Papers by Bertrand M . T . Lin
Resource-requirement minimization in relocation problems with precedence constraints
The relocation problem is a generalized resource-constrained job scheduling problem in the aspect... more The relocation problem is a generalized resource-constrained job scheduling problem in the aspect that the amount of resources returned at the completion of a job is not necessarily equal to that demanded. The authors propose fundamental properties of the basic relocation problem. Also, they consider a variant RPPC into which precedence constraints are introduced. They show that RPPC is NP-complete,
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International Journal of Production Economics, Sep 1, 2008
The relocation problem, based on a public housing project in Boston, USA, is a generalized resour... more The relocation problem, based on a public housing project in Boston, USA, is a generalized resource-constrained scheduling problem in which the amount of resources (new housing units) returned by a completed job (building) is not necessarily the same as the amount of resources (original housing units) it started out with for processing. In this paper we consider a variant where several generalized due dates are specified to define the number of new housing units that should be built in the entire duration of the project. Generalized due dates are different from conventional due dates in that they are job independent and common to all jobs. In the present study each generalized due date is given to specify an expected percentage of completion of the project. Given an initial number of temporary housing units, the goal is to find a feasible reconstruction sequence that maximizes the total reward over all generalized due dates. This paper investigates the time complexity of the problem. Two upper bounds and a dominance property are proposed for the design of branch-and-bound algorithms. Computational experiments are carried out to assess the efficiency of the proposed properties. The results show that the proposed properties can significantly reduce the time required for producing an optimal schedule.
Engineering Applications of Artificial Intelligence, Mar 1, 2011
Since optical WDM networks are becoming one of the alternatives for building up backbones, dynami... more Since optical WDM networks are becoming one of the alternatives for building up backbones, dynamic routing, and wavelength assignment with delay constraints (DRWA-DC) in WDM networks with sparse wavelength conversions is important for a communication model to route requests subject to delay bounds. Since the NP-hard minimum Steiner tree problem can be reduced to the DRWA-DC problem, it is very unlikely to derive optimal solutions in a reasonable time for the DRWA-DC problem. In this paper, we circumvent to apply a meta-heuristic based upon the ant colony optimization (ACO) approach to produce approximate solutions in a timely manner. In the literature, the ACO approach has been successfully applied to several well-known combinatorial optimization problems whose solutions might be in the form of paths on the associated graphs. The ACO algorithm proposed in this paper incorporates several new features so as to select wavelength links for which the communication cost and the transmission delay of routing the request can be minimized as much as possible subject to the specified delay bound. Computational experiments are designed and conducted to study the performance of the proposed algorithm. Comparing with the optimal solutions found by an ILP formulation, numerical results evince that the ACO algorithm is effective and robust in providing quality approximate solutions to the DRWA-DC problem.
European Journal of Operational Research, Aug 1, 1993
There is a set J of h jobs to be processed. For every i, job Ji demands n i units of resources an... more There is a set J of h jobs to be processed. For every i, job Ji demands n i units of resources and returns a i units after completion. The problem is to find the best K schedules whose resource requirements are minimum among all h! ones. In this paper, we present some important structural properties and then propose an O(h log h + hK log K) time algorithm, which runs in polynomial time if K is fixed.
Computer Communications, May 1, 2006
Because optical WDM networks will be realized as network backbone in the near future, multicastin... more Because optical WDM networks will be realized as network backbone in the near future, multicasting in WDM networks needs to be supported for various network applications. In this paper, we propose a new dynamic multicast routing problem under delay constraints (DMR-DC) for finding an optimal light-forest with the minimum multicast cost from these links with available wavelengths for routing a multicast request that arrives in random with a given delay bound in a WDM network with heterogeneous light splitting capabilities, where a light-forest is a set of lighttrees used to set up switches to route the request. Multicast cost is defined by communication cost ratio and wavelength consumption ratio. The problem is to determine a light-forest with less wavelength consumption and less communication cost. This problem is NP-hard because it can be reduced from the minimum Steiner tree problem. In this paper, we propose an efficient three-phase (generation, refinement, and conversion) solution model to find approximate solutions in a reasonable time.
European Journal of Operational Research, 1993
There is a set J of h jobs to be processed. For every i, job Ji demands n i units of resources an... more There is a set J of h jobs to be processed. For every i, job Ji demands n i units of resources and returns a i units after completion. The problem is to find the best K schedules whose resource requirements are minimum among all h! ones. In this paper, we present some important structural properties and then propose an O(h log h + hK log K) time algorithm, which runs in polynomial time if K is fixed.
European Journal of Operational Research, Jul 1, 2022
This article studies two due window scheduling problems to minimize the weighted number of early ... more This article studies two due window scheduling problems to minimize the weighted number of early and tardy jobs in a two-machine flow shop, where the window size is externally determined. These new scheduling models have many practical applications in real life. However, results on these problems have rarely appeared in the literature because of a lack of structural and optimality properties for solving them. In this article, we derive several dominance properties and theorems, including elimination rules and sequencing rules based on Johnson's order, lower bounds on the penalty, and upper bounds on the window location, which help to significantly trim the search space for the problems. We further show that the problems are NP-hard in the ordinary sense only. We finally develop efficient pseudopolynomial dynamic programming algorithms for solving the problems.
Journal of the Operational Research Society, Mar 1, 2004
This paper considers a single-machine scheduling problem of minimizing the maximum completion tim... more This paper considers a single-machine scheduling problem of minimizing the maximum completion time for a set of independent jobs. The processing time of a job is a non-linear step function of its starting time and due date. The problem is already known to be NP-hard in the literature. In this paper, we first show this problem to be NP-hard in the ordinary sense by proposing a pseudo-polynomial time dynamic programming algorithm. Then, we develop two dominance rules and a lower bound to design a branch-and-bound algorithm for deriving optimal solutions. Numerical results indicate that the proposed properties can effectively reduce the time required for exploring the solution space.
Information Systems, Mar 1, 2013
This study investigates sequence optimization of media objects in a multimedia presentation that ... more This study investigates sequence optimization of media objects in a multimedia presentation that is dynamically composed from digital libraries. Each media object can be associated with a due date. The aim is to schedule the media objects in a delayprone network environment such that the overall presentation lag and the due date penalties of the media objects of presentations can be minimized. We formulate the sequencing problem with buffer constraints in the media player into a flowshop scheduling problem and present a reduction strategy with a branch and bound algorithm to derive optimal sequences. The algorithm can be applied in applications with up to a dozen objects to be scheduled. In addition, we propose a modified NEHbased heuristic algorithm which can provide approximate solutions with an average error rate of less than 4%. The computation-efficient heuristic, when deployed in applications with heavily loaded servers, can obtain near-optimal sequences for problems with more than a dozen objects. The proposed algorithms are embedded into a prototype system for providing digital library services.
Engineering Optimization, Jun 1, 2006
Taylor & Francis makes every effort to ensure the accuracy of all the information (the "Content")... more Taylor & Francis makes every effort to ensure the accuracy of all the information (the "Content") contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.
Parallel-machine batch scheduling to minimize the maximum lateness and the number of tardy jobs
International Journal of Production Economics, Sep 1, 2004
... that the single-machine cases 1/batch/L max and 1/batch/∑U i can be optimally solved in polyn... more ... that the single-machine cases 1/batch/L max and 1/batch/∑U i can be optimally solved in polynomial time by the dynamic programming algorithms ... Dispatching phase: In the literature, many approximation endeavors for parallel machine scheduling problems are ...
Minimizing the total completion time in single-machine scheduling with step-deteriorating jobs
Computers & Operations Research, Mar 1, 2005
In this paper, we study a scheduling problem of minimizing the total completion time on a single ... more In this paper, we study a scheduling problem of minimizing the total completion time on a single machine where the processing time of a job is a step function of its starting time and a due date that is common to all jobs. This problem has been shown to be NP -hardin the literature. To d erive optimal solutions from
Engineering Optimization, Dec 28, 2018
A note on parallel-machine scheduling with deteriorating jobs
Journal of the Operational Research Society, Jun 1, 2007
ABSTRACT We consider a parallel-machine scheduling problem of minimizing the total completion tim... more ABSTRACT We consider a parallel-machine scheduling problem of minimizing the total completion time. The processing time of a job is a linear function of its starting time and deterioration rate. This problem is known to be NP-hard, even for the case with two machines. In this note, we generalize an existing lower bound for the two-machine case to the general case with an arbitrary number of machines. Despite the generalization concerning machine number, our bound has one extra term that makes our bound tighter than the existing one.
Engineering Optimization, 2018
Journal of the Operational Research Society, 2004
This paper considers a single-machine scheduling problem of minimizing the maximum completion tim... more This paper considers a single-machine scheduling problem of minimizing the maximum completion time for a set of independent jobs. The processing time of a job is a non-linear step function of its starting time and due date. The problem is already known to be NP-hard in the literature. In this paper, we first show this problem to be NP-hard in the ordinary sense by proposing a pseudo-polynomial time dynamic programming algorithm. Then, we develop two dominance rules and a lower bound to design a branch-and-bound algorithm for deriving optimal solutions. Numerical results indicate that the proposed properties can effectively reduce the time required for exploring the solution space.
A note on parallel-machine scheduling with deteriorating jobs
Journal of the Operational Research Society, 2007
ABSTRACT We consider a parallel-machine scheduling problem of minimizing the total completion tim... more ABSTRACT We consider a parallel-machine scheduling problem of minimizing the total completion time. The processing time of a job is a linear function of its starting time and deterioration rate. This problem is known to be NP-hard, even for the case with two machines. In this note, we generalize an existing lower bound for the two-machine case to the general case with an arbitrary number of machines. Despite the generalization concerning machine number, our bound has one extra term that makes our bound tighter than the existing one.
Information Systems, 2013
This study investigates sequence optimization of media objects in a multimedia presentation that ... more This study investigates sequence optimization of media objects in a multimedia presentation that is dynamically composed from digital libraries. Each media object can be associated with a due date. The aim is to schedule the media objects in a delayprone network environment such that the overall presentation lag and the due date penalties of the media objects of presentations can be minimized. We formulate the sequencing problem with buffer constraints in the media player into a flowshop scheduling problem and present a reduction strategy with a branch and bound algorithm to derive optimal sequences. The algorithm can be applied in applications with up to a dozen objects to be scheduled. In addition, we propose a modified NEHbased heuristic algorithm which can provide approximate solutions with an average error rate of less than 4%. The computation-efficient heuristic, when deployed in applications with heavily loaded servers, can obtain near-optimal sequences for problems with more than a dozen objects. The proposed algorithms are embedded into a prototype system for providing digital library services.
Engineering Optimization, 2006
Taylor & Francis makes every effort to ensure the accuracy of all the information (the "Content")... more Taylor & Francis makes every effort to ensure the accuracy of all the information (the "Content") contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.
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Papers by Bertrand M . T . Lin