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Lebanese American University, Lebanon

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4 Papers

Algorithmic View of Online Prize-collecting Optimization Problems

Topics: Scheduling and Planning; Operational Research; Problem Solving

Authors: Christine Markarian ¹ and Abdul Nasser El-Kassar ²

Affiliations: ¹ Department of Engineering and Information Technology, University of Dubai, U.A.E. , ² Department of Information Technology and Operations Management, Lebanese American University, Lebanon

Digital Object Identifier: 10.5220/0010471507440751

Proceedings of ICEIS 2021, ISBN: 978-989-758-509-8

Quick Abstract

Online algorithms have been a cornerstone of research in network design problems. Unlike in classical offline algorithms, the input to an online algorithm is revealed in portions over time and the online algorithm reacts to each portion while targeting a given optimization goal. Online algorithms are deployed in real-world optimization problems in which provably good decisions are expected in the present without knowing the future. In this paper, we consider a well-established branch of online optimization problems, known as online prize-collecting problems, in which the online algorithm may reject some input portions at the cost of paying an associated penalty. These appear in business applications in which a company decides to lose some customers by paying an associated penalty. Particularly, we study the online prize-collecting variants of three well-known optimization problems: Connected Dominating Set, Vertex Cover, and Non-metric Facility Location, namely, Online Prize-collecting Connected Dominating Set (OPC-CDS), Online Prize-collecting Vertex Cover (OPC-VC), and Online Prize-collecting Non-metric Facility Location (OPC-NFL), respectively. We propose the first online algorithms for these variants and evaluate them using competitive analysis, the standard framework to measure online algorithms, in which the online algorithm is measured against the optimal offline algorithm that knows the entire input sequence in advance and is optimal.

An Algorithmic Approach to Online Multi-Facility Location Problems

Topics: Project Management; Optimization; Game Theory; Network Optimization; Resource Allocation

Authors: Christine Markarian ¹ , Abdul-Nasser Kassar ² and Manal Yunis ²

Digital Object Identifier: 10.5220/0010212200290035

Proceedings of ICORES 2021, ISBN: 978-989-758-485-5

Quick Abstract

Facility Location problems ask to optimally place facilities with respect to some objective so that all clients requesting a facility service are served. These are one of the most well-studied optimization problems spanning many research areas, such as operations research, computer science, and management science. Classical algorithmic study of Facility Location problems is based on the assumption that clients need to be served with one facility each. Nevertheless, in many real-world applications, facilities experience disruptions and to overcome their failures, a robust service is desired. To obtain this, clients are served with more than one facility, and this is commonly represented by an additional input parameter. The aim of the algorithm is then to provide a robust service to all clients while minimizing costs. This is known as the Multi-Facility Location problem (MFL), a well-known optimization problem, studied in the offline setting in which the entire input sequence is known to the algorithm in advance. In this paper, we address MFL in the online setting, in which client requests are not known in advance but revealed over time. We refer to it as the Online Multi-Facility Location problem (OMFL) and study its metric and non-metric variants. We propose the first online algorithms for these variants and measure their performance using the standard notion of competitive analysis. The latter is a worst-case analysis that compares the cost of the online algorithm to that of the optimal offline algorithm that is assumed to know all demands in advance.

A Production Model with Continuous Demand for Imperfect Finished Items Resulting from the Quality of Raw Material

Topics: Decision Analysis; Industrial Engineering; Inventory Theory

Authors: Abdul-Nasser El-Kassar , Manal Yunis and Mohammad Nasr El Dine

Affiliation: Information Technology & Operations Management Department, Lebanese American University, Lebanon

Digital Object Identifier: 10.5220/0009181702630269

Proceedings of ICORES 2020, ISBN: 978-989-758-396-4

Quick Abstract

The purpose of this paper is to present a production process in which the quality of a single type of raw material used to produce the finished product is considered. The common modeling approach followed by previous research is based on discarding the imperfect quality items of raw material. In this paper, we consider the case where both perfect and imperfect quality items of raw are used in the production process resulting in two types of qualiy of the finished product. It is assumed that both perfect and imperfect quality items of the finished product have continuous demand. This modeling approach has yet to be deployed. Two models that depend on the length inventory cycle of each type of the finished product are developed. Numerical examples are provided to illustrate the determination of the optimal production quantity. Theoretical and practical implications are discussed, and recommendations are presented.

Online Deterministic Algorithms for Connected Dominating Set & Set Cover Leasing Problems

Topics: Optimization; Game Theory; Resource Allocation

Authors: Christine Markarian ¹ and Abdul-Nasser Kassar ²

Affiliations: ¹ Department of Mathematical Sciences, Haigazian University, Beirut, Lebanon , ² Department of Information Technology and Operations Management, Lebanese American University, Beirut, Lebanon

Digital Object Identifier: 10.5220/0008866701210128

Proceedings of ICORES 2020, ISBN: 978-989-758-396-4

Quick Abstract

Connected Dominating Set (CDS) and Set Cover (SC) are classical optimization problems that have been widely studied in both theory and practice, as many variants and in different settings, motivated by applications in wireless and social networks. In this paper, we consider the online setting, in which the input sequence arrives in portions over time and the so-called online algorithm needs to react to each portion. Online algorithms are measured using the notion of competitive analysis. An online algorithm A is said to have competitive ratio r, where r is the worst-case ratio, over all possible instances of a given minimization problem, of the solution constructed by A to the solution constructed by an offline optimal algorithm that knows the entire input sequence in advance. Online Connected Dominating Set (OCDS) (Hamann et al., 2018) is an online variant of CDS that is currently solved by a randomized online algorithm with optimal competitive ratio. We present in this paper the first deterministic online algorithm for OCDS, with optimal competitive ratio. We further introduce generalizations of OCDS, in the leasing model (Meyerson, 2005) and in the multiple hop model (Coelho et al., 2017), and design deterministic online algorithms for each of these generalizations. We also propose the first deterministic online algorithm for the leasing variant of SC (Abshoff et al., 2016), that is currently solved by a randomized online algorithm.