We consider the problem of scheduling n jobs on m parallel machines with inclusive processing set... more We consider the problem of scheduling n jobs on m parallel machines with inclusive processing set restrictions. Each job has a given release date, and all jobs have equal processing times. The objective is to minimize the makespan of the schedule. Li and Li (2015) have developed an O(n2+mn log n) time algorithm for this problem. In this note, we present a modified algorithm with an improved time complexity of O(min{m, log n} ⋅ n log n).
We consider the multidepot capacitated vehicle routing problems and analyze the tour partitioning... more We consider the multidepot capacitated vehicle routing problems and analyze the tour partitioning heuristics for different versions of the model. We prove that the worst-case ratios of the heuristics are bounded by some fixed numbers. Examples are provided to show that the worst-case bounds are tight or asymptotically tight for almost all versions. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
Let G be an undirected graph on n nodes, and let k be an integer that divides n .A k-equipartitio... more Let G be an undirected graph on n nodes, and let k be an integer that divides n .A k-equipartition … of G is a partition of V (G )i nto k equal-sized pieces V1, :::, Vk. A pair Vi, Vj of distinct sets in … is called a bad pair if there is at least one edge vi ¡¡
The focus of this work is on the effects of learning on economic production quantity in batch pro... more The focus of this work is on the effects of learning on economic production quantity in batch production systems. We assumed that both unit variable manufacturing time and setup time follow a learning curve. We modified the classical Economic Production Quantity model to incorporate these two types of learning phenomena. We also incorporated the forgetting effect in our model so that a fraction of the learning is lost between consecutive lots. We developed a dynamic program to obtain the optimal solution to the problem. We investigated the nonincreasing lot size property and used it to improve the efficiency of our dynamic program. We consider a special case of the model in which all lot sizes are assumed equal. After theoretical treatment, we carried out a computational study of the effect of assuming equal lot sizes on the optimal solutions. The results of our examples strongly indicate that the assumption of equal lot sizes not only simplifies the determination of the optimal sol...
... we have proved Claim 1. 46 Volume 13, Number 1 OPERATIONS RESEARCH LETTERS February 1993 Clai... more ... we have proved Claim 1. 46 Volume 13, Number 1 OPERATIONS RESEARCH LETTERS February 1993 Claim 2. If for instance I', there exists a schedule V for N2 such that max max Eyo) , max Ty(i) L, then for instance I there exists a schedule U for N1 such that max wi max Ey(i ...
This article analyzes the computational complexity of a single machine scheduling problem to mini... more This article analyzes the computational complexity of a single machine scheduling problem to minimize total compression plus weighted flow cost. Vickson [Oper. Res. 28 (1980) 1155–1167] studied this problem and conjectured that it was NP-hard. The complexity of this problem remained open since then. We give a positive answer to this conjecture, showing that this problem is NP-hard.
We consider a problem of scheduling nindependent and simultaneously available jobs on munrelated ... more We consider a problem of scheduling nindependent and simultaneously available jobs on munrelated parallel machines. The job processing times can be compressed through incurring an additional cost, which is a convex function of the amount of compression. Two problems are formulated as assignment problems, which can be solved inO (nm + nm log(nm))time. One is to minimize the total compression
ABSTRACT We consider a single-machine scheduling problem in which every job has a given target st... more ABSTRACT We consider a single-machine scheduling problem in which every job has a given target start time and a due-date. A job is early if processing commences before its start time and is tardy if it is completed after its due-date. The objective is to minimize the weighted number of early and tardy jobs, with the restriction that the start times and due-dates are “agreeable”, i.e., the start times must increase in the same sequence as the due-dates. We show that the problem is NP-complete in the strong sense. The complexity issues and algorithms for some special cases of this problem are discussed, and heuristic algorithms are developed for the general problem. Computational experiments are conducted to show the effectiveness of the heuristics.
We consider the problem of scheduling n jobs on m parallel machines with inclusive processing set... more We consider the problem of scheduling n jobs on m parallel machines with inclusive processing set restrictions. Each job has a given release date, and all jobs have equal processing times. The objective is to minimize the makespan of the schedule. Li and Li (2015) have developed an O(n2+mn log n) time algorithm for this problem. In this note, we present a modified algorithm with an improved time complexity of O(min{m, log n} ⋅ n log n).
We consider the multidepot capacitated vehicle routing problems and analyze the tour partitioning... more We consider the multidepot capacitated vehicle routing problems and analyze the tour partitioning heuristics for different versions of the model. We prove that the worst-case ratios of the heuristics are bounded by some fixed numbers. Examples are provided to show that the worst-case bounds are tight or asymptotically tight for almost all versions. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
Let G be an undirected graph on n nodes, and let k be an integer that divides n .A k-equipartitio... more Let G be an undirected graph on n nodes, and let k be an integer that divides n .A k-equipartition … of G is a partition of V (G )i nto k equal-sized pieces V1, :::, Vk. A pair Vi, Vj of distinct sets in … is called a bad pair if there is at least one edge vi ¡¡
The focus of this work is on the effects of learning on economic production quantity in batch pro... more The focus of this work is on the effects of learning on economic production quantity in batch production systems. We assumed that both unit variable manufacturing time and setup time follow a learning curve. We modified the classical Economic Production Quantity model to incorporate these two types of learning phenomena. We also incorporated the forgetting effect in our model so that a fraction of the learning is lost between consecutive lots. We developed a dynamic program to obtain the optimal solution to the problem. We investigated the nonincreasing lot size property and used it to improve the efficiency of our dynamic program. We consider a special case of the model in which all lot sizes are assumed equal. After theoretical treatment, we carried out a computational study of the effect of assuming equal lot sizes on the optimal solutions. The results of our examples strongly indicate that the assumption of equal lot sizes not only simplifies the determination of the optimal sol...
... we have proved Claim 1. 46 Volume 13, Number 1 OPERATIONS RESEARCH LETTERS February 1993 Clai... more ... we have proved Claim 1. 46 Volume 13, Number 1 OPERATIONS RESEARCH LETTERS February 1993 Claim 2. If for instance I', there exists a schedule V for N2 such that max max Eyo) , max Ty(i) L, then for instance I there exists a schedule U for N1 such that max wi max Ey(i ...
This article analyzes the computational complexity of a single machine scheduling problem to mini... more This article analyzes the computational complexity of a single machine scheduling problem to minimize total compression plus weighted flow cost. Vickson [Oper. Res. 28 (1980) 1155–1167] studied this problem and conjectured that it was NP-hard. The complexity of this problem remained open since then. We give a positive answer to this conjecture, showing that this problem is NP-hard.
We consider a problem of scheduling nindependent and simultaneously available jobs on munrelated ... more We consider a problem of scheduling nindependent and simultaneously available jobs on munrelated parallel machines. The job processing times can be compressed through incurring an additional cost, which is a convex function of the amount of compression. Two problems are formulated as assignment problems, which can be solved inO (nm + nm log(nm))time. One is to minimize the total compression
ABSTRACT We consider a single-machine scheduling problem in which every job has a given target st... more ABSTRACT We consider a single-machine scheduling problem in which every job has a given target start time and a due-date. A job is early if processing commences before its start time and is tardy if it is completed after its due-date. The objective is to minimize the weighted number of early and tardy jobs, with the restriction that the start times and due-dates are “agreeable”, i.e., the start times must increase in the same sequence as the due-dates. We show that the problem is NP-complete in the strong sense. The complexity issues and algorithms for some special cases of this problem are discussed, and heuristic algorithms are developed for the general problem. Computational experiments are conducted to show the effectiveness of the heuristics.
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