A Bicriteria Approximation for the Reordering Buffer Problem

In the reordering buffer problem (RBP), a server is asked to process a sequence of requests lying in a metric space. To process a request the server must move to the corresponding point in the metric. The requests can be processed slightly out of order; in particular, the server has a buffer of capacity k which can store up to k requests as it reads in the sequence. The goal is to reorder the requests in such a manner that the buffer constraint is satisfied and the total travel cost of the server is minimized. The RBP arises in many applications that require scheduling with a limited buffer capacity, such as scheduling a disk arm in storage systems, switching colors in paint shops of a car manufacturing plant, and rendering 3D images in computer graphics. We study the offline version of RBP and develop bicriteria approximations. When the underlying metric is a tree, we obtain a solution of cost no more than 9OPT using a buffer of capacity 4k + 1 where OPT is the cost of an optimal solution with buffer capacity k. Constant factor approximations were known previously only for the uniform metric (Avigdor-Elgrabli et al., 2012). Via randomized tree embeddings, this implies an O(log n) approximation to cost and O(1) approximation to buffer size for general metrics. Previously the best known algorithm for arbitrary metrics by Englert et al. (2007) provided an O(log^2 k log n) approximation without violating the buffer constraint.Comment: 13 page

Preemptive scheduling on uniform parallel machines with controllable job processing times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan

Enhanced genetic algorithm-based fuzzy multiobjective strategy to multiproduct batch plant design

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessary involves how equipment may be utilized, which means that plant scheduling and production must constitute a basic part of the design problem. Rather than resorting to a traditional probabilistic approach for modeling the imprecision on product demands, this work proposes an alternative treatment by using fuzzy concepts. The design problem is tackled by introducing a new approach based on a multiobjective genetic algorithm, combined wit the fuzzy set theory for computing the objectives as fuzzy quantities. The problem takes into account simultaneous maximization of the fuzzy net present value and of two other performance criteria, i.e. the production delay/advance and a flexibility index. The delay/advance objective is computed by comparing the fuzzy production time for the products to a given fuzzy time horizon, and the flexibility index represents the additional fuzzy production that the plant would be able to produce. The multiobjective optimization provides the Pareto's front which is a set of scenarios that are helpful for guiding the decision's maker in its final choices. About the solution procedure, a genetic algorithm was implemented since it is particularly well-suited to take into account the arithmetic of fuzzy numbers. Furthermore because a genetic algorithm is working on populations of potential solutions, this type of procedure is well adapted for multiobjective optimization

Enhanced genetic algorithm-based fuzzy multiobjective strategy to multiproduct batch plant design

The design of such plants necessary involves how equipment may be utilized, which means that plant scheduling and production must form an integral part of the design problem. This work proposes an alternative treatment of the imprecision (demands) by using fuzzy concepts. In this study, we introduce a new approach to the design problem based on a multiobjective genetic algorithm, taking into account simultaneously maximization of the net present value NPV ~ and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The methodology provides a set of scenarios that are helpful to the decision’s maker and constitutes a very promising framework for taken imprecision into account in new product development stage. Besides, a hybrid selection method Pareto rank-tournament was proposed and showed a better performance than the classical Goldberg’s wheel, systematically leading to a higher number of non-dominated solutions

An analysis of pure robotic cycles

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 2008.Thesis (Master's) -- Bilkent University, 20068Includes bibliographical references leaves 84-87.This thesis is focused on scheduling problems in robotic cells consisting of a number of CNC machines producing identical parts. We consider two different cell layouts which are in-line robotic cells and robot centered cells. The problem is to find the robot move sequence and processing times on machines minimizing the total manufacturing cost and cycle time simultaneously. The automation in manufacturing industry increased the flexibility, however it is not widely studied in the literature. The flexibility of machines enables us to process all the required operations for a part on the same machine. Furthermore, the processing times on CNC machines can be increased or decreased by changing the feed rate and cutting speed. Hence, we assume that a part is processed on one of the machines and the processing times are assumed to be controllable. The flexibility of machines results in a new class of cycles named pure cycles. We determined efficient pure cycles and corresponding processing times dominating the rest of pure cycles in the specified cycle time regions. In addition, for in-line robotic cells, the optimum number of machines is determined for given parameters.Yıldız, SerdarM.S

An Efficient Algorithm for a Bicriteria Single-Machine Scheduling Problem

This paper considers a single-machine scheduling problem in which the maximum tardiness and the total flowtime are two objectives to be minimized. Instead of enumerating all efficient schedules, the author considers the problem of minimizing the maximum of the weighted values of these two objective functions, which arises in interactive multicriteria decision making. The author proposes a strongly polynomial algorithm for this problem which runs in O(n^2 log n) time

Scheduling problems with two competing agents

We consider the scheduling problems arising when two agents, each with a set of nonpreemptive jobs, compete to perform their respective jobs on a common processing resource. Each agent wants to minimize a certain objective function, which depends on the completion times of its jobs only. The objective functions we consider in this paper are maximum of regular functions (associated with each job), number of late jobs, and total weighted completion times. We obtain different scenarios, depending on the objective function of each agent, and on the structure of the processing system (single machine or shop). For each scenario, we address the complexity of various problems, namely, finding the optimal solution for one agent with a constraint on the other agent's cost function, finding single nondominated schedules (i.e., such that a better schedule for one of the two agents necessarily results in a worse schedule for the other agent), and generating all nondominated schedules