Number Of Job Types Research Articles

Polynomiality for Bin Packing with a Constant Number of Item Types

We consider the bin packing problem with d different item sizes s i and item multiplicities a i , where all numbers are given in binary encoding. This problem formulation is also known as the one-dimensional cutting stock problem . In this work, we provide an algorithm that, for constant d , solves bin packing in polynomial time. This was an open problem for all d\ge 3 . In fact, for constant d our algorithm solves the following problem in polynomial time: Given two d -dimensional polytopes P and Q , find the smallest number of integer points in P whose sum lies in Q . Our approach also applies to high multiplicity scheduling problems in which the number of copies of each job type is given in binary encoding and each type comes with certain parameters such as release dates, processing times, and deadlines. We show that a variety of high multiplicity scheduling problems can be solved in polynomial time if the number of job types is constant.

A branch-and-bound algorithm for makespan minimization in differentiation flow shops

This article considers a differentiation flow-shop model, where the jobs are divided into various categories, each of which consists of two stages of operations. All products should be processed first on the single common machine at stage 1. At the second stage, each individual product proceeds to a dedicated machine according to its type. The problem of makespan minimization under the setting with two product types is known to be strongly NP hard. This article considers an arbitrary number of job types by developing a lower bound and two dominance rules, based upon which branch-and-bound algorithms are designed. Computational experiments are carried out to examine the performance of the proposed properties. The statistics show that the proposed properties can substantially reduce the computing efforts required for finding optimal solutions.

Occupational Characteristics and Patterns as Risk Factors for Parkinson's Disease (P07.133)

Objective: To evaluate the role of personality as indicated by occupational choices and employment patterns in the risk for Parkinson9s disease (PD). Background PD has been associated with employment in certain fields. Most occupational studies focused on toxic exposures as potential causal explanations of these associations. However, PD also has been associated with personality characteristics including decreased risk-taking and novelty-seeking that may influence occupational choices and patterns. Design/Methods: In-person interviews were conducted to assess occupational histories and early-adult personality indicators among 89 PD patients and 99 controls recruited from academic medical clinics. Logistic regressions controlling for age, sex and education examined associations between occupational characteristics, personality and risk for PD. Results: PD cases had fewer jobs in their lifetime than controls (mean ± SD for cases = 4.38 ± 2.20; mean ± SD for controls = 5.00 ± 2.26; p=0.03). However, there was no association between the number of categories of employment or the duration of the primary job and PD. Among women, PD was positively associated with more complex work with people (OR=0.69 (95% CI 0.53-0.89)), representing a 95% increased risk for PD comparing women whose jobs required the greatest complexity of work with those requiring the least complexity with people. Female cases also did less complex work with things compared with controls (OR=1.45 (95% CI 1.11-1.88)), translating into a 13-fold increased risk for PD among women whose work involved the least complex work with things compared with the most. The number of jobs and number of job types was associated with taking more activity risks as a young adult. Conclusions: Cases with PD held fewer lifetime jobs compared with controls. Occupational complexity was associated with the risk for PD among women, but not men. Further consideration of the possible influence of personality on occupational choices is warranted. Disclosure: Dr. Borenstein has nothing to disclose. Dr. Sullivan has nothing to disclose. Dr. Wang has nothing to disclose. Dr. Zesiewicz has received personal compensation for activities with Teva Pharmaceuticals as a speaker. Dr. Zesiewicz has received research support from Bobby Allison Ataxia Research Center, National Ataxia Foundation, Astellas Pharmaceuticals, Pfizer, Friedreich9s Ataxia Research Alliance, Takeda, Biovail Corporation, Southern Illinois University, and Allon Pharmaceuticals. Dr. Brownlee has received personal compensation for activities with Amylin Pharmaceuticals, Eli Lilly & Company, and Boehringer Ingelheim Pharmaceuticals, Inc. Dr. Mortimer has received personal compensation for activities with Davies, McFarland, and Carroll.

A PTAS FOR MINIMIZING TOTAL COMPLETION TIME OF BOUNDED BATCH SCHEDULING

We consider a batch processing system {pi : i = 1, 2,…,n} where pi is the processing time of job i, and up to B jobs can be processed together such that the handling time of a batch is the longest processing time among jobs in the batch. The number of job types m is not fixed and all the jobs are released at the same time. Jobs are executed non-preemptively. Our objective is to assign jobs to batches and sequence the batches so as to minimize the total completion time. The best previously known result is a 2–approximation algorithm. In this paper, we establish the first polynomial time approximation scheme (PTAS) for the problem.