Resource augmentation in load balancing

We consider load-balancing in the following setting. The on-line algorithm is allowed to use $n$ machines, whereas the optimal off-line algorithm is limited to $m$ machines, for some fixed $m < n$. We show that while the greedy algorithm has a competitive ratio which decays linearly in the inverse of $n/m$, the best on-line algorithm has a ratio which decays exponentially in $n/m$. Specifically, we give an algorithm with competitive ratio of 1+2^{- frac{n{m (1- o (1)), and a lower bound of 1+ e^{ - frac{n{m (1+ o(1)) on the competitive ratio of any randomized algorithm. We also consider the preemptive case. We show an on-line algorithm with a competitive ratio of 1+ e^{ - frac{n{m (1+ o(1)). We show that the algorithm is optimal by proving a matching lower bound. We also consider the non-preemptive model with temporary tasks. We prove that for $n=m+1$, the greedy algorithm is optimal. (It is not optimal for permanent tasks.

On Discrete Hyperbox Packing

Bin packing is a very important and popular research area in the computer science field. Past work showed many good and real-world packing algorithms. How- ever, due to the complexity of the problem in multiple-dimensional bin packing, also called hyperbox packing, we need more practical packing algorithms for its real-world applications. In this dissertation, we extend 1D packing algorithms to hyperbox packing prob- lems via a general framework that takes two inputs of a 1D packing algorithm and an instance of hyperbox packing problem and outputs a hyperbox packing algorithm. The extension framework significantly enriches the family of hyperbox-packing algorithms, generates many framework-based algorithms, and simultaneously calls for the analysis for those algorithms. We also analyze the performance of a couple of framework-based algorithms from two perspectives of worst-case performance and average-case performance. In worst- case analysis, we use the worst-case performance ratio as our metric and analyze the relationship of the ratio of framework-based algorithms and that of the corresponding 1D algorithms. We also compare their worst-case performance against two baselines: strip optimal algorithms and optimal algorithms. In average-case analysis, we use expected waste as a metric, analyze the waste of optimal hyperbox packing algorithms, and estimate the asymptotic forms of the waste for framework-based algorithms

Healthcare Logistics: the art of balance

Healthcare management is a very complex and demanding business. The pro - cesses involved – operational, tactical and strategic – are extremely divers, sophisticated, and we see medical-technological advancements following on each other’s heels at breathtaking speed. And then there is the constant great pressure exerted from many sides: ever-increasing needs and demands from patients and society, thinking about organizations, growing competition, necessity to incorporate these rapidly succeeding medical-technological advancements into the organization, strict cost containment, growing demand for healthcare, and a constant tightening of budgets. These developments force healthcare managers in the individual organizations to find a balance between said developments, the feasibilities of organization in question, and the desired healthcare outcomes in an ever-changing world. The search for individual organizational balances requires that the world of professional competencies, i.e. the clinicians, and the world of healthcare managers should speak the same language when weighing the various developments and translating the outcomes into organizational choices. For the clinicians to make the right choices they must be facilitated to appraise the effects of their choices on organizational outcomes. Likewise, the healthcare managers’ decision- making process should include the effects on the medical policies pursued by the individual clinicians in the own organization. This thesis places a focus on developing methods for allocation of hospital resources within a framework that enables clinicians and healthcare managers to balance the developments on the various levels, thus providing a basis for policymaking

1 Applying Extra-Resource Analysis to Load Balancing

Previously, extra-resource analysis has been used to argue that certain on-line algorithms are good choices for solving specific problems because these algorithms perform well with respect to the optimal off-line algorithm when given extra resources. We now introduce a new application for extra-resource analysis: deriving a qualitative divergence between off-line and on-line algorithms. We do this for the load balancing problem, the problem of assigning a list of jobs on m identical machines to minimize the makespan, the maximum load on any machine. We analyze the worst-case performance of on-line and off-line approximation algorithms relative to the performance of the optimal off-line algorithm when the approximation algorithms have k extra machines. Our main results are the following: The Longest-Processing-Time (LPT) algorithm will produce a schedule with makespan no larger than that of the optimal off-line algorithm if LPT has at least (4m − 1)/3 machines while the optimal off-line algorithm has m machines. In contrast, no on-line algorithm can guarantee the same with any number of extra machines