A new adaptive algorithm for convex quadratic multicriteria optimization

We present a new adaptive algorithm for convex quadratic multicriteria optimization. The algorithm is able to adaptively refine the approximation to the set of efficient points by way of a warm-start interior-point scalarization approach. Numerical results show that this technique is faster than a standard method used for this problem

Scheduling Jobs with Variable Job Processing Times on Unrelated Parallel Machines

m unrelated parallel machines scheduling problems with variable job processing times are considered, where the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to determine the optimal resource allocation and the optimal schedule to minimize a total cost function that dependents on the total completion (waiting) time, the total machine load, the total absolute differences in completion (waiting) times on all machines, and total resource cost. If the number of machines is a given constant number, we propose a polynomial time algorithm to solve the problem

BALANCING TRADE-OFFS IN ONE-STAGE PRODUCTION WITH PROCESSING TIME UNCERTAINTY

Stochastic production scheduling faces three challenges, first the inconsistencies among key performance indicators (KPIs), second the trade-offs between the expected return and the risk for a portfolio of KPIs, and third the uncertainty in processing times. Based on two inconsistent KPIs of total completion time (TCT) and variance of completion times (VCT), we propose our trade-off balancing (ToB) heuristic for one-stage production scheduling. Through comprehensive case studies, we show that our ToB heuristic with preference =0.0:0.1:1.0 efficiently and effectively addresses the three challenges. Moreover, our trade-off balancing scheme can be generalized to balance a number of inconsistent KPIs more than two. Daniels and Kouvelis (DK) proposed a scheme to optimize the worst-case scenario for stochastic production scheduling and proposed the endpoint product (EP) and endpoint sum (ES) heuristics to hedge against processing time uncertainty. Using 5 levels of coefficients of variation (CVs) to represent processing time uncertainty, we show that our ToB heuristic is robust as well, and even outperforms the EP and ES heuristics on worst-case scenarios at high levels of processing time uncertainty. Moreover, our ToB heuristic generates undominated solution spaces of KPIs, which not only provides a solid base to set up specification limits for statistical process control (SPC) but also facilitates the application of modern portfolio theory and SPC techniques in the industry

TRADE-OFF BALANCING FOR STABLE AND SUSTAINABLE OPERATING ROOM SCHEDULING

The implementation of the mandatory alternative payment model (APM) guarantees savings for Medicare regardless of participant hospitals ability for reducing spending that shifts the cost minimization burden from insurers onto the hospital administrators. Surgical interventions account for more than 30% and 40% of hospitals total cost and total revenue, respectively, with a cost structure consisting of nearly 56% direct cost, thus, large cost reduction is possible through efficient operation management. However, optimizing operating rooms (ORs) schedules is extraordinarily challenging due to the complexities involved in the process. We present new algorithms and managerial guidelines to address the problem of OR planning and scheduling with disturbances in demand and case times, and inconsistencies among the performance measures. We also present an extension of these algorithms that addresses production scheduling for sustainability. We demonstrate the effectiveness and efficiency of these algorithms via simulation and statistical analyses

The completion time variance problem and its extensions.

Ng Chi To.Thesis (Ph.D.)--Chinese University of Hong Kong, 1996.Includes bibliographical references (leaves 169-173).Acknowledgements --- p.iAbstract --- p.iiChapter Chapter 1 --- INTRODUCTION --- p.1Chapter 1.1 --- Problem Formulation and Motivation --- p.1Chapter 1.2 --- Past Research Works --- p.3Chapter 1.3 --- Results of the Study --- p.5Chapter 1.4 --- Organization of the Thesis --- p.7Chapter Part I --- THE CTV PROBLEM --- p.9Chapter Chapter 2 --- A GENERALIZATION OF SCHRAGE'S CONJEC- TURE --- p.10Chapter 2.1 --- Schrage's Conjecture --- p.10Chapter 2.2 --- Generalization --- p.13Chapter Chapter 3 --- ASYMPTOTIC OPTIMALITY --- p.15Chapter 3.1 --- Optimal Sequences under a Symmetric Structure --- p.17Chapter 3.2 --- An Upper Bound for the Relative Error --- p.21Chapter 3.3 --- Asymptotical Probabilistic Analysis --- p.25Chapter Chapter 4 --- ADDITIONAL FINDINGS --- p.37Chapter Chapter 5 --- THE BEST V-SHAPED SEQUENCE --- p.46Chapter 5.1 --- Transformation of the CTV Problem to a Boolean Optimization Problem --- p.47Chapter 5.2 --- Minimization of the Expected CTV among All the V-shaped Fixed Sequences --- p.48Chapter Chapter 6 --- THE WORST CASE ANALYSIS --- p.65Chapter 6.1 --- A Lower Bound for the CTV Problem --- p.66Chapter 6.2 --- A Worst Case Bound --- p.71Chapter Part II --- EXTENSIONS --- p.75Chapter Chapter 7 --- A MORE GENERAL MODEL --- p.76Chapter 7.1 --- Some Basic Concepts --- p.76Chapter 7.2 --- Problem Description --- p.78Chapter 7.3 --- Applications and Difficulties --- p.80Chapter Chapter 8 --- THE ZERO STARTING PROBLEM --- p.83Chapter 8.1 --- Problem Transformation --- p.85Chapter 8.2 --- Properties --- p.88Chapter 8.3 --- Algorithm A and Promising Solutions --- p.93Chapter 8.4 --- Time Complexity of Algorithm A --- p.94Chapter Chapter 9 --- PROBABILISTIC ANALYSIS OF PROMISING SO- LUTIONS --- p.95Chapter 9.1 --- Promising Solutions under a Symmetric Structure --- p.95Chapter 9.2 --- An Upper Bound for the Relative Error of Promising Solutions --- p.100Chapter 9.3 --- Probabilistic Analysis on the Relative Error of Promising Solutions --- p.106Chapter Chapter 10 --- CONCLUDING REMARKS AND FUTURE RESEARCH WORK --- p.118Appendix A Preliminary Results for Analysis --- p.122Appendix B Proofs of Some Lemmas --- p.127Appendix C Proofs of Some Theorems --- p.149Appendix D Proofs of Some Properties --- p.160Appendix E An Alternative to Completion Time Variance --- p.167Bibliography --- p.16