Enrique Gerstl - Academia.edu (original) (raw)

Papers by Enrique Gerstl

International Journal of Production Economics, 2014

ABSTRACT We study a batch-scheduling problem of unit-time jobs on a two-stage flexible flowshop. ... more ABSTRACT We study a batch-scheduling problem of unit-time jobs on a two-stage flexible flowshop. The objective functions are minimum makespan and minimum flowtime. Unlike previously studied models: (i) a general number of machines in both stages of the flowshop is allowed, and (ii) there is no restriction on the number of batches to be processed on each machine. Efficient exact dynamic programming algorithms are introduced. Extensions to the case of machine-dependent setup times are studied as well. All the proposed algorithms run in polynomial time in the number of jobs.

Journal of the Operational Research Society, 2015

ABSTRACT We study a special two-stage flexible flowshop, which consists of several parallel ident... more ABSTRACT We study a special two-stage flexible flowshop, which consists of several parallel identical machines in the first stage and a single machine in the second stage. We assume identical jobs, and the option of batching, with a required setup time prior to the processing of a new batch. We also consider the option to use only a subset of the available machines. The objective is minimum makespan. A unique optimal solution is introduced, containing the optimal number of machines to be used, the sequence of batch sizes, and the batch schedule. The running time of our proposed solution algorithm is independent of the number of jobs, and linear in the number of machines

We study a two-stage flowshop, where each job is processed on the first (critical) machine, and t... more We study a two-stage flowshop, where each job is processed on the first (critical) machine, and then continues to one of two second-stage (dedicated) machines. We assume identical (but machine-dependent) job processing times. Jobs are processed on the critical machine in batches, and a setup time is required when starting a new batch. The setting assumes batch-availability, i.e., jobs become available for the second stage only when their entire batch is completed on the critical machine. We consider three objective functions: minimum makespan, minimum total load, and minimum weighted flow-time. Polynomial time dynamic programming algorithms are introduced, which are numerically shown to be able to solve problems of medium size in reasonable time. A heuristic for makespan minimization is presented and shown numerically to be both accurate and efficient..

Naval Research Logistics (NRL), 2014

ABSTRACT In scheduling problems with two competing agents, each one of the agents has his own set... more ABSTRACT In scheduling problems with two competing agents, each one of the agents has his own set of jobs to be processed and his own objective function, and both share a common processor. In the single-machine problem studied in this article, the goal is to find a joint schedule that minimizes the total deviation of the job completion times of the first agent from a common due-date, subject to an upper bound on the maximum deviation of job completion times of the second agent. The problem is shown to be NP-hard even for a nonrestrictive due-date, and a pseudopolynomial dynamic program is introduced and tested numerically. For the case of a restrictive due-date (a sufficiently small due-date that may restrict the number of early jobs), a faster pseudopolynomial dynamic program is presented. We also study the multiagent case, which is proved to be strongly NP-hard. A simple heuristic for this case is introduced, which is tested numerically against a lower bound, obtained by extending the dynamic programming algorithm. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

Journal of Scheduling, 2014

ABSTRACT We study practical scheduling problems with a major decision referring to the number of ... more ABSTRACT We study practical scheduling problems with a major decision referring to the number of machines to be used. We focus on a two-stage flexible flowshop, where each job is processed on the first (critical) machine, and then continues to one of the second-stage parallel machines. Jobs are assumed to have identical processing times, and are processed in batches. A setup time is required when starting a new batch. We consider two objective functions: minimum makespan and minimum flowtime. In both cases, a closed form expression for the optimal number of machines to be used is introduced, and a unique and unusual sequence of decreasing batch sizes is shown to be optimal.

International Journal of Production Economics, 2013

ABSTRACT The decision whether to use all the available machines in the shop becomes very relevant... more ABSTRACT The decision whether to use all the available machines in the shop becomes very relevant when the capacity exceeds the demand. In such cases, it might be optimal to use only a subset of the machines. We study this option in a two-stage flowshop environment. Jobs are assumed to be identical, and are processed in batches, where a machine-dependent setup time is required when starting a new batch. The objective function is minimum makespan. We introduce an exact efficient dynamic programming algorithm, which is shown numerically to be able to solve medium size instances in very reasonable time. For the solution of large instances, we propose an asymptotically optimal heuristic procedure and a lower bound on the makespan value, which produce extremely small optimality gaps.

Information Processing Letters, 2012

ABSTRACT We solve scheduling problems which combine the option of job-rejection and general posit... more ABSTRACT We solve scheduling problems which combine the option of job-rejection and general position-dependent processing times. The option of rejection reflects a very common scenario, where the scheduler may decide not to process a job if it is not profitable. The assumption of position-dependent processing time is a common generalization of classical settings, and contains the well-known and extensively studied special cases of “learning” and “aging”. The machine setting is parallel identical machines, and two scheduling measures are considered: total flow-time and total load. When the number of jobs is given, both problems are shown to be solved in polynomial time in the number of jobs. The special case of non-decreasing job-position processing times (“aging”) is shown to be solved much faster.

Information Processing Letters, 2013

ABSTRACT We study a due-window assignment problem on parallel identical machines, with unit proce... more ABSTRACT We study a due-window assignment problem on parallel identical machines, with unit processing time jobs. The objective function is minimum total cost, consisting of earliness, tardiness, due-window starting time and due-window size. A recent paper [A. Janiak et al., 4OR 10, No. 4, 347–360 (2012; Zbl 1261.68034)] introduced a solution algorithm requiring O(n 5 /m 2 ) time, where n is the number of jobs, and m is the number of machines. We propose a significantly faster procedure, requiring O(n 3 ) only.

European Journal of Operational Research, 2013

ABSTRACT A scheduling problem with a common due-window, earliness and tardiness costs, and identi... more ABSTRACT A scheduling problem with a common due-window, earliness and tardiness costs, and identical processing time jobs is studied. We focus on the setting of both (i) job-dependent earliness/tardiness job weights and (ii) parallel uniform machines. The objective is to find the job allocation to the machines and the job schedule, such that the total weighted earliness and tardiness cost is minimized. We study both cases of a non-restrictive (i.e. sufficiently late), and a restrictive due-window. For a given number of machines, the solutions of the problems studied here are obtained in polynomial time in the number of jobs.

Computers & Operations Research, 2012

ABSTRACT We study a scheduling problem with job classes on parallel uniform machines. All the job... more ABSTRACT We study a scheduling problem with job classes on parallel uniform machines. All the jobs of a given class share a common due-date. General, non-decreasing and class-dependent earliness and tardiness cost functions are assumed. Two objectives are considered: (i) minmax, where the scheduler is required to minimize the maximum earliness/tardiness cost among all the jobs and (ii) minmax-minsum, where the scheduler minimizes the sum of the maximum earliness/tardiness cost in all job classes. The problem is easily shown to be NP-hard, and we focus here on the introduction of simple heuristics. We introduce LPT (Largest Processing Time first)-based heuristics for the allocation of jobs to machines within each class, followed by a solution of an appropriate non-linear program, which produces for this job allocation an optimal schedule of the classes. We also propose a lower bound, based on balancing the load on the machines. Our numerical tests indicate that the heuristics result in very small optimality gaps.

Computers & Operations Research, 2013

We study scheduling problems with two competing agents, sharing the same machines. All the jobs o... more We study scheduling problems with two competing agents, sharing the same machines. All the jobs of both agents have identical processing times and a common due date. Each agent needs to process a set of jobs, and has his own objective function. The objective of the first agent is total weighted earlinesstardiness, whereas the objective of the second agent is maximum weighted deviation from the common due date. Our goal is to minimize the objective of the first agent, subject to an upper bound on the objective value of the second agent. We consider a single machine, and parallel (both identical and uniform) machine settings. An optimal solution in all cases is shown to be obtained in polynomial time by solving a number of linear assignment problems. We show that the running times of the single and the parallel identical machine algorithms are O(n m þ 3 ), where n is the number of jobs and m is the number of machines. The algorithm for solving the problem on parallel uniform machine requires O(n m þ 3 m 3 ) time, and under very reasonable assumptions on the machine speeds, is reduced to O(n m þ 3 ). Since the number of machines is given, these running times are polynomial in the number of jobs.

Applied Mathematics and Computation, 2013

ABSTRACT We study a class of due-window assignment problems. The objective is to find the job seq... more ABSTRACT We study a class of due-window assignment problems. The objective is to find the job sequence and the window starting time and size, such that the total cost of earliness, tardiness and due-window is minimized. The study assumes unit-time jobs, and considers settings of a single machine and of parallel identical machines. Both the due-window starting time and size are decision variables. For the single machine setting, we study a complete set of problems consisting of all possible combinations of the decision variables and four cost factors (earliness, tardiness, due-window size and due-window starting time). For parallel identical machines, we study a complete set of problems consisting of all possible combinations of the decision variables and three cost factors (earliness, tardiness and due-window size). All the problems are shown to be solvable in no more than O(n(3)) time, where n is the number of jobs.

Annals of Operations Research, 2013

ABSTRACT In a standard DIF due-date assignment model, customers may consider late due-dates as un... more ABSTRACT In a standard DIF due-date assignment model, customers may consider late due-dates as unacceptable, i.e., if a due-date is assigned later than a pre-specified lead time, the supplier is penalized. This note extends this setting by adding a lower bound on the acceptable lead-time, reflecting e.g., the time needed by the customer for preparation of storage space. Thus, in addition to the standard earliness/tardiness penalties of jobs, our model contains penalties for early and tardy due-dates. The objective is of a minmax type, i.e. we try to minimize the highest (job and due-date) cost. An efficient O(n) solution algorithm (where n is the number of jobs) is introduced.

Information Processing Letters, 2015

ABSTRACT In most cases, an extension of a polynomial time solution of a scheduling problem on a s... more ABSTRACT In most cases, an extension of a polynomial time solution of a scheduling problem on a single machine to a proportionate flowshop leads to a similar (polynomial time) solution. One of the rare cases where the problem becomes hard, is that of maximizing the weighted number of Just-in-Time jobs on a proportionate flowshop. We introduce a (pseudo-polynomial) solution algorithm for this problem, which is faster by a factor of n than the algorithm published in the literature. We also introduce a (polynomial time) solution algorithm for the “no-wait” proportionate flowshop.