PURPOSE To analyze the prevalence of SARS-CoV-2 infection in patients with cancer in hospital care after implementation of institutional and governmental safety measurements. METHODS Patients with cancer routinely tested for SARS-CoV-2 RNA by nasal swab and real-time polymerase chain reaction between March 21 and May 4, 2020, were included. The results of this cancer cohort were statistically compared with the SARS-CoV-2 prevalence in the Austrian population as determined by a representative nationwide random sample study (control cohort 1) and a cohort of patients without cancer presenting to our hospital (control cohort 2). RESULTS A total of 1,688 SARS-CoV-2 tests in 1,016 consecutive patients with cancer were performed. A total of 270 of 1,016 (26.6%) of the patients were undergoing active anticancer treatment in a neoadjuvant/adjuvant and 560 of 1,016 (55.1%) in a palliative setting. A total of 53 of 1,016 (5.2%) patients self-reported symptoms potentially associated with COVID-19. In 4 of 1,016 (0.4%) patients, SARS-CoV-2 was detected. At the time of testing at our department, all four SARS-CoV-2–positive patients were asymptomatic, and two of them had recovered from symptomatic COVID-19. Viral clearance was achieved in three of the four patients 14-56 days after testing positive. The estimated odds ratio of SARS-CoV-2 prevalence between the cancer cohort and control cohort 1 was 1.013 (95% CI, 0.209 to 4.272; P = 1), and between control cohort 2 and the cancer cohort it was 18.333 (95% CI, 6.056 to 74.157). CONCLUSION Our data indicate that continuation of active anticancer therapy and follow-up visits in a large tertiary care hospital are feasible and safe after implementation of strict population-wide and institutional safety measures during the current COVID-19 pandemic. Routine SARS-CoV-2 testing of patients with cancer seems advisable to detect asymptomatic virus carriers and avoid uncontrolled viral spread.

Ordering problems assign weights to each ordering and ask to find an ordering of maximum weight. We consider problems where the cost function is either linear or quadratic. In the first case, there is a given profit if the element u is before v in the ordering. In the second case, the profit depends on whether u is before v and r is before s.The linear ordering problem is well studied, with exact solution methods based on polyhedral relaxations. The quadratic ordering problem does not seem to have attracted similar attention. We present a systematic investigation of semidefinite optimization based relaxations for the quadratic ordering problem, extending and improving existing approaches. We show the efficiency of our relaxations by providing computational experience on a variety of problem classes.

Abstract. The single-row facility layout problem (SRFLP) is an NP-hard combinatorial optimization problem that is concerned with the arrangement of n departments of given lengths on a line so as to minimize the weighted sum of the distances between department pairs. (SRFLP) is the one-dimensional version of the facility layout problem that seeks to arrange rectangular facilities so as to minimize the overall interaction cost. This paper compares the different modelling approaches for (SRFLP) and applies a recent SDP approach for general quadratic ordering problems from Hungerländer and Rendl to (SRFLP). In particular, we report optimal solutions for several (SRFLP) instances from the literature with up to 42 departments that remained unsolved so far. Secondly we significantly reduce the best known gaps and running times for large instances with up to 100 departments.

A primal-dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of Kunisch and Rendl [17]. Based on a guess of the active set, a primal-dual pair (x,α) is computed that satisfies stationarity and the complementary condition. If x is not feasible, the variables connected to the infeasibilities are added to the active set and a new primal-dual pair (x,α) is computed. This process is iterated until a primal feasible solution is generated. Then a new active set is determined based on the feasibility information of the dual variable α. Strict convexity of the quadratic problem is sufficient for the algorithm to stop after a finite number of steps with an optimal solution. Computational experience indicates that this approach also performs well in practice.

Highlights• We present a new model for the Multi-Row Facility Layout Problem.• We expresses the problem as a discrete optimization problem.• We construct a semidefinite relaxation of the discrete optimization formulation.• The proposed approach yields promising computational results.• This is the first global optimization approach for general multi-row layouts. AbstractThis paper is concerned with the Multi-Row Facility Layout Problem. Given a set of rectangular departments, a fixed number of rows, and weights for each pair of departments, the problem consists of finding an assignment of departments to rows and the positions of the departments in each row so that the total weighted sum of the center-to-center distances between all pairs of departments is minimized. We show how to extend our recent approach for the Space-Free Multi-Row Facility Layout Problem to general Multi-Row Facility Layout as well as some special cases thereof. To the best of our knowledge this is the first global optimization approach for multi-row layout that is applicable beyond the double-row case. A key aspect of our proposed approach is a model for multi-row layout that expresses the problem as a discrete optimization problem, and thus makes it possible to exploit the underlying combinatorial structure. In particular we can explicitly control the number and size of the spaces between departments. We construct a semidefinite relaxation of the discrete optimization formulation and present computational results showing that the proposed approach gives promising results for several variants of multi-row layout problems on a variety of benchmark instances.