Robust Appointment Scheduling

Health care providers are under tremendous pressure to reduce costs and increase quality of their services. It has long been recognized that well-designed appointment systems have the potential to improve utilization of expensive personnel and medical equipment and to reduce waiting times for patients. In a widely influential survey on outpatient scheduling, Cayirli and Veral (2003) concluded that the "biggest challenge for future research will be to develop easy-to-use heuristics." We analyze the appointment scheduling problem from a robust-optimization perspective, and we establish the existence of a closed-form optimal solution--arguably the simplest and best `heuristic\u27 possible. In case the order of patients is changeable, the robust optimization approach yields a novel formulation of the appointment scheduling problem as that of minimizing a concave function over a supermodular polyhedron. We devise the first constant-factor approximation algorithm for this case

Algorithms for discrete, non-linear and robust optimization problems with applications in scheduling and service operations

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 101-107).This thesis presents efficient algorithms that give optimal or near-optimal solutions for problems with non-linear objective functions that arise in discrete, continuous and robust optimization. First, we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination of more than one function. Examples of such problems include those in which the objective function is a product or ratio of two or more linear functions, parallel machine scheduling problems with the makespan objective, robust versions of weighted multi-objective optimization problems, and assortment optimization problems with logit choice models. For many of these problems, we give the first fully polynomial time approximation scheme using our framework. Next, we present approximation schemes for optimizing a rather general class of non-linear functions of low rank over a polytope. In contrast to existing results in the literature, our approximation scheme does not require the assumption of quasi-concavity of the objective function. For the special case of minimizing a quasi-concave function of low-rank, we give an alternative algorithm which always returns a solution which is an extreme point of the polytope. This algorithm can also be used for combinatorial optimization problems where the objective is to minimize a quasi-concave function of low rank. We also give complexity-theoretic results with regards to the inapproximability of minimizing a concave function over a polytope. Finally, we consider the problem of appointment scheduling in a robust optimization framework. The appointment scheduling problem arises in many service operations, for example health care. For each job, we are given its minimum and maximum possible execution times. The objective is to find an appointment schedule for which the cost in the worst case scenario of the realization of the processing times of the jobs is minimized. We present a global balancing heuristic, which gives an easy to compute closed form optimal schedule when the underage costs of the jobs are non-decreasing. In addition, for the case where we have the flexibility of changing the order of execution of the jobs, we give simple heuristics to find a near-optimal sequence of the jobs.by Shashi Mittal.Ph.D

Optimization of FFF process parameters by naked mole-rat algorithms with enhanced exploration and exploitation capabilities

Fused filament fabrication (FFF) has numerous process parameters that influence the mechanical strength of parts. Hence, many optimization studies are performed using conventional tools and algorithms. Although studies have also been performed using advanced algorithms, limited research has been reported in which variants of the naked mole-rat algorithm (NMRA) are implemented for solving the optimization issues of manufacturing processes. This study was performed to scrutinize optimum parameters and their levels to attain maximum impact strength, flexural strength and tensile strength based on five different FFF process parameters. The algorithm yielded better results than other studies and successfully achieved a maximum response, which may be helpful to enhance the mechanical strength of FFF parts. The study opens a plethora of research prospects for implementing NMRA in manufacturing. Moreover, the findings may help identify critical parametric levels for the fabrication of customized products at the commercial level and help to attain the objectives of Industry 4.0

An FPTAS for optimizing a class of low-rank functions over a polytope

We present a fully polynomial time approximation scheme (FPTAS) for optimizing a very general class of non-linear functions of low rank over a polytope. Our approximation scheme relies on constructing an approximate Pareto-optimal front of the linear functions which constitute the given low-rank function. In contrast to existing results in the literature, our approximation scheme does not require the assumption of quasi-concavity on the objective function. For the special case of quasi-concave function minimization, we give an alternative FPTAS, which always returns a solution which is an extreme point of the polytope. Our technique can also be used to obtain an FPTAS for combinatorial optimization problems with non-linear objective functions, for example when the objective is a product of a fixed number of linear functions. We also show that it is not possible to approximate the minimum of a general concave function over the unit hypercube to within any factor, unless P = NP. We prove this by showing a similar hardness of approximation result for supermodular function minimization, a result that may be of independent interest

Amplified centrosomes and mitotic index display poor concordance between patient tumors and cultured cancer cells

Centrosome aberrations (CA) and abnormal mitoses are considered beacons of malignancy. Cancer cell doubling times in patient tumors are longer than in cultures, but differences in CA between tumors and cultured cells are uncharacterized. We compare mitoses and CA in patient tumors, xenografts, and tumor cell lines. We find that mitoses are rare in patient tumors compared with xenografts and cell lines. Contrastingly, CA is more extensive in patient tumors and xenografts (~35–50% cells) than cell lines (~5–15%), although CA declines in patient-derived tumor cells over time. Intratumoral hypoxia may explain elevated CA in vivo because exposure of cultured cells to hypoxia or mimicking hypoxia pharmacologically or genetically increases CA, and HIF-1α and hypoxic gene signature expression correlate with CA and centrosomal gene signature expression in breast tumors. These results highlight the importance of utilizing low-passage-number patient-derived cell lines in studying CA to more faithfully recapitulate in vivo cellular phenotypes

Association of acute toxic encephalopathy with litchi consumption in an outbreak in Muzaffarpur, India, 2014: a case-control study

Background Outbreaks of unexplained illness frequently remain under-investigated. In India, outbreaks of an acute neurological illness with high mortality among children occur annually in Muzaffarpur, the country’s largest litchi cultivation region. In 2014, we aimed to investigate the cause and risk factors for this illness. Methods In this hospital-based surveillance and nested age-matched case-control study, we did laboratory investigations to assess potential infectious and non-infectious causes of this acute neurological illness. Cases were children aged 15 years or younger who were admitted to two hospitals in Muzaffarpur with new-onset seizures or altered sensorium. Age-matched controls were residents of Muzaffarpur who were admitted to the same two hospitals for a non-neurologic illness within seven days of the date of admission of the case. Clinical specimens (blood, cerebrospinal fluid, and urine) and environmental specimens (litchis) were tested for evidence of infectious pathogens, pesticides, toxic metals, and other non-infectious causes, including presence of hypoglycin A or methylenecyclopropylglycine (MCPG), naturally-occurring fruit-based toxins that cause hypoglycaemia and metabolic derangement. Matched and unmatched (controlling for age) bivariate analyses were done and risk factors for illness were expressed as matched odds ratios and odds ratios (unmatched analyses). Findings Between May 26, and July 17, 2014, 390 patients meeting the case definition were admitted to the two referral hospitals in Muzaffarpur, of whom 122 (31%) died. On admission, 204 (62%) of 327 had blood glucose concentration of 70 mg/dL or less. 104 cases were compared with 104 age-matched hospital controls. Litchi consumption (matched odds ratio [mOR] 9·6 [95% CI 3·6 – 24]) and absence of an evening meal (2·2 [1·2–4·3]) in the 24 h preceding illness onset were associated with illness. The absence of an evening meal significantly modified the effect of eating litchis on illness (odds ratio [OR] 7·8 [95% CI 3·3–18·8], without evening meal; OR 3·6 [1·1–11·1] with an evening meal). Tests for infectious agents and pesticides were negative. Metabolites of hypoglycin A, MCPG, or both were detected in 48 [66%] of 73 urine specimens from case-patients and none from 15 controls; 72 (90%) of 80 case-patient specimens had abnormal plasma acylcarnitine profiles, consistent with severe disruption of fatty acid metabolism. In 36 litchi arils tested from Muzaffarpur, hypoglycin A concentrations ranged from 12·4 μg/g to 152·0 μg/g and MCPG ranged from 44·9 μg/g to 220·0 μg/g. Interpretation Our investigation suggests an outbreak of acute encephalopathy in Muzaffarpur associated with both hypoglycin A and MCPG toxicity. To prevent illness and reduce mortality in the region, we recommended minimising litchi consumption, ensuring receipt of an evening meal and implementing rapid glucose correction for suspected illness. A comprehensive investigative approach in Muzaffarpur led to timely public health recommendations, underscoring the importance of using systematic methods in other unexplained illness outbreaks

Statistical Machine Translation: Robust parameter estimation from noisy corpus

Abstract. In this report, we describe our study of effect of noise on parameter estimation for statistical machine translation. So far, no study has been done on this topic, even though the algorithm used for parameter estimation for statistical machine translation (the EM algorithm) is known to be highly sensitive to noise. We present in detail the experiments performed to observe the influence of noise on parameter estimation, and the various methods investigated to counter this effect.