Single machine scheduling problems: early-tardy penalties

Ankara : The Department of Industrial Engineering and The Institute of Engineering and Science of Bilkent Univ., 1993.Thesis (Ph.D.) -- Bilkent University, 1993.Includes bibliographical references leaves 120-126.The primary concern of this dissertation is to analyze single machine total earliness and tardiness scheduling problems with different due dates and to develop both a dynamic programming formulation for its exact solution and heuristic algorithms for its approximate solution within acceptable limits. The analyses of previous works on the single machine earliness and tardiness scheduling problems reveal that the research mainly focused on a restricted problem type in which no idle time insertion is allowed in the schedule. This study deals with the general case where idle time insertion is allowed whenever necessary. Even though this problem is known to be A'P-hard in the ordinary sense, there is still a need to develop an optimizing algorithm through dynamic programming formulation. Development of such an algorithm is necessary for further identifying an approximation scheme for the problem which is an untouched issue in the earliness and tardiness scheduling theory. Furthermore, the developed dynamic programming formulation is extended to an incomplete dynamic programming which forms the core of one of the heuristic procedure proposed.A second aspect of this study is to investigate two special structures for the different due dates, namely Equal-Slack and Total-Work-Content rules, and to discuss computational complexity of the problem with these special structures. Consequently, solution procedures which bear on the characteristics of the special due date structures are proposed. This research shows that the total earliness and tardiness scheduling problem with Equal-Slack rule is A/’P-hard but can be solvable in polynomial time in certain cases. Moreover, a very efficient heuristic algorithm is proposed for the problem with the other due date structure and the results of this part leads to another heuristic algorithm for the general due date structure. Finally, a lower bound procedure is presented which is motivated from the structure of the optimal solution of the problem. This lower bound is compared with another lower bound from the literature and it is shown that it performs well on randomly generated problems.Oguz, CeydaPh.D

Single machine earliness-tardiness scheduling problems using the equal-slack rule

The purpose of this paper is to analyze a special case of the non-pre-emptive single machine scheduling problem where the distinct due dates for each job are related to processing times according to the Equal-Slack rule. The scheduling objective is to minimize the sum of earliness and tardiness penalties. After determining some properties of the problem, the unrestricted case is shown to be equivalent to a polynomial time solvable problem, whereas the restricted case is shown to be NP-hard, and suggestions are made for further research

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

Parallel Machine Scheduling with Additional Resources: A Lagrangian-Based Constraint Programming Approach

This study deals with an unrelated parallel machine scheduling problem with one additional resource type (e. g., machine operators). The objective is to minimize the total completion time. After giving the integer programming model of the problem, a Lagrangian relaxation problem (LRP) is introduced by relaxing the constraint set concerning the additional resource. A general subgradient optimization procedure is applied to a series of LRPs to maximize the lower bound for the original problem. To generate efficient upper bounds for the original problem, a constraint programming (CP) model is applied by taking the LRP solutions as input regarding the machine assignments. For the problem, a pure CP model is also developed to evaluate its performance. All the solution approaches are evaluated through a range of test problems. The initial computational results show that Lagrangian-based CP approach produces promising results especially for larger problem sizes

Hybrid Flow-Shop: a Memetic Algorithm Using Constraint-Based Scheduling for Efficient Search

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Variable neighborhood search for minimum cost berth allocation

The berth allocation problem is to allocate space along the quayside to incoming ships at a container terminal in order to minimize some objective function. We consider minimization of total costs for waiting and handling as well as earliness or tardiness of completion, for all ships. We assume ships can arrive at any given time, i.e., before or after the berths become available. The resulting problem, which subsumes several previous ones, is expressed as a linear mixed 0-1 program. As it turns out to be too time-consuming for exact solution of instances of realistic size, a Variable Neighborhood Search (VNS) heuristic is proposed, and compared with Multi-Start (MS), a Genetic Search algorithm (GA) and a Memetic Search algorithm (MA). VNS provides optimal solutions for all instances solved to optimality in a previous paper of the first two authors and outperforms MS, MA and GA on large instances.

Metaheuristic Approaches to the Hybrid Flow Shop Scheduling Problem with a Cost-Related Criterion

In the paper, the flow-shop scheduling problem with parallel machines at each stage (machine center) is studied. For each job its release and due date as well as a processing time for its each operation are given. The scheduling criterion consists of three parts: the total weighted earliness, the total weighted tardiness and the total weighted waiting time. The criterion takes into account the costs of storing semi-manufactured products in the course of production and ready-made products as well as penalties for not meeting the deadlines stated in the conditions of the contract with customer. To solve the problem, three constructive algorithms and three metaheuristics (based one Tabu Search and Simulated Annealing techniques) are developed and experimentally analyzed. All the proposed algorithms operate on the notion of so-called operation processing order, i.e. the order of operations on each machine. We show that the problem of schedule construction on the base of a given operation processing order can be reduced to the linear programming task. We also propose some approximation algorithm for schedule construction and show the conditions of its optimality