Scheduling surgical cases in a day-care environment: a branch-and-price approach.

In this paper we will investigate how to sequence surgical cases in a day-care facility so that multiple objectives are simultaneously optimized. The limited availability of resources and the occurrence of medical precautions, such as an additional cleaning of the operating room after the surgery of an infected patient, are taken into account. A branch-and-price methodology will be introduced in order to develop both exact and heuristic algorithms. In this methodology, column generation is used to optimize the linear programming formulation of the scheduling problem. Both a dynamic programming approach and an integer programming approach will be specified in order to solve the pricing problem. The column generation procedure will be combined with various branching schemes in order to guarantee the integrality of the solutions. The resulting solution procedures will be thoroughly tested and evaluated using real-life data of the surgical day-care center at the university hospital Gasthuisberg in Leuven (Belgium). Computational results will be summarized and conclusions will eventually be formulated.Branch-and-price; Column generation; Health care operations; Scheduling;

A Genetic Algorithm based Approach for Topological Optimization of Interconnection Networks

AbstractThe paper addresses the two terminal reliability while designing the interconnection networks. Thus a topological optimization problem is defined as the existence of at least a reliable path between a pair of nodes satisfying the predefined cost of the network. A new method based on Genetic Algorithm is proposed to solve the above said problem. In the proposed method the chromosome as well as the genes are efficiently encoded so that the cross over provides the optimal solution with better convergence rate. The reliability of some benchmark interconnection networks are evaluated by the proposed method. The population size and the computational time of the said networks as reported in this paper ensures that the proposed method converges to it's optimal solution in very few cpu secondss, while maximizing the value of the reliability of the said network to a greater extent

Analytical Models in Rail Transportation: An Annotated Bibliography

Not AvailableThis research has been supported, in part, by the U.S. Department of Transportation under contract DOT-TSC-1058, Transportation Advanced Research Program (TARP)

Exact models for selection problems: from clinical trials to network design

Discrete optimization is becoming an increasingly important tool for solving problems in the real world. The matching problem and the network design problem are two well studied selection problems in this area. They can be considered as modelling relations between nodes of a bi-graph or a graph, respectively. Using acute stroke trials as a context, the assignment algorithm is utilized to investigate a complex relationship between the overall degree of individual matching, the size of samples, and the quality of matching on variables. It is concluded that the post-hoc individual matching in parallel group randomized clinical trials cannot be recommended as a technique for treatment effect estimation. Based on the concept of the transshipment problem we proposed a mixed integer programming model to solve the asymmetric traveling salesman problems. The formulation is extendable to other transportation scheduling problems which are related to the traveling salesman problem (TSP) such as the Multiple TSP (m-TSP) and the Selective TSP (STSP). In addition to avoiding any cycles and being easy to implement, the model has a reasonable order of space complexity. It can be built on either a directed graph or an undirected graph. The reserve network design problem is a variation of the STSP which maximizes some utilities subject to various constraints. These constraints include a budget limitation and spatial attributes such as connectivity and compactness. The proposed model achieves the contiguity and to some extent compactness attributes. It does this without incurring the problem of sub-tours and requiring any regular shape assumptions. Furthermore, where full connectivity is not required, the model enables the trade-off between the number of contiguous areas and utility to be determined easily. The combinatorial structure of the reserve network design problem places it in the category of NP-hard problems which have exponential time complexity. We explored approaches to reduce the computational effort and introduced an approach with improved efficiency. Using this approach, the experimental results show the solution time significantly reduced on average

Application of mathematical programming techniques to power system optimization

Imperial Users onl

Green Supply Chain Design: A Lagrangian Approach

The expansion of supply chains into global networks has drastically increased the distance travelled along shipping lanes in a logistics system. Inherently, the increase in travel distances produces increased carbon emissions from transport vehicles. When increased emissions are combined with a carbon tax or emissions trading system, the result is a supply chain with increased costs attributable to the emission generated on the transportation routes. Most traditional supply chain design models do not take emissions and carbon costs into account. Hence, there is a need to incorporate emission costs into a supply chain optimization model to see how the optimal supply chain configuration may be affected by the additional expenses. This thesis presents a mathematical programming model for the design of green supply chains. The costs of carbon dioxide (CO2) emissions were incorporated in the objective function, along with the fixed and transportation costs that are typically modeled in traditional facility location models. The model also determined the unit flows between the various nodes of the supply chain, with the objective of minimizing the total cost of the system by strategically locating warehouses throughout the network. The literature shows that CO2 emissions produced by a truck are dependent on the weight of the vehicle and can be modeled using a concave function. Hence, the carbon emissions produced along a shipping lane are dependent upon the number of units and the weight of each unit travelling between the two nodes. Due to the concave nature of the emissions, the addition of the emission costs to the problem formulation created a nonlinear mixed integer programming (MIP) model. A solution algorithm was developed to evaluate the new problem formulation. Lagrangian relaxation was used to decompose the problem by echelon and by potential warehouse site, resulting in a problem that required less computational effort to solve and allowed for much larger problems to be evaluated. A method was then suggested to exploit a property of the relaxed formulation and transform the problem into a linear MIP problem. The solution method computed the minimum cost for a complete network that would satisfy all the needs of the customers. A primal heuristic was introduced into the Lagrangian algorithm to generate feasible solutions. The heuristic utilized data from the Lagrangian subproblems to produce good feasible solutions. Due to the many characteristics of the original problem that were carried through to the subproblems, the heuristic produced very good feasible solutions that were typically within 1% of the Lagrangian bound. The proposed algorithm was evaluated through a number of tests. The rigidity of the problem and cost breakdown were varied to assess the performance of the solution method in many situations. The test results indicated that the addition of emission costs to a network can change the optimal configuration of the supply chain. As such, this study concluded that emission costs should be considered when designing supply chains in jurisdictions with carbon costs. Furthermore, the tests revealed that in regions without carbon costs it may be possible to significantly reduce the emissions produced by the supply chain with only a small increase in the cost to operate the system

Robust optimization for network-based resource allocation problems under uncertainty

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering; and, (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007.Includes bibliographical references (p. 129-131).We consider large-scale, network-based, resource allocation problems under uncertainty, with specific focus on the class of problems referred to as multi-commodity flow problems with time-windows. These problems are at the core of many network-based resource allocation problems. Inherent data uncertainty in the problem guarantees that deterministic optimal solutions are rarely, if ever, executed. Our work examines methods of proactive planning, that is, robust plan generation to protect against future uncertainty. By modeling uncertainties in data corresponding to service times, resource availability, supplies and demands, we can generate solutions that are more robust operationally, that is, more likely to be executed or easier to repair when disrupted. The challenges are the following: approaches to achieve robustness 1) can be extremely problem-specific and not general; 2) suffer from issues of tractability; or 3) have unrealistic data requirements. We propose in this work a modeling and algorithmic framework that addresses the above challenges.(cont.) Our modeling framework involves a decomposition scheme that separates problems involving multi-commodity flows with time-windows into routing (that is, a routing master problem) and scheduling modules (that is, a scheduling sub-problem), and uses an iterative scheme to provide feedback between the two modules, both of which are more tractable than the integrated model. The master problem has the structure of a multi-commodity flow problem and the sub-problem is a set of network flow problems. This decomposition allows us to capture uncertainty while maintaining tractability. Uncertainty is captured in part by the master problem and in part by the sub-problem. In addition to solving problems under uncertainty, our decomposition scheme can also be used to solve large-scale resource allocation problems without uncertainty. As proof-of-concept, we apply our approach to a vehicle routing and scheduling problem and compare its solutions to those of other robust optimization approaches. Finally, we propose a framework to extend our robust, decomposition approach to the more complex problem of network design.by Lavanya Marla.S.M