Tree decomposition methods for the periodic event scheduling problem

This paper proposes an algorithm that decomposes the Periodic Event Scheduling Problem (PESP) into trees that can efficiently be solved. By identifying at an early stage which partial solutions can lead to a feasible solution, the decomposed components can be integrated back while maintaining feasibility if possible. If not, the modifications required to regain feasibility can be found efficiently. These techniques integrate dynamic programming into standard search methods. The performance of these heuristics are very satisfying, as the problem using publicly available benchmarks can be solved within a reasonable amount of time, in an alternative way than the currently accepted leading-edge techniques. Furthermore, these heuristics do not necessarily rely on linearity of the objective function, which facilitates the research of timetabling under nonlinear circumstances

The Ground-Set-Cost Budgeted Maximum Coverage Problem

We study the following natural variant of the budgeted maximum coverage problem: We are given a budget B and a hypergraph G = (V, E), where each vertex has a non-negative cost and a non-negative profit. The goal is to select a set of hyperedges T subseteq E such that the total cost of the vertices covered by T is at most B and the total profit of all covered vertices is maximized. Besides being a natural generalization of the well-studied maximum coverage problem, our motivation for investigating this problem originates from its application in the context of bid optimization in sponsored search auctions, such as Google AdWords. It is easily seen that this problem is strictly harder than budgeted max coverage, which means that the problem is (1-1/e)-inapproximable. The difference of our problem to the budgeted maximum coverage problem is that the costs are associated with the covered vertices instead of the selected hyperedges. As it turns out, this difference refutes the applicability of standard greedy approaches which are used to obtain constant factor approximation algorithms for several other variants of the maximum coverage problem. Our main results are as follows: - We obtain a (1 - 1/sqrt(e))/2-approximation algorithm for graphs. - We derive a fully polynomial-time approximation scheme (FPTAS) if the incidence graph of the hypergraph is a forest (i.e., the hypergraph is Berge-acyclic). We also extend this result to incidence graphs with a fixed-size feedback hyperedge node set. - We give a (1-epsilon)/(2d^2)-approximation algorithm for every epsilon > 0, where d is the maximum degree of a vertex in the hypergraph

The ground-set-cost budgeted maximum coverage problem

We study the following natural variant of the budgeted maximum coverage problem: We are given a budget B and a hypergraph G = (V,E), where each vertex has a non-negative cost and a non-negative profit. The goal is to select a set of hyperedges T c E such that the total cost of the vertices covered by T is at most B and the total profit of all covered vertices is maximized. Besides being a natural generalization of the well-studied maximum coverage problem, our motivation for investigating this problem originates from its application in the context of bid optimization in sponsored search auctions, such as Google AdWords. It is easily seen that this problem is strictly harder than budgeted max coverage, which means that the problem is (1 - 1/e)-inapproximable. The difference of our problem to the budgeted maximum coverage problem is that the costs are associated with the covered vertices instead of the selected hyperedges. As it turns out, this difference refutes the applicability of standard greedy approaches which are used to obtain constant factor approximation algorithms for several other variants of the maximum coverage problem. Our main results are as follows: We obtain a (1 - 1/ p e)/2-approximation algorithm for graphs. We derive a fully polynomial-time approximation scheme (FPTAS) if the incidence graph of the hypergraph is a forest (i.e., the hypergraph is Berge-acyclic). We also extend this result to incidence graphs with a fixed-size feedback hyperedge node set. We give a (1 - ϵ)/(2d2)-approximation algorithm for every ϵ > 0, where d is the maximum degree of a vertex in the hypergraph

Stochastic scheduling techniques for integrated optimization of catheterization laboratories and wards

In catheterization laboratories (cath labs), doctors are required to perform invasive cardiovascu-lar procedures under a variety of specific constraints .Patients undergoing a treatment in a cath lab, generally also require preparative and aftercare at one of the hospital's wards, which complicate the scheduling pro-cess significantly .Still, in practice, scheduling of procedures for cath labs is mainly done by hand, which partly can be explained by the fact that many models make simplistic assumptions that ignore the actual practical complexity of the problem, such as the inherent randomness. In this paper, we propose an Integer Linear Programming based technique that integrates optimization for both cath labs and wards, while incorporating randomness within the scheduling process .Since the natural objective function is non-linear, the key insight for applying this method is that the objective function can be linearized under specific assumptions . These models have been tested on a case study of the VU Medical Center, for which the results are shown to be effective, as useful blueprints for the daily schedules are generated according to the preference of the hospital

Stochastic scheduling techniques for integrated optimization of catheterization laboratories and wards

In catheterization laboratories (cath labs), doctors are required to perform invasive cardiovascu-lar procedures under a variety of specific constraints .Patients undergoing a treatment in a cath lab, generally also require preparative and aftercare at one of the hospital's wards, which complicate the scheduling pro-cess significantly .Still, in practice, scheduling of procedures for cath labs is mainly done by hand, which partly can be explained by the fact that many models make simplistic assumptions that ignore the actual practical complexity of the problem, such as the inherent randomness. In this paper, we propose an Integer Linear Programming based technique that integrates optimization for both cath labs and wards, while incorporating randomness within the scheduling process .Since the natural objective function is non-linear, the key insight for applying this method is that the objective function can be linearized under specific assumptions . These models have been tested on a case study of the VU Medical Center, for which the results are shown to be effective, as useful blueprints for the daily schedules are generated according to the preference of the hospital

The ground-set-cost budgeted maximum coverage problem

We study the following natural variant of the budgeted maximum coverage problem: We are given a budget B and a hypergraph G = (V,E), where each vertex has a non-negative cost and a non-negative profit. The goal is to select a set of hyperedges T c E such that the total cost of the vertices covered by T is at most B and the total profit of all covered vertices is maximized. Besides being a natural generalization of the well-studied maximum coverage problem, our motivation for investigating this problem originates from its application in the context of bid optimization in sponsored search auctions, such as Google AdWords. It is easily seen that this problem is strictly harder than budgeted max coverage, which means that the problem is (1 - 1/e)-inapproximable. The difference of our problem to the budgeted maximum coverage problem is that the costs are associated with the covered vertices instead of the selected hyperedges. As it turns out, this difference refutes the applicability of standard greedy approaches which are used to obtain constant factor approximation algorithms for several other variants of the maximum coverage problem. Our main results are as follows: We obtain a (1 - 1/ p e)/2-approximation algorithm for graphs. We derive a fully polynomial-time approximation scheme (FPTAS) if the incidence graph of the hypergraph is a forest (i.e., the hypergraph is Berge-acyclic). We also extend this result to incidence graphs with a fixed-size feedback hyperedge node set. We give a (1 - ϵ)/(2d2)-approximation algorithm for every ϵ > 0, where d is the maximum degree of a vertex in the hypergraph

Stochastic scheduling techniques for integrated optimization of catheterization laboratories and wards

In catheterization laboratories (cath labs), doctors are required to perform invasive cardiovascu-lar procedures under a variety of specific constraints .Patients undergoing a treatment in a cath lab, generally also require preparative and aftercare at one of the hospital's wards, which complicate the scheduling pro-cess significantly .Still, in practice, scheduling of procedures for cath labs is mainly done by hand, which partly can be explained by the fact that many models make simplistic assumptions that ignore the actual practical complexity of the problem, such as the inherent randomness. In this paper, we propose an Integer Linear Programming based technique that integrates optimization for both cath labs and wards, while incorporating randomness within the scheduling process .Since the natural objective function is non-linear, the key insight for applying this method is that the objective function can be linearized under specific assumptions . These models have been tested on a case study of the VU Medical Center, for which the results are shown to be effective, as useful blueprints for the daily schedules are generated according to the preference of the hospital