An improved primal-dual approximation algorithm for the k-means problem with penalties

In the k-means problem with penalties, we are given a data set ${\cal D} \subseteq \mathbb{R}^\ell $ of n points where each point $j \in {\cal D}$ is associated with a penalty cost p j and an integer k. The goal is to choose a set ${\rm{C}}S \subseteq {{\cal R}^\ell }$ with |CS| ≤ k and a penalized subset ${{\cal D}_p} \subseteq {\cal D}$ to minimize the sum of the total squared distance from the points in D / D p to CS and the total penalty cost of points in D p , namely $\sum\nolimits_{j \in {\cal D}\backslash {{\cal D}_p}} {d^2}(j,{\rm{C}}S) + \sum\nolimits_{j \in {{\cal D}_p}} {p_j}$ . We employ the primal-dual technique to give a pseudo-polynomial time algorithm with an approximation ratio of (6.357+ε) for the k-means problem with penalties, improving the previous best approximation ratio 19.849+∊ for this problem given by Feng et al. in Proceedings of FAW (2019).

Design of robust layout for unequal area dynamic facility layout problems with flexible bays structure

Purpose The purpose of this paper is to develop a mathematical model for the design of robust layout for unequal area-dynamic facility layout problem with flexible bay structure (UA-DFLP with FBS) and test the suitability of generated robust layout in a dynamic environment. Design/methodology/approach This research adopts formulation of a mathematical model for generating a single layout for unequal area facility layout problems with flexible bay structure under dynamic environment. The formulated model for the robust layout formation is solved by developing a simulated annealing algorithm. The proposed robust approach model for UA-DFLP with FBS is validated by conducting numerical experiments on standard UA-DFLPs reported in the literature. The suitability of the generated robust layout in a dynamic environment is tested with total penalty cost criteria. Findings The proposed model has given a better solution for some UA-DFLPs with FBS in comparison with the adaptive approach’s solution reported in the literature. The total penalty cost is within the specified limit given in the literature, for most of the layouts generated for UA-DFLPs with FBS. In the proposed model, there is no rearrangement of facilities in various periods of planning horizon and thus no disruptions in operations. Research limitations/implications The present work has limitations that when the area and aspect ratio of the facilities are required to change from one period to another, then it is not possible to make application of the robust approach-based formulation to the dynamic environment facility layout problems. Practical implications Rearrangement of facilities in adaptive approach disrupts the operations whereas in the proposed approach no disruption of production. The FBS approach is more suitable for layout planning where proper aisle structure is required. The solution of the proposed approach helps to create a proper aisle structure in the detailed layout plan. Thus, easy interaction of the material handling equipment, men and materials is possible. Originality/value This paper proposes a mathematical formulation for the design of robust layout for UA-FLPs with FBS in a dynamic environment and an efficient simulated annealing algorithm as its solution procedure. The proposed robust approach generates a single layout for the entire planning horizon. This approach is more useful for facilities which are difficult/sensitive to relocate in various periods of the planning horizon.

Glosa do wyroku Trybunału Konstytucyjnego z dnia 11 czerwca 2019 r. (P 20/17, OTK-A 2019, poz. 29)

<p>The author agrees with the Constitutional Tribunal’s opinion that Article 87 § 1 of the Penal Code to the extent that it imposes an obligation on the court to combine imprisonment and restriction of liberty and to impose a total penalty of deprivation of liberty after converting the penalty of restriction of liberty into imprisonment is inconsistent with the Constitution of the Republic of Poland. In addition, the author raised the problem of <em>ratio legis</em> of Article 87 of the Penal Code and indicated why the deficiencies in regulation were noticed so late in the case law.</p>

Production Scheduling considering Outsourcing Options and Carrier Costs

We consider a single-machine scheduling problem with outsourcing options in an environment where the cost information of the downstream is available via some information sharing technologies. The due date is assigned to the position differently from the traditional due date. Each job can be processed in-house or outsourced. Note that, for cost saving, as many due dates as the number of outsourced jobs should be canceled. An in-house job incurs a stepwise penalty cost for tardiness, and an outsourced job incurs an outsourcing cost. Thus, the objective is to minimize the total penalty and outsourcing cost minus the total profit from cost savings. We show that the problem is weakly NP-hard and investigate some polynomially solvable cases. Due to the high complexity of the dynamic programming, we developed heuristics and verified their performance through numerical experiments.

Proportionate Flow Shop Scheduling with Rejection

We consider the problem of scheduling [Formula: see text] jobs with rejection on a set of [Formula: see text] machines in a proportionate flow shop system where the job processing times are machine-independent. The goal is to find a schedule to minimize the scheduling cost of all accepted jobs plus the total penalty of all rejected jobs. Two variations of the scheduling cost are considered. The first is the maximum tardiness and the second is the total weighted completion time. For the first problem, we first show that it is [Formula: see text]-hard, then we construct a pseudo-polynomial time algorithm to solve it and an [Formula: see text] time for the case where the jobs have the same processing time. For the second problem, we first show that it is [Formula: see text]-hard, then we design [Formula: see text] time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time.

Abstract 027: Comparing Changes in Hospital Readmission Rates by Frequency and Total Financial Penalties Over the First Five Years

Objective: To compare changes in risk-standardized readmission rates (RSRRs) for acute myocardial infarction (AMI), congestive heart failure (CHF), and pneumonia (PN) between hospitals receiving more frequent or higher total penalties under the Hospital Readmission Reduction Program (HRRP) over the first five years (fiscal year [FY] 2013-2017). Methods: Using publically available HRRP penalty data, we categorized hospitals as receiving penalties in all five years vs. fewer than five years. We also summed the penalty amounts over the first five years by hospital and hospitals based on their quartile of summed penalty amount vs. receiving no penalties. Using generalized linear regression, we estimated the average change in RSRRs for AMI, CHF, and PN by penalty frequency (all years vs. not all years) and amount (quartile of total penalty vs. no penalty) between FY 2013 and FY 2017, adjusting for hospital characteristics in the American Hospital Association Annual Survey and Medicare Impact File (both 2009-2011). Results: There were 3,346 hospitals eligible for HRRP penalties between FY 2013 and FY 2017. From this sample, 1,938 hospitals had RSRRs for AMI in both years, 2,821 hospitals had RSRRs for CHF, and 2,876 hospitals had RSRRs for PN. The average change in RSRRs for AMI, CHF, and PN was -2.8%, -2.8%, and -1.4%, respectively. Declines in RSRRs were greater for hospitals receiving penalties in all five years compared to hospitals penalized fewer than five years in AMI (-0.9%, p<0.001), CHF (-0.9%, p<0.001), and PN (-0.4%, p<0.001). Similarly, hospitals receiving the highest total penalties in the first five years of the HRRP had the largest decline in RSRRs compared to hospitals never receiving a penalty for AMI (-1.2%, p<0.001) and CHF (-0.9%, p<0.001), but not for PN (-0.2%, p = not significant). Conclusions: Hospitals receiving more frequent and higher total penalties had greater reductions in RSRRs for AMI and CHF, and to a lesser extent for PN. Our findings suggest that HRRP penalties did not limit hospitals’ ability to reduce readmissions.

Batch Scheduling with Proportional-Linear Deterioration and Outsourcing

We consider the bounded parallel-batch scheduling with proportional-linear deterioration and outsourcing, in which the actual processing time is pj=αj(A+Dt) or pj=αjt. A job is either accepted and processed in batches on a single machine by manufactures themselves or outsourced to the third party with a certain penalty having to be paid. The objective is to minimize the maximum completion time of the accepted jobs and the total penalty of the outsourced jobs. For the pj=αj(A+Dt) model, when all the jobs are released at time zero, we show that the problem is NP-hard and present a pseudo-polynomial time algorithm, respectively. For the pj=αjt model, when the jobs have distinct m (<n) release dates, we provide a dynamic programming algorithm, where n is the number of jobs.