Multi-agent Online Scheduling: MMS Allocations for Indivisible Items

We consider the problem of fairly allocating a sequence of indivisible items that arrive online in an arbitrary order to a group of n agents with additive normalized valuation functions. We consider both the allocation of goods and chores and propose algorithms for approximating maximin share (MMS) allocations. When agents have identical valuation functions the problem coincides with the semi-online machine covering problem (when items are goods) and load balancing problem (when items are chores), for both of which optimal competitive ratios have been achieved. In this paper, we consider the case when agents have general additive valuation functions. For the allocation of goods, we show that no competitive algorithm exists even when there are only three agents and propose an optimal 0.5-competitive algorithm for the case of two agents. For the allocation of chores, we propose a (2-1/n)-competitive algorithm for n>=3 agents and a square root of 2 (approximately 1.414)-competitive algorithm for two agents. Additionally, we show that no algorithm can do better than 15/11 (approximately 1.364)-competitive for two agents.Comment: 29 pages, 1 figure (to appear in ICML 2023

Worker scheduling with induced learning in a semi-on-line setting

Scheduling is a widely researched area with many interesting fields. The presented research deals with a maintenance area in which preventative maintenance and emergency jobs enter the system. Each job has varying processing time and must be scheduled. Through learning the operators are able to expand their knowledge which enables them to accomplish more tasks in a limited time. Two MINLP models have been presented, one for preventative maintenance jobs alone, and another including emergency jobs. The emergency model is semi-on-line as the arrival time is unknown. A corresponding heuristic method has also been developed to decrease the computational time of the MINLP models. The models and heuristic were tested in several areas to determine their flexibility. It has been demonstrated that the inclusion of learning has greatly improved the efficiency of the workers and of the system

The composition of first-year engineering curricula and its relationships to matriculation models and institutional characteristics

The preparation of technically excellent and innovative engineering graduates urges for a reform of the engineering curriculum to meet critical challenges in society (National Academy of Engineering, 2005). An examination of the current engineering curricula is needed to offer a baseline to further discuss if the curriculum reform meets the critical challenges. Meanwhile, concern about engineering retention prioritizes a review of the first-year engineering curricula. The existing literature does not include a nationwide examination of the first-year engineering curricula and introductory engineering courses. This study aspired to fill the gap by providing a detail description of the composition of first-year engineering curricula and introductory engineering courses of all ABET EAC-accredited programs. Furthermore, this study investigated the degree to which first-year engineering curricula and institutional characteristics varied by the matriculation policies of engineering programs. ^ To this end, this study analyzed the recommended first-year course sequences of 1,969 engineering programs and descriptions of 2,222 first-year engineering courses at all 408 U.S. institutions with ABET EAC-accredited programs. Keywords extracted from the engineering course descriptions were classified using a revised First-Year Engineering Course Classification Scheme (Reid, Reeping, & Spingola, 2013). In addition, institutional characteristics of 408 institutions grouped by matriculation models were examined. ^ There were five major findings. First, engineering courses took up 14-17% of total credit hours in the first year. Most first-year engineering courses were mandatory instead of elective or optional. Mathematics and science still formed the basis of the early engineering curriculum by accounting for more than half of the first-year credit hours. Second, the composition of first-year engineering curricula, the composition of first-year engineering courses, and the time when the first engineering course was required all varied by matriculation models. Third, topics related to engineering technologies and tools were listed most frequently in first-year engineering course descriptions, followed by topics related to design and the engineering profession. Topics related to global interest were seldom listed. Fourth, while first-year course composition varied by matriculation model, the most frequently listed topics were shared by programs with varied matriculation models, suggesting that content selection of first-year engineering courses was homogenous nationally. Lastly, institutions with different matriculation models had distinct characteristics, demonstrating the existence of relationships between institution-level and unit-level variables shown in the Model of Academic Plans in Context (Lattuca & Stark, 2009). ^ Findings of this study addressed fundamental questions of engineering education research, and had the potential to help program administrators and instructors with program and curriculum planning purposes

Packing, Scheduling and Covering Problems in a Game-Theoretic Perspective

Many packing, scheduling and covering problems that were previously considered by computer science literature in the context of various transportation and production problems, appear also suitable for describing and modeling various fundamental aspects in networks optimization such as routing, resource allocation, congestion control, etc. Various combinatorial problems were already studied from the game theoretic standpoint, and we attempt to complement to this body of research. Specifically, we consider the bin packing problem both in the classic and parametric versions, the job scheduling problem and the machine covering problem in various machine models. We suggest new interpretations of such problems in the context of modern networks and study these problems from a game theoretic perspective by modeling them as games, and then concerning various game theoretic concepts in these games by combining tools from game theory and the traditional combinatorial optimization. In the framework of this research we introduce and study models that were not considered before, and also improve upon previously known results.Comment: PhD thesi

Identical parallel machine scheduling problems: structural patterns, bounding techniques and solution procedures

The work is about fundamental parallel machine scheduling problems which occur in manufacturing systems where a set of jobs with individual processing times has to be assigned to a set of machines with respect to several workload objective functions like makespan minimization, machine covering or workload balancing. In the first chapter of the work an up-to-date survey on the most relevant literature for these problems is given, since the last review dealing with these problems has been published almost 20 years ago. We also give an insight into the relevant literature contributed by the Artificial Intelligence community, where the problem is known as number partitioning. The core of the work is a universally valid characterization of optimal makespan and machine-covering solutions where schedules are evaluated independently from the processing times of the jobs. Based on these novel structural insights we derive several strong dominance criteria. Implemented in a branch-and-bound algorithm these criteria have proved to be effective in limiting the solution space, particularly in the case of small ratios of the number of jobs to the number of machines. Further, we provide a counter-example to a central result by Ho et al. (2009) who proved that a schedule which minimizes the normalized sum of squared workload deviations is necessarily a makespan-optimal one. We explain why their proof is incorrect and present computational results revealing the difference between workload balancing and makespan minimization. The last chapter of the work is about the minimum cardinality bin covering problem which is a dual problem of machine-covering with respect to bounding techniques. We discuss reduction criteria, derive several lower bound arguments and propose construction heuristics as well as a subset sum-based improvement algorithm. Moreover, we present a tailored branch-and-bound method which is able to solve instances with up to 20 bins

A note on semi-online machine covering

In the machine cover problem we are given m machines and n jobs to be assigned (scheduled) so that the smallest load of a machine is as large as possible. A semi-online algorithm is given in advance the optimal value of the smallest load for the given instance, and then the jobs are scheduled one by one as they arrive, without any knowledge of the following jobs. We present a deterministic algorithm with competitive ratio 11/6 ≤ 1.834 for machine covering with any number of machines and a lower bound showing that no deterministic algorithm can have a competitive ratio below 43/24 ≥ 1.791

A note on semi-online machine covering

In the machine cover problem we are given m machines and n jobs to be assigned (scheduled) so that the smallest load of a machine is as large as possible. A semi-online algorithm is given in advance the optimal value of the smallest load for the given instance, and then the jobs are scheduled one by one as they arrive, without any knowledge of the following jobs.We present a deterministic algorithm with competitive ratio 11/6 = 1.834 for machine covering with any number of machines and a lower bound showing that no deterministic algorithm can have a competitive ratio below 43/24 = 1.791

A note on semi-online machine covering

In the machine cover problem we are given m machines and n jobs to be assigned (scheduled) so that the smallest load of a machine is as large as possible. A semi-online algorithm is given in advance the optimal value of the smallest load for the given instance, and then the jobs are scheduled one by one as they arrive, without any knowledge of the following jobs.We present a deterministic algorithm with competitive ratio 11/6 = 1.834 for machine covering with any number of machines and a lower bound showing that no deterministic algorithm can have a competitive ratio below 43/24 = 1.791