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## Publications

Publications (235)

An even cycle C in a graph G is a nice cycle if G−V(C) has a perfect matching. A graph G is cycle-nice if each even cycle in G is a nice cycle. An even cycle C in an orientation of a graph G is clockwise odd if the number of its edges directed in the clockwise sense is odd. A graph G is Pfaffian if there is an orientation of G such that each nice c...

For integer k≥2, a graph G is called k-leaf-connected if |V(G)|≥k+1 and given any subset S⊆V(G) with |S|=k, G always has a spanning tree T such that S is precisely the set of leaves of T. Thus a graph is 2-leaf-connected if and only if it is Hamilton-connected. Gurgel and Wakabayashi (1986) provided a sufficient condition based upon the size for a...

We consider the single-machine Pareto-scheduling problem to minimize the weighted number of tardy jobs and total weighted late work simultaneously. The problem is to find the set of all the Pareto-optimal points, that is, the Pareto frontier, and their corresponding Pareto-optimal schedules. We consider the corresponding weighted-sum scheduling pro...

In this paper, we consider the single-machine bi-criteria preemptive scheduling for minimizing the total weighted late work and the weighted number of tardy jobs, where weights of the jobs for the two criteria are independent, and so, each job has two unrelated weights. The Pareto-scheduling problem is studied in this paper, which includes the hier...

In this paper, we consider the ND two-agent scheduling problem with rejection on a
single machine. In this problem, there are two agents A and B and the job sets of them are denoted by $\mathcal{J}^A$ and $\mathcal{J}^B$, respectively. In the classical CO two-agent scheduling, two agents are competitive, i.e., $\mathcal{J}^A\cap \mathcal{J}^B=\empt...

We revisit the single-machine preemptive scheduling problem to minimize total completion time with release times and deadlines. Du and Leung (1993) showed that the problem is binary NP-hard. But the exact complexity (unary NP-hardness or pseudo-polynomial-time solvability) of the problem is a long standing open problem. We show in this paper that t...

We consider the Pareto-scheduling of two competing agents on a single machine, in which the jobs of each agent have their "own equal processing times" (shortly, OEPT). In the literature, two special versions of the OEPT model, in which the jobs have either unit or equal processing times, have been well studied, where the criteria are given by vario...

We consider two supply chain scheduling problems in which s suppliers preprocess different parts of the jobs to be assembled by the manufacturer under the common sequence constraint, with the goal of minimizing the total weighted number of tardy parts and minimizing the total late work of the parts, respectively. Ren et al. (Information Processing...

We consider the single-machine scheduling problem to tradeoff between the number and the length of accepted jobs. The algorithm introduced by Lin and Wang (2007) (called Lin-Wang's algorithm), for solving the single-machine scheduling problem to minimize the number of tardy jobs, is closely related to our research. The original version of Lin-Wang'...

We consider single-machine bicriteria scheduling of n jobs with preemption to minimize the total late work and maximum tardiness. Given the earliest due date order of the jobs in advance, we present an O(n)-time algorithm for the hierarchical scheduling problem and an O(nlogn)-time algorithm for the constrained scheduling problem. For the Pareto-sc...

We study Pareto-scheduling on an unbounded parallel-batch machine that can process any number of jobs simultaneously in a batch. The processing time of a batch is equal to the maximum processing time of the jobs in the batch. We consider two Pareto-scheduling problems. In one problem, the jobs are partitioned into families and the jobs from differe...

We consider the single-machine preemptive Pareto-scheduling problem with two competing agents A and B, where agent A wants to minimize the number of its jobs (the A-jobs) that is tardy, while agent B wants to minimize the total late work of its jobs (the B-jobs). We provide an O(nnAlognA+nBlognB)\documentclass[12pt]{minimal} \usepackage{amsmath} \u...

In this paper we consider the single-machine hierarchical scheduling problems with release dates and preemption, where the primary criterion is the total completion time and the secondary criterion is an arbitrarily regular scheduling criterion, which is of either the sum-form or the max-form. We aim to find a feasible preemptive schedule that mini...

We consider three‐agent scheduling on a single machine in which the criteria of the three agents are to minimize the total weighted completion time, the weighted number of tardy jobs, and the total weighted late work, respectively. The problem is to find the set of all the Pareto‐optimal points, that is, the Pareto frontier, and their corresponding...

In this paper, we study the scheduling of proportional-linearly deteriorating jobs with positional due indices, release dates, deadlines and precedence relations on a single machine. The scheduling criteria studied in this paper include the makespan, maximum lateness, maximum tardiness, maximum flow time, maximum weighted completion time, maximum s...

We consider Pareto-scheduling with two competing agents A and B on a single machine, in which each job has a positional due index and a deadline. The jobs of agents A and B are called the A-jobs and B-jobs, respectively, where the A-jobs have a common processing time, while the B-jobs are restricted by their precedence constraint. The objective is...

We study the bicriteria scheduling of equal length jobs on uniform parallel machines. By introducing a new scheduling model, called single-machine scheduling with generated completion times (shortly, GCT-scheduling), we show that the scheduling of equal length jobs on uniform parallel machines can be polynomially transformed into the single-machine...

We study the unbounded parallel-batch scheduling problem with the jobs having agreeable release dates and processing times to minimize the total weighted number of tardy jobs. In this problem, we consider two types of jobs: batch jobs and drop-line jobs. For batch jobs, the completion time of a job is given by the completion time of the batch conta...

We consider scheduling a set of jobs with deadlines to minimize the total weighted late work on a single machine, where the late work of a job is the amount of processing of the job that is scheduled after its due date and before its deadline. This is the first study on scheduling with the late work criterion under the deadline restriction. In this...

In this paper, we study unbounded parallel-batch scheduling with drop-line tasks to minimize a regular objective function, where by “drop-line tasks” we mean that the completion time of each task (job) is equal to the sum of the starting time of the batch containing the task and the processing time of the task. In the problems considered in this pa...

In this paper, we study multi-agent scheduling with release dates and preemption on a single machine, where the scheduling objective function of each agent to be minimized is regular and of the maximum form (max-form). The multi-agent aspect has three versions, namely ND-agent (multiple agents with non-disjoint job sets), ID-agent (multiple agents...

We revisit the classical single-machine scheduling problem to minimize total tardiness with deadlines. The problem is binary NP-hard even without the deadline restrictions. It was reported early in Koulamas and Kyparisis (Eur J Oper Res 133:447–453, 2001) that the exact complexity (unary NP-hardness or pseudo-polynomial-time solvability) of the pro...

In an edge-colored graph (G,c), let dc(v) be the number of colors on the edges incident to vertex v and let δc(G) be the minimum value of dc(v) over all vertices v∈V(G). A cycle of (G,c) is called proper if any two adjacent edges of the cycle have distinct colors. An edge-colored graph (G,c) on n≥3 vertices is called properly vertex-pancyclic if ea...

In this paper, we study single-machine scheduling problems with due dates, positional due indices, deadlines and positional deadlines. The scheduling criteria studied in this paper include the number of position-violated tasks, the weighted number of position-violated tasks, and the maximum positional lateness of tasks, by also combining with other...

This paper investigates semi-online hierarchical scheduling problems on two identical machines, with the purpose of minimizing the lp-norm of the machines' loads. We consider two semi-online versions with knowing the total processing time T of all jobs, or knowing the total processing time Ti of the jobs of hierarchy i for i = 1, 2 in advance. For...

We re-visit the two-agent scheduling on a parallel-batch machine to minimize makespan, where jobs have release dates and linear deteriorating processing times. The objective is to minimize the makespan of agent A with the makespan of agent B being bounded. In the paper Tang, Zhao, Liu, and Leung (2017), the authors reported comprehensive research f...

In this paper, we consider the online scheduling of incompatible family jobs with equal length on an unbounded parallel-batch machine with job delivery. The jobs arrive online over time and belong to (Formula presented.) incompatible job families, where (Formula presented.) is known in advance. The jobs are first processed in batches on an unbounde...

We study two-agent scheduling on a single sequential and compatible batching machine in which jobs in each batch are processed sequentially and compatibility means that jobs of distinct agents can be processed in a common batch. A fixed setup time is required before each batch is started. Each agent seeks to optimize some scheduling criterion that...

We introduce and study the rescheduling on a single machine to minimize the maximum lateness under the sequence disruptions of original jobs. In the problem, each original job (Formula presented.) has a constraint disruption on its sequence respect to an original optimal schedule (Formula presented.), i.e., (Formula presented.). That is, if (Formul...

We study the multi-agent scheduling on a single machine with a fixed number of competing agents, in which, the objective function of each agent is either the number of tardy jobs or the makespan, and the goal of the problem is to minimize the weighted sum of agents’ objective functions. In the literature, the computational complexity of this proble...

We consider the online scheduling on a single machine, in which jobs are released over time and each job can be either accepted and scheduled on the machine or rejected under a certain rejection cost. The goal is to minimize the total weighted completion time of the accepted jobs plus the total rejection cost of the rejected jobs. For this problem,...

For the two-agent scheduling on an unbounded serial-batch machine with batch delivery cost, Yin et al. (2016) presented a comprehensive study, where the objective of each agent (A or B) is calculated by his scheduling cost plus his batch delivery cost proportional to the number of batches of this agent. Among their results, they provided a polynomi...

A $k$-matching cover of a graph $G$ is a union of $k$ matchings of $G$ which covers $V(G)$. A matching cover of $G$ is optimal if it consists of the fewest matchings of $G$. In this paper, we present an algorithm for finding an optimal matching cover of a graph on $n$ vertices and $m$ edges in $O(nm)$ time. This algorithm corrects an error of Match...

In this paper, we consider the semi-online hierarchical scheduling for load balancing on two identical machines. In the problem, the jobs are available online over list and the objective is to minimize the \(l_p\)-norm of the two machines’ loads. Two semi-online versions are investigated: the buffer version and the rearrangement version. We design...

The Internet of Things (IoT) enables these objects to collect and exchange data and it is an important character of smart city. Multi-agent scheduling is one necessary part of Internet of Things. In this paper, we investigate the Pareto optimization scheduling on a single machine with two competing agents and linear non-increasing deterioration, wh...

We study the rescheduling with new orders on a single machine under the general maximum allowable time disruptions. Under the restriction of general maximum allowable time disruptions, each original job has an upper bound for its time disruption (regarded as the maximum allowable time disruption of the job), or equivalently, in every feasible sched...

We consider the online scheduling of equal length jobs on unbounded parallel batch processing machines to minimize makespan with limited restart. In the problem \(m\) identical unbounded parallel batch processing machines are available to process the equal length jobs arriving over time. The processing batches are allowed limited restart. Here, “re...

For single machine scheduling to minimize the number of tardy jobs with deadlines, Lawler showed in 1983 that the problem is binary NP-hard. But the exact complexity (unary NP-hard or pseudo-polynomial-time solvability) is a long- standing open problem. We show in this paper that the problem is unary NP-hard. Our research also implies that the sche...

We study the computational complexities of three problems on multi-agent scheduling on a single machine. Among the three problems, the computational complexities of the first two problems were still open and the last problem was shown to be unary NP-hard in the literature. We show in this paper that the first two problems are unary NP-hard. We also...

In this paper, we consider the two-stage scheduling problem in which n jobs are first processed on m identical machines at a manufacturing facility and then delivered to their customers by one vehicle which can deliver one job at each shipment. In the problem, a set of n delivery times is given in advance, and in a schedule, the n delivery times sh...

In this paper, we study the online scheduling of linear deteriorating jobs on a single machine to minimize the total weighted completion time. In the problem, a set of n independent linear deteriorating jobs arriving online over time has to be scheduled on a single machine, where the information of each job including its deterioration rate and weig...

This paper investigates the Pareto optimization scheduling problem on a single machine with two competing agents A and B in which agent A wants to minimize the number of tardy A-jobs and agent B wants to minimize the maximum cost of B-jobs. In the literature, the constrained optimization problem of minimizing the number of tardy A-jobs under the re...

We consider the online scheduling on m unbounded drop-line batch machines with delivery times. Here a drop-line batch machine can process several jobs in a batch so that the processing time of a batch is equal to the longest processing time of the jobs in the batch, the jobs in a batch have the same starting time, and the completion time of a job i...

In this paper, we introduce a new environment of online scheduling in which jobs have kind release times (KRT). Under the KRT assumption, no jobs can be released when all of the machines are busy. Then we study the competitive ratio of the online LPT algorithm to minimize makespan on \(m\) identical parallel machines under the KRT assumption. The o...

In the scheduling with generalized due dates, the due dates are sequenced in the EDD order and assigned to the jobs by the increasing order of their completion times such that the th completed job receives the th due date. The exact complexity of the single machine scheduling of minimizing total weighted tardiness with generalized due dates is a lo...

This paper studies the online preemptive scheduling of equal-length intervals on a single machine with lookahead. Let p be the length (processing time) of all intervals. In the problem, at every time point t, online algorithms can foresee all the intervals that will arrive in the time segment (t,t + L) for a certain L. When L = p, Zheng et al. [Com...

This paper discusses the minimum spanning subgraph problem with given cyclomatic number k, where the cyclomatic number of a graph G, denoted by beta(G), is the dimension of its cycle space. For a given weighted graph G = (V, E, w), the problem asks to find a spanning subgraph F of G such that beta(F) = k and w(F) is as small as possible. We show th...

We consider the online (over time) scheduling of equal length jobs on a bounded parallel batch machine with batch capacity
b
to minimize the time by which all jobs have been delivered with limited restart. Here, “restart” means that a running batch may be interrupted, losing all the work done on it, and jobs in the interrupted batch are then rele...

We consider the online scheduling with job rejection to minimize the total weighted completion time of the scheduled jobs plus the total rejection penalty of the rejected jobs. In the problem, a set of independent jobs arriving online over time has to be scheduled with the flexibility of rejecting some of the jobs, where preemption is not allowed a...

In this paper, we consider the two-machine open-shop scheduling problem with rejection. The objective is to minimize the sum of the makespan of accepted jobs and the total rejection cost of rejected jobs. We show that the problem is NP-hard even in three special cases and then provide a pseudo-polynomial time algorithm for this problem, which means...

In this paper, we study the Pareto optimization scheduling problem on a single machine with positional due indices of jobs to minimize the total completion time and a maximum cost. For this problem, we give two O(n4)-time algorithms. © 2015, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press and Springer-...

This paper revisits the scheduling problem on an unbounded parallel batch machine for minimizing a maximum cost . It was reported in the literature that the decision version of the problem is solvable in time, where n is the number of jobs and P is the total processing time of jobs. This implies that the optimization version for minimizing can be s...

The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. A graph is called perfect matching compact (shortly, PM-compact), if its perfect matching polytope has diameter one. This paper gives a complete characterization of simple PM-compact Hamiltonian bipartite graphs. We first define two...

In this paper, we consider the following single machine online tradeoff scheduling problem. A set of n independent jobs arrive online over time. Each job (Formula presented.) has a release date (Formula presented.), a processing time (Formula presented.) and a delivery time (Formula presented.). The characteristics of a job are unknown until it arr...

In this paper, we consider a two-stage scheduling problem on identical machines in which the jobs are first processed preemptively on m identical machines at a manufacturing facility and then delivered to their customers by one vehicle which can deliver one job at each shipment. The objective is to minimize the maximum delivery completion time, i.e...

We consider scheduling problems with job processing time compatibility on a single unbounded batch machine. Each job's processing time is characterized by an interval. Any number of jobs can be processed in a batch under the condition that the processing time intervals of the jobs in the same batch have a nonempty intersection. The processing time...

In this paper, we study the single machine scheduling to minimize the total earliness and tardiness (i.e., the total deviation) with generalized or assignable due dates. Under the assumption of assignable due dates, the due dates are treated as variables and must be assigned to the individual jobs in a schedule. The assumption of generalized due da...

This paper studies the Pareto optimization scheduling problem of family jobs on an unbounded parallel-batching machine to minimize makespan and maximum lateness. In the problem, the jobs are partitioned into families and scheduled in batches, where each batch is a set of jobs belonging to a common family and the processing time of a batch is define...

In this paper, we consider the online-list scheduling on a single bounded parallel-batch machine to minimize makespan. In the problem, the jobs arrive online over list. The first unassigned job in the list should be assigned to a batch before the next job is released. Each batch can accommodate up to b jobs. For b = 2, we establish a lower bound 1...

For computing all Pareto-optimal schedules on a single machine to minimize the total completion time and a maximum cost, Hoogeveen and van de Velde (1995) presented an -time algorithm. However, the complexity analysis of their algorithm is invalid. We here present a new algorithm and show that it achieves the computation time .

In this paper we introduce the concept of online tradeoff scheduling to minimize two objective functions f 1 and f 2 simultaneously. An online algorithm A is called (ρ1,ρ2)(ρ1,ρ2)-competitive for minimizing f 1 and f 2 if A is ρ 1-competitive for minimizing f 1 and ρ 2-competitive for minimizing f 2. A (ρ1,ρ2)(ρ1,ρ2)-competitive online algorithm A...

Online scheduling is a rapidly developed branch in scheduling theory. In this paper, we present an extensive survey for online over time scheduling on parallel-batch machines. Some open problems are proposed for further research.

We consider the online bounded-batch scheduling to minimize total weighted completion time on parallel machines. In the problem, a set of n independent jobs arriving online over time has to be scheduled on m given machines, where the information of each job including its processing time and weight is not known in advance. Each machine can process u...

A k-matching cover of a graph \(G\) is a union of \(k\) matchings of \(G\) which covers \(V(G)\) . The matching cover number of \(G\) , denoted by \(mc(G)\) , is the minimum number \(k\) such that \(G\) has a \(k\) -matching cover. A matching cover of \(G\) is optimal if it consists of \(mc(G)\) matchings of \(G\) . In this paper, we present an alg...

If a graph has a unique perfect matching, we call it a UPM-graph. In this paper we study UPM-graphs. It was shown by Kotzig that a connected UPM-graph has a cut edge belonging to its unique perfect matching. We strengthen this result to a further structural characterization. Using the stronger result, we present a characterization of claw-free UPM-...

We consider online scheduling of unit length jobs on m identical parallel-batch machines. Jobs arrive over time. The objective is to minimize maximum flow-time, with the flow-time of a job being the difference of its completion time and its release time. A parallel-batch machine can handle up to b jobs simultaneously as a batch. Here, the batch cap...

In this paper, the problem of minimizing maximum cost and makespan simultaneously on an unbounded parallel-batching machine is considered. An unbounded parallel-batching machine is a machine that can handle any number of jobs in a batch and the processing time of a batch is the largest processing time of jobs in the batch. The main goal of a multic...

Let G be a mixed graph and L(G)L(G) be the Laplacian matrix of the mixed graph G . The first eigenvalue of G is referred to the least nonzero eigenvalue of L(G)L(G). Let MG(n,k)MG(n,k) be the set of nonsingular mixed graphs with n vertices and k pendant vertices, where n≥4n≥4. In this paper, up to a signature matrix, we determine the unique graph w...

We consider the online (over time) scheduling of equal length jobs on a bounded parallel batch machine with a capacity b to minimize makespan with restart or limited restart. Let α≈0.29α≈0.29, β≈0.47β≈0.47, γ≈0.38γ≈0.38, and φ≈0.40φ≈0.40 be four parameters defined in the text. When b=2b=2, we present a best possible online algorithm HL(b=2)HL(b=2)...

We consider the online scheduling of incompatible unit-length job families on an unbounded parallel-batch machine with lookahead. In this paper online means that jobs arrive over time. The objective is to mininize the makespan. In the lookahead model, at a time instant t , an online algorithm can foresee the information of all jobs arriving in the...

We consider the online scheduling of equal-length jobs with incompatible families on
$m$
identical batch machines. Each job has a release time, a deadline and a weight. Each batch machine can process up to
$b$
jobs (which come from the same family) simultaneously as a batch, where
$b$
is called the capacity of the machines. Our goal is to det...

In this paper, we consider two problems about the preemptive scheduling of a set of jobs with release times on a single machine. In the first problem, each job has a deadline. The objective is to find a feasible schedule which minimizes the total completion time of the jobs. In the second problem (called two-agent scheduling problem), the set of jo...

An induced forest kk-partition of a graph GG is a kk-partition (V1,V2,…,Vk)(V1,V2,…,Vk) of the vertex set of GG such that, for each ii with 1≤i≤k1≤i≤k, the subgraph induced by ViVi is a forest. The vertex-arboricity of a graph GG is the minimum kk such that GG has an induced forest kk-partition. In the literature, it has been shown that every plana...

In this paper, we study a new primary–secondary bicriteria scheduling problem on identical machines. The primary objective is to minimize the total completion time of all jobs and the secondary objective is to minimize the maximum T-time of all machines, where the T-time of a machine is defined as the total completion time of the jobs scheduled on...

We consider the single-machine online scheduling with job rejection to minimize the total completion time of the scheduled jobs plus the total rejection cost of the rejected jobs under an agreeable condition on the processing times and rejection penalties of the jobs. In the problem, a set of independent jobs arriving online over time has to be sch...

The inverse and reverse counterparts of the single-machine scheduling problem
$1||L_{\max }$
are studied in [2], in which the complexity classification is provided for various combinations of adjustable parameters (due dates and processing times) and for five different types of norm:
$\ell _{1},\ell _{2},\ell _{\infty },\ell _{H}^{\Sigma } $
,...

This paper revisits the classic single-machine scheduling to minimize the total earliness and tardiness. It is known that the problem is NP-hard in the ordinary sense, but the exact complexity of the problem is long-standing open. We show in this paper that this problem is strongly NP-hard.

This paper studies the two-agent scheduling on an unbounded parallel-batching machine. In the problem, there are two agents A and B with each having their own job sets. The jobs of a common agent can be processed in a common batch. Moreover, each agent has an objective function to be minimized. The objective function of agent A is the makespan of h...

We consider the rescheduling on a single machine with release dates to minimize the makespan and total sequence disruption simultaneously. In the literature, a polynomial-time algorithm was presented for minimizing the makespan under a limit on the total sequence disruption. But the algorithm is not strongly polynomial. We present a strongly polyno...

Let U (n, k) be the set of non-bipartite unicyclic graphs with n vertices and k pendant vertices, where n ≥ 4. In this paper, the unique graph with the minimal least eigenvalue of the signless Laplacian among all graphs in U (n, k) is determined. Furthermore, it is proved that the minimal least eigenvalue of the signless Laplacian is an increasing...

We consider the online scheduling of incompatible job families on an unbounded parallel-batch machine to minimize the makespan, where jobs arrive over time and the number of job families, ff, is known in advance. We provide an optimal online algorithm for the problem with a competitive ratio of 1+4f2+1−12f.

Let U(n, k) be the set of non-bipartite unicyclic graphs with n vertices and k pendant vertices, where n ≥ 4. In this paper, the unique graph with the minimal least eigenvalue of the signless Laplacian among all graphs in U(n, k) is determined. Furthermore, it is proved that the minimal least eigenvalue of the signless Laplacian is an increasing fu...

Let Tn,n-4 be the set of trees on n vertices with diameter n - 4. In this paper, we determine the unique tree which has the minimal Laplacian spectral radius among all trees Tn,n-4 The work is related with that of Yuan [The minimal spectral radius of graphs of order n with diameter n - 4, Linear Algebra Appl. 428 (2008) 2840-2851], which determined...

We consider two-agent scheduling on a single machine with release dates and preemption to minimize the maximum lateness. In this scheduling model, there are two agents \(A\hbox { and }B\) each having his own job set \(\mathcal{J}_A= \{ J^a_1, \ldots , J^a_{n_a}\}\hbox { and }\mathcal{J}_B= \{ J^b_1, \ldots , J^b_{n_b}\}\) , respectively. Each job \...

We consider the online scheduling on an unbounded parallel-batch machine and a standard machine to minimize makespan. In the problem, the jobs arrive online over time and to be processed on two machines M1M1 and M2M2. M1M1 is an unbounded parallel-batch machine and M2M2 is a standard machine. The objective is to minimize the makespan, i.e., the max...

We consider the online scheduling on two identical parallel machines with chain precedence constraints to minimize makespan, where jobs arrive over time and have identical processing times. For this online scheduling problem, Huo and Leung [Y. Huo and J.Y.-T. Leung, Online scheduling of precedence constrained tasks, SIAM Journal on Computing, 34 (2...

We consider the scheduling problems arising when two agents, each with a family of jobs, compete to perform their respective jobs on a common unbounded parallel-batching machine. The batching machine can process any number of jobs simultaneously in a batch. The processing time of a batch is equal to the maximum processing time of the jobs in the ba...

This paper studies the online scheduling of equal-length jobs with incompatible families on multiple batch machines which can process the jobs from a common family in batches, where each batch has a capacity b with b=∞b=∞ in the unbounded batching and b<∞b<∞ in the bounded batching. Each job J has an equal-length integral processing time p>0p>0, an...

We study an on-line single parallel-batch machine scheduling problem where each job has a processing time and a delivery time. Jobs arrive over time and the batch capacity is unbounded. Jobs can be processed in a common batch, and each job is delivered independently and immediately at its completion time on the machine. The objective is to minimize...

This paper considers bi-criteria scheduling on a single parallel-batch machine to minimizing two regular scheduling criteria that are non-decreasing in the job completion times. For minimizing the total weighted completion time and the makespan simultaneously, we prove that the problem is NP-hard in the ordinary sense and possesses a fully polynomi...

We consider the on-line version of the single machine unbounded parallel-batching scheduling with delivery times of jobs. Each jobʼs information, such as processing time pj and delivery time qj, is not known in advance and becomes known at its arrival time. Once the processing of a job is completed, we deliver it to the destination. Here, the time...

We consider online scheduling on m unbounded parallel-batch machines to minimize maximum flow-time of the jobs. We show that no online algorithm can have a competitive ratio less than 1+αm, where αm is the positive root of α2+(m+1)α−1=0, and this lower bound is still valid even when all jobs have the same processing times. Then we provide an online...