Sequential testing of a series system in batches

In this thesis, we study a new extension of the Sequential Testing problem with a modified cost structure that allows performing of some tests in batches. As in the Sequential Testing problem, we assume a certain dependence between the test results and the conclusion. Namely, we stop testing once a positive result is obtained or all tests are negative. Our extension, motivated by health care applications, considers fixed cost associated with executing a batch of tests, with the general notion that the more tests are performed in batches, the smaller the contribution of the total fixed cost of the sequential testing process. The goal is to minimize the expected cost of testing by finding the optimal choice and sequence of the batches available. We separately study two different cases for this problem; one where only some subsets of all tests can be performed together and one with no restrictions over tests. We analyze the problem, develop solution algorithms and evaluate the performance of the algorithms on random problem instances for both both cases of the problem

Approximation algorithms for sequential batch-testing of series systems

We introduce and study a generalization of the classic sequential testing problem, asking to identify the correct state of a given series system that consists of independent stochastic components. In this setting, costly tests are required to examine the state of individual components, which are sequentially tested until the correct system state can be uniquely identified. The goal is to propose a policy that minimizes the expected testing cost, given a-priori probabilistic information on the stochastic nature of each individual component. Unlike the classic setting, where variables are tested one after the other, we allow multiple tests to be conducted simultaneously, at the expense of incurring an additional set-up cost. The main contribution of this article consists in showing that the batch testing problem can be approximated in polynomial time within factor inline image, for any fixed inline image. In addition, we explain how, in spite of its highly nonlinear objective function, the batch testing problem can be formulated as an approximate integer program of polynomial size, while blowing up its expected cost by a factor of at most inline image. Finally, we conduct extensive computational experiments, to demonstrate the practical effectiveness of these algorithms as well as to evaluate their limitations

Sequential testing in batches

Özgür Özlük (MEF Author)We study a new extension of the Sequential Testing problem with a modified cost structure that allows performing of some tests in batches. As in the Sequential Testing problem, we assume a certain dependence between the test results and the conclusion. Namely, we stop testing once a positive result is obtained or all tests are negative. Our extension, motivated by health care applications, considers a fixed cost associated with executing a batch of tests, with the general notion that the more tests are performed in batches, the smaller the total contribution of fixed costs to the sequential testing process. The goal is to minimize the expected cost of testing by finding the optimal choice and sequence of the batches available. The resulting NP-hard model is a variation of the set partitioning problem. We propose various heuristic algorithms for the effective solution of the problem and then demonstrate the performances of the algorithms through extensive numerical experiments.WOS:000402127000006Scopus - Affiliation ID: 60105072Science Citation Index ExpandedQ2ArticleUluslararası işbirliği ile yapılmayan - HAYIRHaziran2017YÖK - 2016-1

Crew constrained home care routing problem with time windows

This paper addresses the Vehicle Routing Problem (VRP) of a Home Health Care (HCC) service provider that serves patients requesting different types of care. In this problem, HCC services are provided by two types of personnel, nurses and health care aides, and the number of each type of personnel is limited. Each patient must be visited exactly once even if her servicing requires both personnel and is associated with a strict time window during which the service must be provided. We first present the 0-1 mixed integer programming formulation of the problem. Since the arising VRP is NP-hard, we then develop a Variable Neighborhood Search (VNS) algorithm to solve it. Next, we randomly generate a set of small-sized instances based on Solomon's benchmark problems for the VRP with Time-Windows and solve them using IBM ILOG CPLEX. To test the effectiveness of the VNS algorithm, we compare these solutions to those achieved by VNS. Our preliminary experiments show that VNS is able to find good results fast, yet the HCC crew constraints may complicate the problem