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24
Scheduling to Minimize Average Completion Time: Offline and Online Algorithms
, 1996
"... Timeindexed linear programming formulations have recently received a great deal of attention for their practical effectiveness in solving a number of singlemachine scheduling problems. We show that these formulations are also an important tool in the design of approximation algorithms with good wo ..."
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Cited by 227 (24 self)
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Timeindexed linear programming formulations have recently received a great deal of attention for their practical effectiveness in solving a number of singlemachine scheduling problems. We show that these formulations are also an important tool in the design of approximation algorithms with good worstcase performance guarantees. We give simple new rounding techniques to convert an optimal fractional solution into a feasible schedule for which we can prove a constantfactor performance guarantee, thereby giving the first theoretical evidence of the strength of these relaxations. Specifically, we consider the problem of minimizing the total weighted job completion time on a single machine subject to precedence constraints, and give a polynomialtime (4 + ffl)approximation algorithm, for any ffl ? 0; the best previously known guarantee for this problem was superlogarithmic. With somewhat larger constants, we also show how to extend this result to the case with release date constraints, ...
The Quickest Transshipment Problem
 MATHEMATICS OF OPERATIONS RESEARCH
, 1995
"... A dynamic network consists of a graph with capacities and transit times on its edges. The quickest transshipment problem is defined by a dynamic network with several sources and sinks; each source has a specified supply and each sink has a specified demand. The problem is to send exactly the righ ..."
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Cited by 73 (1 self)
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A dynamic network consists of a graph with capacities and transit times on its edges. The quickest transshipment problem is defined by a dynamic network with several sources and sinks; each source has a specified supply and each sink has a specified demand. The problem is to send exactly the right amount of flow out of each source and into each sink in the minimum overall time. Variations of
Minimizing Average Completion Time in the Presence of Release Dates
, 1995
"... A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order to minimize the average completion time of the set of jobs. In con ..."
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Cited by 53 (8 self)
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A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order to minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when all jobs are available at time 0, all the problems that we consider are NPhard, and essentially nothing was known about constructing good approximations in polynomial time. We give the first constantfactor approximation algorithms for several variants of the single and parallel machine model. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of average weighted completion time as well. 1 Introduction Two important characteristics of many realw...
Scheduling Unrelated Machines by Randomized Rounding
 SIAM Journal on Discrete Mathematics
, 1999
"... In this paper, we provide a new class of randomized approximation algorithms for parallel machine scheduling problems. The most general model we consider is scheduling unrelated machines with release dates (or even network scheduling) so as to minimize the average weighted completion time. We introd ..."
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Cited by 36 (5 self)
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In this paper, we provide a new class of randomized approximation algorithms for parallel machine scheduling problems. The most general model we consider is scheduling unrelated machines with release dates (or even network scheduling) so as to minimize the average weighted completion time. We introduce an LP relaxation in timeindexed variables for this problem. The crucial idea to derive approximation results is not to use standard list scheduling, but rather to assign jobs randomly to machines (by interpreting LP solutions as probabilities), and to perform list scheduling on each of them. Our main result is a (2 + e)approximation algorithm for this general model which improves upon performance guarantee 16=3 due to Hall, Shmoys, and Wein. In the absence of nontrivial release dates, we get a (3=2 + e)approximation. At the same time we prove corresponding bounds on the quality of the LP relaxation. A perhaps surprising implication for identical parallel machines is that jobs are ra...
Offline Admission Control for General Scheduling Problems
 Journal of Scheduling
, 2000
"... We consider a class of scheduling problems which includes a variety of problems that are exceedingly difficult to approximate (unless P=NP). In the face of very strong hardness results, we consider a relaxed notion of approximability and show that under this notion the problems yield constantfactor ..."
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Cited by 34 (1 self)
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We consider a class of scheduling problems which includes a variety of problems that are exceedingly difficult to approximate (unless P=NP). In the face of very strong hardness results, we consider a relaxed notion of approximability and show that under this notion the problems yield constantfactor approximation algorithms (of a kind). Specifically we give a pseudopolynomialtime algorithm that, given an njob instance whose optimal schedule has optimality criterion of value OPT , schedules a constant fraction of the n jobs within a constant factor times OPT . In many cases this can be converted to a fully polynomialtime algorithm. We then study the experimental performance of this algorithm and some additional heuristics. Specifically, we consider a set of instances of a onemachine scheduling problem that we have studied previously in the context of traditional approximation algorithms, where the goal is to optimize average weighted flow time. We show that for the instances that we...
SchedulingLPs bear probabilities: Randomized approximations for minsum criteria
 IN R. BURKARD AND G.J. WOEGINGER EDS, ESA'97, LNCS 1284
, 1997
"... In this paper, we provide a new class of randomized approximation algorithms for scheduling problems by directly interpreting solutions to socalled timeindexed LPs as probabilities. The most general model we consider is scheduling unrelated parallel machines with release dates (or even network sc ..."
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Cited by 31 (5 self)
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In this paper, we provide a new class of randomized approximation algorithms for scheduling problems by directly interpreting solutions to socalled timeindexed LPs as probabilities. The most general model we consider is scheduling unrelated parallel machines with release dates (or even network scheduling) so as to minimize the average weighted completion time. The crucial idea for these multiple machine problems is not to use standard list scheduling but rather to assign jobs randomly to machines (with probabilities taken from an optimal LP solution) and to perform list scheduling on each of them. For the general model, we give a (2+ e)approximation algorithm. The best previously known approximation algorithm has a performance guarantee of 16/3 [HSW96]. Moreover, our algorithm also improves upon the best previously known approximation algorithms for the special case of identical parallel machine scheduling (performance guarantee (2.89 + e) in general [CPS+96] and 2.85 for the average completion time [CMNS97], respectively). A perhaps surprising implication for identical parallel machines is that jobs are randomly assigned to machines, in which each machine is equally likely. In addition, in this case the algorithm has running time O(n log n) and performance guarantee 2. The same algorithm also is a 2approximation for the corresponding preemptive scheduling problem on identical parallel machines. Finally, the results for identical parallel machine scheduling apply to both the offline and the online settings with no difference in performance guarantees. In the online setting, we are scheduling jobs that continually arrive to be processed and, for each time t, we must construct the schedule until time t without any knowledge of the jobs that will arrive afterwards.
An Adversarial Model for Distributed Dynamic Load Balancing
, 1998
"... We study the problem of balancing the load on processors of an arbitrary network. If jobs arrive or depart during the process of load balancing, we have the dynamic load balancing problem; otherwise, we have the static load balancing problem. While static load balancing on arbitrary and special netw ..."
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Cited by 19 (2 self)
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We study the problem of balancing the load on processors of an arbitrary network. If jobs arrive or depart during the process of load balancing, we have the dynamic load balancing problem; otherwise, we have the static load balancing problem. While static load balancing on arbitrary and special networks has been well studied, very little is known about dynamic load balancing. The difficulty lies in modeling the arrivals and departures of jobs in a clean manner. In this paper, we initiate the study of dynamic load balancing by modeling job traffic using an adversary. Our main result is that a simple, local control distributed load balancing algorithm maintains the load of the network within a stable level against this powerful adversary. Our results hold for different models of traffic patterns and processor communication. 1 Introduction An important problem in a distributed system is to balance the total workload among the various processors of the underlying system. Such load balan...
Strategic, Tactical and Operational Decisions in Multinational Logistics Networks: A Review and Discussion of Modeling Issues
 International Journal of Production Research
, 2000
"... The rapidly developing, worldwide marketplace is leading to the geographical dispersion of production, assembly and distribution operations. This paper deals with three aspects of international logistics networks: strategic, tactical and operational. The strategic level designs the logistics networ ..."
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Cited by 11 (0 self)
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The rapidly developing, worldwide marketplace is leading to the geographical dispersion of production, assembly and distribution operations. This paper deals with three aspects of international logistics networks: strategic, tactical and operational. The strategic level designs the logistics network, including prescribing facility locations, production technologies and plant capacities. The tactical level prescribes material flow management policies, including production levels at all plants, assembly policy, inventory levels, and lot sizes. The operational level schedules operations to assure intime delivery of final products to customers. This paper reviews the literature that deals with strategic, tactical and operational levels and discusses relevant modeling issues.
Job Scheduling in Rings
"... We give distributed approximation algorithms for job scheduling in a ring architecture. In contrast to almost all other parallel scheduling models, the model we consider captures the influence of the underlying communications network by specifying that task migration from one processor to anot ..."
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Cited by 10 (2 self)
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We give distributed approximation algorithms for job scheduling in a ring architecture. In contrast to almost all other parallel scheduling models, the model we consider captures the influence of the underlying communications network by specifying that task migration from one processor to another takes time proportional to the distance between those two processors in the network. As a result, our algorithms must balance both computational load and communication time. The algorithms are simple, require no global control, and work in a variety of settings. All come with small constantfactor approximation guarantees; the basic algorithm yields schedules of length at most 4:22 times optimal. We also give a lower bound on the performance of any distributed algorithm and the results of simulation experiments, which give better results than our worstcase analysis.