J.A. Hoogeveen (Han)
http://repub.eur.nl/ppl/14670/
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http://repub.eur.nl/
RePub, Erasmus University RepositoryLower bounds for minimizing total completion time in a two-machine flow shop
http://repub.eur.nl/pub/76364/
Fri, 01 Dec 2006 00:00:01 GMT<div>J.A. Hoogeveen</div><div>N. Norden, van</div><div>S.L. van de Velde</div>
For the NP -hard problem of scheduling n jobs in a two-machine flow shop so as to minimize the total completion time, we present two equivalent lower bounds that are computable in polynomial time. We formulate the problem by the use of positional completion time variables, which results in two integer linear programming formulations with O(n 2) variables and O(n) constraints. Solving the linear programming relaxation renders a very strong lower bound with an average relative gap of only 0.8% for instances with more than 30 jobs. We further show that relaxing the formulation in terms of positional completion times by applying Lagrangean relaxation yields the same bound, no matter which set of constraints we relax.Combining column generations and Lagrangean relaxation: an application to a single-machine common due date scheduling problem
http://repub.eur.nl/pub/12331/
Tue, 01 Jan 2002 00:00:01 GMT<div>M. Akker, van den</div><div>J.A. Hoogeveen</div><div>S.L. van de Velde</div>
Column generation has proved to be an effective technique for solving the linear programming relaxation ofhuge set covering or set partitioning problems,and column generation approaches have led to state-of-the-art so-called branch-and-price algorithms for various archetypical combinatorial optimization problems. We use combination of column generation and Lagrangean relaxation to tackle single-machine common due date problem,where Lagrangean relaxation is exploited for early termination of the column generation algorithm and for speeding up the pricing algorithm.We show that the Lagrangean lower bound dominates the lower bound that can be derived from the column generation algorithm when applied to the standard linear programming formulation, but we also show how the linear programming formulation can be adapted such that the corresponding lower bound is equal to the Lagrangean lower bound. Our comprehensive computational study shows that the combined algorithm is by far superior to two existing purely column generation algorithms: it solves instances with up to 125 jobs to optimality, while purely column generation algorithm can solve instances with up to only 60 jobs.Scheduling with target start times
http://repub.eur.nl/pub/12333/
Sat, 01 Jan 2000 00:00:01 GMT<div>J.A. Hoogeveen</div><div>S.L. van de Velde</div>
We address the single-machine problem of scheduling n independent jobs subject to target start times. Target start times are essentially release times that may be violated at a certain cost. The objective is to minimize a bicriteria objective function that is composed of total completion time and maximum promptness, which measures the observance of these target start times. We show that in case of a linear objective function the problem is solvable in O(n4) time if preemption is allowed or if total completion time outweighs maximum promptness.Parallel machine scheduling by column generation
http://repub.eur.nl/pub/12334/
Fri, 01 Jan 1999 00:00:01 GMT<div>M. Akker, van den</div><div>J.A. Hoogeveen</div><div>S.L. van de Velde</div>
Parallel machine scheduling problems concern the scheduling of n jobs on m machines to minimize some function of the job completion times. If preemption is not allowed, then most problems are not only &Nscipt;&Pscript;-hard, but also very hard from a practical point of view. In this paper, we show that strong and fast linear programming lower bounds can be computed for an important class of machine scheduling problems with additive objective functions. Characteristic of these problems is that on each machine the order of the jobs in the relevant part of the schedule is obtained through some priority rule. To that end, we formulate these parallel machine scheduling problems as a set covering problem with an exponential number of binary variables, n covering constraints, and a single side constraint. We show that the linear programming relaxation can be solved efficiently by column generation because the pricing problem is solvable in pseudo-polynomial time. We display this approach on the problem of minimizing total weighted completion time on m identical machines. Our computational results show that the lower bound is singularly strong and that the outcome of the linear program is often integral. Moreover, they show that our branch-and-bound algorithm that uses the linear programming lower bound outperforms the previously best algorithm.Scheduling by positional completion times: Analysis of a two-stage flow shop problem with a batching machine
http://repub.eur.nl/pub/12338/
Thu, 01 Jan 1998 00:00:01 GMT<div>J.A. Hoogeveen</div><div>S.L. van de Velde</div>
We consider a scheduling problem introduced by Ahmadi et al., Batching and scheduling jobs on batch and discrete processors, Operation Research 40 (1992) 750–763, in which each job has to be prepared before it can be processed. The preparation is performed by a batching machine; it can prepare at mostc jobs in each run, which takes an amount of time that is independent of the number and identity of the jobs under preparation. We present a very strong Lagrangian lower bound by using the new concept of positional completion times. This bound can be computed in O(n logn) time only, wheren is the number of jobs. We further present two classes of O(n logn) heuristics that transform an optimal schedule for the Lagrangian dual problem into a feasible schedule. Any heuristic in one class has performance guarantee of 3/2. We further show that even the most naive heuristic in this class has a compelling empirical performance.
An earlier draft of this paper has appeared in the Proceedings of the Fourth International IPCO Conference, Lecture Notes in Computer Science, vol. 920, Springer, Berlin.Scheduling a batching machine
http://repub.eur.nl/pub/12341/
Thu, 01 Jan 1998 00:00:01 GMT<div>P. Brucker</div><div>A. Gladky</div><div>J.A. Hoogeveen</div><div>M. Kovalyov</div><div>C. Potts</div><div>T. Tautenhahn</div><div>S.L. van de Velde</div>
We address the problem of scheduling n jobs on a batching machine to minimize regular scheduling criteria that are non-decreasing in the job completion times. A batching machine is a machine that can handle up to b jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is equal to the largest processing time of any job in the batch. We analyse two variants: the unbounded model, where bn; and the bounded model, where b<n.
For the unbounded model, we give a characterization of a class of optimal schedules, which leads to a generic dynamic programming algorithm that solves the problem of minimizing an arbitrary regular cost function in pseudopolynomial time. The characterization leads to more efficient dynamic programming algorithms for specific cost functions: a polynomial algorithm for minimizing the maximum cost, an O(n3) time algorithm for minimizing the number of tardy jobs, an O(n2) time algorithm for minimizing the maximum lateness, and an O(n log n) time algorithm for minimizing the total weighted completion time. Furthermore, we prove that minimizing the weighted number of tardy jobs and the total weighted tardiness are NP-hard problems.
For the bounded model, we derive an O(nb(b-1)) time dynamic programming algorithm for minimizing total completion time when b>1; for the case with m different processing times, we give a dynamic programming algorithm that requires O(b2m22m) time. Moreover, we prove that due date based scheduling criteria give rise to NP-hard problems. Finally, we show that an arbitrary regular cost function can be minimized in polynomial time for a fixed number of batches.Earliness-tardiness scheduling around almost equal due dates
http://repub.eur.nl/pub/12343/
Wed, 01 Jan 1997 00:00:01 GMT<div>J.A. Hoogeveen</div><div>S.L. van de Velde</div>
Discusses the existence of another class of problems that are structurally less complicated than the general earliness-tardiness problem. Details of common due date problems; Logic behind Emmons' matching algorithm; List of earliness-tardiness problems to which the optimality principle of the dynamic algorithm applies; Properties that apply to the variants of dynamic programming.A branch-and-bound algorithm for single-machine earliness-tardiness scheduling with idle time
http://repub.eur.nl/pub/12345/
Mon, 01 Jan 1996 00:00:01 GMT<div>J.A. Hoogeveen</div><div>S.L. van de Velde</div>
Presents a branch-and-bound algorithm which is based upon many dominance rules and various lower bound approaches, including relaxation of the machine capacity, data manipulation and Lagrangian relaxation. Insertion of the idle time for a given sequence; Properties of the proposed lower bounds.Stronger Lagrangian bounds by use of slack variables: applications to machine scheduling problems
http://repub.eur.nl/pub/12347/
Sun, 01 Oct 1995 00:00:01 GMT<div>J.A. Hoogeveen</div><div>S.L. van de Velde</div>
Lagrangian relaxation is a powerful bounding technique that has been applied successfully to manyNP-hard combinatorial optimization problems. The basic idea is to see anNP-hard problem as an easy-to-solve problem complicated by a number of nasty side constraints. We show that reformulating nasty inequality constraints as equalities by using slack variables leads to stronger lower bounds. The trick is widely applicable, but we focus on a broad class of machine scheduling problems for which it is particularly useful. We provide promising computational results for three problems belonging to this class for which Lagrangian bounds have appeared in the literature: the single-machine problem of minimizing total weighted completion time subject to precedence constraints, the two-machine flow-shop problem of minimizing total completion time, and the single-machine problem of minimizing total weighted tardiness.Minimizing total completion time and maximum cost simultaneously is solvable in polynomial time
http://repub.eur.nl/pub/12348/
Sun, 01 Jan 1995 00:00:01 GMT<div>J.A. Hoogeveen</div><div>S.L. van de Velde</div>
We prove that the bicriteria single-machine scheduling problem of minimizing total completion time and maximum cost simultaneously is solvable in polynomial time. Our result settles a long-standing open problem.New lower and upper bounds for scheduling around a small common due date
http://repub.eur.nl/pub/12351/
Sat, 01 Jan 1994 00:00:01 GMT<div>J.A. Hoogeveen</div><div>H. Oosterhout</div><div>S.L. van de Velde</div>
We consider the single-machine problem of scheduling n jobs to minimize the sum of the deviations of the job completion times from a given small common due date. For this NP-hard problem, we develop a branch-and-bound algorithm based on Lagrangian lower and upper bounds that are found in O(n log n) time. We identify conditions under which the bounds concur; these conditions can be expected to be satisfied by many instances with n not too small. In our experiments with processing times drawn from a uniform distribution, the bounds concur for ≥ 40. For the case where the bounds do not concur, we present a refined lower bound that is obtained by solving a subset-sum problem of small dimension to optimality. We further develop a 4/3-approximation algorithm based upon the Lagrangian upper bound.Complexity of scheduling multiprocessor tasks with prespecified processor allocations
http://repub.eur.nl/pub/12352/
Sat, 01 Jan 1994 00:00:01 GMT<div>J.A. Hoogeveen</div><div>S.L. van de Velde</div><div>B. Veltman</div>
We investigate the computational complexity of scheduling multiprocessor tasks with prespecified processor allocations. We consider two criteria: minimizing schedule length and minimizing the sum of the task completion times. In addition, we investigate the complexity of problems when precedence constraints or release dates are involved.A new lower bound approach for single-machine multicriteria scheduling
http://repub.eur.nl/pub/12355/
Wed, 01 Jan 1992 00:00:01 GMT<div>J.A. Hoogeveen</div><div>S.L. van de Velde</div>
The concept of maximum potential improvement has played an important role in computing lower bounds for single-machine scheduling problems with composite objective functions that are linear in the job completion times. We introduce a new method for lower bound computation; objective splitting. We show that it dominates the maximum potential improvement method in terms of speed and quality.Scheduling around a small common due date
http://repub.eur.nl/pub/12356/
Tue, 01 Jan 1991 00:00:01 GMT<div>J.A. Hoogeveen</div><div>S.L. van de Velde</div>
A set of n jobs has to be scheduled on a single machine which can handle only one job at a time. Each job requires a given positive uninterrupted processing time and has a positive weight. The problem is to find a schedule that minimizes the sum of weighted deviations of the job completion times from a given common due date d, which is smaller than the sum of the processing times. We prove that this problem is NP-hard even if all job weights are equal. In addition, we present a pseudopolynomial algorithm that requires O(n2d) time and O(nd) space.