Four decades of research on the open-shop scheduling problem to minimize the makespan

One of the basic scheduling problems, the open-shop scheduling problem has a broad range of applications across different sectors. The problem concerns scheduling a set of jobs, each of which has a set of operations, on a set of different machines. Each machine can process at most one operation at a time and the job processing order on the machines is immaterial, i.e., it has no implication for the scheduling outcome. The aim is to determine a schedule, i.e., the completion times of the operations processed on the machines, such that a performance criterion is optimized. While research on the problem dates back to the 1970s, there have been reviving interests in the computational complexity of variants of the problem and solution methodologies in the past few years. Aiming to provide a complete road map for future research on the open-shop scheduling problem, we present an up-to-date and comprehensive review of studies on the problem that focuses on minimizing the makespan, and discuss potential research opportunities

Theoretical and Computational Research in Various Scheduling Models

Nine manuscripts were published in this Special Issue on “Theoretical and Computational Research in Various Scheduling Models, 2021” of the MDPI Mathematics journal, covering a wide range of topics connected to the theory and applications of various scheduling models and their extensions/generalizations. These topics include a road network maintenance project, cost reduction of the subcontracted resources, a variant of the relocation problem, a network of activities with generally distributed durations through a Markov chain, idea on how to improve the return loading rate problem by integrating the sub-tour reversal approach with the method of the theory of constraints, an extended solution method for optimizing the bi-objective no-idle permutation flowshop scheduling problem, the burn-in (B/I) procedure, the Pareto-scheduling problem with two competing agents, and three preemptive Pareto-scheduling problems with two competing agents, among others. We hope that the book will be of interest to those working in the area of various scheduling problems and provide a bridge to facilitate the interaction between researchers and practitioners in scheduling questions. Although discrete mathematics is a common method to solve scheduling problems, the further development of this method is limited due to the lack of general principles, which poses a major challenge in this research field

Scheduling Series-Parallel Orders Subject to 0/1-Communication Delays

We consider the problem P}&;| prec},cij&;{0,1}|κ of scheduling jobs with arbitrary processing times on sufficiently many parallel processors subject to series-parallel precedence constraints and 0/1-communication delays in order to minimize a regular performance measure κ. Such schedules without processor restrictions are used for generating approximate solutions for a restricted number of processors

Resource Allocation in Networked and Distributed Environments

A central challenge in networked and distributed systems is resource management: how can we partition the available resources in the system across competing users, such that individual users are satisfied and certain system-wide objectives of interest are optimized? In this thesis, we deal with many such fundamental and practical resource allocation problems that arise in networked and distributed environments. We invoke two sophisticated paradigms -- linear programming and probabilistic methods -- and develop provably-good approximation algorithms for a diverse collection of applications. Our main contributions are as follows. Assignment problems: An assignment problem involves a collection of objects and locations, and a load value associated with each object-location pair. Our goal is to assign the objects to locations while minimizing various cost functions of the assignment. This setting models many applications in manufacturing, parallel processing, distributed storage, and wireless networks. We present a single algorithm for assignment which generalizes many classical assignment schemes known in the literature. Our scheme is derived through a fusion of linear algebra and randomization. In conjunction with other ideas, it leads to novel guarantees for multi-criteria parallel scheduling, broadcast scheduling, and social network modeling. Precedence constrained scheduling: We consider two precedence constrained scheduling problems, namely sweep scheduling and tree scheduling, which are inspired by emerging applications in high performance computing. Through a careful use of randomization, we devise the first approximation algorithms for these problems with near-optimal performance guarantees. Wireless communication: Wireless networks are prone to interference. This prohibits proximate network nodes from transmitting simultaneously, and introduces fundamental challenges in the design of wireless communication protocols. We develop fresh geometric insights for characterizing wireless interference. We combine our geometric analysis with linear programming and randomization, to derive near-optimal algorithms for latency minimization and throughput capacity estimation in wireless networks. In summary, the innovative use of linear programming and probabilistic techniques for resource allocation, and the novel ways of connecting them with application-specific ideas is the pivotal theme and the focal point of this thesis

Research in Supply Chain Management: Issue and Area Development

Today the study of supply chain management (SCM) is growing rapidly and provides a great opportunity to do research both empirical and theoretical development. Research opportunities in SCM has been reviewed by many researchers and grouped into many categories. This paper contains a review of research SCM and classify into 7 categories, namely (1) SCM Operational Management & Strategy, (2) knowledge management, (3) Relationship Management, (4) Information Technology in SCM, (5) Supply Chain Design, Logistics & Infrastructure, (6) Global Issues, (7) Environment, Legal & Regulations. The issue in each category and research opportunities will be discussed in this paper. Keywords: Supply Chain Management, Research Opportunities in SCM, Issue in SC