaluate the memoryless assumption, we compare the performance of the original model to that of a modified model in which the workstation downtimes do not follow memoryless distributions. The performance of the modified model is obtained via simulation.

A branch & bound algorithm for the 0-1 mixed integer knapsack problem with linear multiple choice constraints

This paper presents a branch and bound (B&B) algorithm for the 0-1 mixed integer knapsack problem with linear multiple choice constraints. The formulation arose in an application to transportation management for allocating funds to highway improvements. Several model properties are developed and utilized to design a B&B solution algorithm. The algorithm solves at each node of the B&B tree a linear relaxation using an adaptation of an existing algorithm for the linear multiple choice knapsack problem. The special relationship between the parent and children subproblems is exploited by the algorithm. This results in high efficiency and low storage space requirements. The worst case complexity of the algorithm is analyzed and computational results that demonstrate its efficiency in the average case are reported.

An exact solution algorithm for maximizing the fleet availability of a unit of aircraft subject to flight and maintenance requirements

We address the Flight and Maintenance Planning (FMP) problem, i.e., the problem of deciding which available aircraft to fly and for how long, and which grounded aircraft to perform maintenance operations on in a group of aircraft that comprise a unit. The aim is to maximize the unit fleet availability over a multi-period planning horizon, while also ensuring that certain flight and maintenance requirements are satisfied. Heuristic approaches that are used in practice to solve the FMP problem often perform poorly, generating solutions that are far from the optimum. On the other hand, the exact optimization models that have been developed to tackle the problem handle small problems effectively, but tend to be computationally inefficient for larger problems, such as the ones that arise in practice. With these in mind, we develop an exact solution algorithm for the FMP problem, which is capable of identifying the optimal solution of considerably large realistic problems in reasonable computational times. The algorithm solves suitable relaxations of the original problem, utilizing valid cuts that guide the search towards the optimal solution. We present extensive experimental results, which demonstrate that the algorithms performance on realistic problems is superior to that of two popular commercial optimization software packages, whereas the opposite is true for a class of problems with special characteristics that deviate considerably from those of realistic problems. The important conclusion of this research is that the proposed algorithm, complemented by generic optimization software, can handle effectively a large variety of FMP problem instances.

Solving the linear multiple choice knapsack problem with two objectives: profit and equity

Abstract In this paper, we study an extension of the Linear Multiple Choice Knapsack (LMCK) Problem that considers two objectives. The problem can be used to find the optimal allocation of an available resource to a group of disjoint sets of activities, while also ensuring that a certain balance on the resource amounts allocated to the activity sets is attained. The first objective maximizes the profit incurred by the implementation of the considered activities. The second objective minimizes the maximum difference between the resource amounts allocated to any two sets of activities. We present the mathematical formulation and explore the fundamental properties of the problem. Based on these properties, we develop an efficient algorithm that obtains the entire nondominated frontier. The algorithm is more efficient than the application of the general theory of multiple objective linear programming (MOLP), although there is a close underlying relationship between the two. We present theoretical findings which provide insight into the behavior of the algorithm, and report computational results which demonstrate its efficiency for randomly generated problems.

Recovery mechanisms in day-ahead electricity markets with non-convexities - Part I: Design and evaluation methodology

In centralized day-ahead electricity markets with marginal pricing, unit commitment costs and capacity constraints give rise to non-convexities which may result in losses to some of the participating generating units. Therefore, a recovery mechanism is required to compensate them. In this paper, we present and analyze several recovery mechanisms that result in recovery payments after the market is cleared. Each of these mechanisms results in a different type and/or amount of payments for each participating unit that exhibits losses. We also propose a methodology for evaluating the bidding strategy behavior of the participating units for each mechanism. This methodology is based on the execution of a numerical procedure aimed at finding joint optimal bidding strategies of the profit-maximizing units. In a companion follow-up paper (Part II), we apply this methodology to evaluate the performance and incentive compatibility of the suggested recovery mechanisms on a simplified test case model of the Greek electricity market.

Energy-reserve markets with non-convexities: An empirical analysis

In this paper, we address the design of a joint energy — reserve electricity market with non-convexities which are due to the fixed costs and capacity constraints of the generation units. Motivated by the relevant literature [1]-[5], we state a bid recovery mechanism that applies to the day-ahead scheduling problem, which is modeled as a mixed-integer linear programming problem. However, the particularly complex nature of the problem, especially if we consider it in its full scale, makes it extremely difficult if not impossible to analytically assess the market operation, under various market designs. Therefore, we proceed to an empirical analysis that aims to provide useful insight in evaluating the incentive compatibility of pricing and compensation schemes based on marginal pricing theory. In order to understand the bidding behavior of the participants and exhibit the proposed methodology, we present an illustrative example, based on Greeces day-ahead energy — reserve market.

Recovery mechanisms in day-ahead electricity markets with non-convexities - Part II: Implementation and numerical evaluation

In centralized day-ahead electricity markets with marginal pricing, unit commitment costs and capacity constraints give rise to non-convexities which may result in losses to some of the participating generating units. To compensate them for these losses, a recovery mechanism is required. In Part I of this two-part paper, we present certain recovery mechanisms that result in recovery payments after the market is cleared. We also propose a methodology for evaluating the bidding strategy behavior of the participating units for each mechanism. In this paper (Part II), we apply this methodology to evaluate the performance and incentive compatibility properties of each recovery mechanism on a test case model representing the Greek joint energy/reserve day-ahead electricity market. Lastly, we perform sensitivity analysis with respect to key parameters and assumptions and we provide directions for further research.

The linear multiple choice knapsack problem with equity constraints

In this paper, we introduce an important variation of a well known problem, the linear multiple choice knapsack problem with equity constraints, which finds application in the allocation of funds to highway improvements. The multiple choice constraints are used to model the interactions that arise among different improvements. The equity constraints are introduced to ensure a balance on the budget amounts allocated to different sets of improvements. We present the mathematical formulation and show that this problem structure has several fundamental properties. These are used to develop an optimal two phase greedy algorithm for its solution. We report computational results which indicate that the algorithm is more efficient than a commercial linear programming package and the outperformance increases with problem size.

Recovery mechanisms in a joint energy/reserve day-ahead electricity market with non-convexities

The goal of this paper is to evaluate the incentive compatibility of several cost- and bid-based recovery mechanisms that may be implemented in a wholesale electricity market to make the generation units whole in the presence of non-convexities, which are due to unit commitment costs and capacity constraints. To this end, we simulate the bidding behavior of the participants in a simplified model of the Greek joint energy/reserve day-ahead electricity market, where we assume that the players (units) participate as potential price-makers in a non-cooperative game with complete information that is repeated for many rounds. The results suggest that a mechanism based on bid recovery with a regulated cap is quite promising.