Cooperation in one machine scheduling

A combinatorial optimization problem can often be understood as the problem to minimize cost in a complex situation. If more than one party is involved, the solution of the optimization problem is not the end of the story. In addition it has to be decided how the minimal total cost has to be distributed among the parties involved. In this paper cost allocation problems will be considered arising from one-machine scheduling under additive and weakly increasing cost functions. The approach of the problem will be game theoretical and we shall in fact show that in many cases the games related to the cost allocation problems are balanced.     

Multi-agent single machine scheduling

We consider the scheduling problems arising when several agents, each owning a set of nonpreemptive jobs, compete to perform their respective jobs on one shared processing resource. Each agent wants to minimize a certain cost function, which depends on the completion times of its jobs only. The cost functions we consider in this paper are maximum of regular functions (associated with each job), number of late jobs and total weighted completion time. The different combinations of the cost functions of each agent lead to various problems, whose computational complexity is analysed in this paper. In particular, we investigate the problem of finding schedules whose cost for each agent does not exceed a given bound for each agent.     

Uniform machine scheduling with machine available constraints

1.IntroductionIntheclassicalparallelmachineschedulingareaweassumethatmachinesarealwaysavailable.However,aspointedin[1],inrealindustrysettingsthisassumptionmaynotbetrue.Forexample,machinesmaynotalwaysbeavailablebecauseoftheirpreventivemaintenanceduringtheschedulingperiod.Thatistosay,eachmachineiisunavailablefromsibuntilrib(05sib5rib),where0SkSm,withmbeingthenumberofunavailabilityperiodsformachineiduringtheplanninghorizon.Inotherwords,somepapersstatethatmachinesareavailableintimewindows,whichi…     

Single machine scheduling with semi-resumable machine availability constraints

This paper considers the semi-resumable model of single machine scheduling with a non-availability period. The machine is not available for processing during a given time interval. A job cannot be completed before the non-availability period will have to partially restart after the machine has become available again. For the problem with objective of minimizing makespan, the tight worst-case ratio of algorithm LPT is given, and an FPTAS is also proposed. For the problem with objective of minimizing total weighted completion time, an approximation algorithm with worst-case ratio smaller than 2 is presented. Two special cases of the latter problem are also considered, and improved algorithms are given.     

Parallel machine scheduling with machine availability and eligibility constraints

In this paper we consider the problem of scheduling n independent jobs on m identical machines incorporating machine availability and eligibility constraints while minimizing the makespan. Each machine is not continuously available at all times and each job can only be processed on specified machines. A network flow approach is used to formulate this scheduling problem into a series of maximum flow problems. We propose a polynomial time binary search algorithm to either verify the infeasibility of the problem or solve it optimally if a feasible schedule exists.     

机器和工人都有加工资质约束的平行机排序问题研究

研究一类新型的平行机排序问题, 即在机器和工人都是必需的加工资源并且都有加工资质约束的情况下, 如何在一组平行机上进行工件排序(或称调度)以最小化时间表长C_max. 将研究工件加工时间均为单位时间的情况, 通过建立网络流模型以及采用二分搜索技术, 可以在多项式时间内精确地求解上述问题, 算法复杂度为O(n^{3}logn). 同时提供了一种基于双重动态柔性选择\,(DDFS)\,策略的启发式算法,可以获得较好的排序效果, 算法复杂度为O(n^{2}).     

Uniform parallel machine scheduling problems with fixed machine cost

This paper considers two uniform parallel machine scheduling problems with fixed machine cost under the background of cloud manufacturing. The goal is to minimize the makespan with a given budget of total cost, \(\hat{U}\). All the jobs are homogeneous, i.e., the processing times of the jobs are identical. Non-preemptive and preemptive problems are studied. For the non-preemptive problem, we give a \(2[1+1{/}(h-1)]\)-approximation algorithm, where h is the number of the machine which can not be selected the first time. For the preemptive problem, we give an algorithm whose worst-case bound equals to \(1+1{/}(h-1)\). Preliminary experimental results indicate that the proposed algorithms are reasonably accurate compared with the lower bounds.     

Match-up scheduling under a machine breakdown

When a machine breakdown forces a modified flow shop (MFS) out of the prescribed state, the proposed strategy reschedules part of the initial schedule to match up with the preschedule at some point. The objective is to create a new schedule that is consistent with the other production planning decisions like material flow, tooling and purchasing by utilizing the time critical decision making concept. We propose a new rescheduling strategy and a match-up point determination procedure through a feedback mechanism to increase both the schedule quality and stability. The proposed approach is compared with alternative reactive scheduling methods under different experimental settings.     

Nonpreemptive flowshop scheduling with machine dominance

Flowshop scheduling deals with processing a set of jobs through a set of machines, where all jobs have to pass among machines in the same order. With the exception of minimizing a makespan on two machines, almost all other flowshop problems in a general setup are known to be computationally intractable. In this paper we study special cases of flowshop defined by additional machine dominance constraints. These constraints impose certain relations among the job processing times on different machines and make the studied problems tractable.     

Parallel machine scheduling with high multiplicity

In high-multiplicity scheduling problems, identical jobs are encoded in the efficient format of describing one of the jobs and the number of identical jobs. Similarly, identical machines are efficiently encoded in the same manner. We investigate parallel-machine, high-multiplicity problems, where there are three possible machine speed structures: identical, proportional, or unrelated. For the objectives of minimizing the sum of job completion times and minimizing the makespan, we consider both nonpreemptive and preemptive problems. For some problems, we develop polynomial time algorithms. For several problems, we demonstrate that the recognition versions can be solved in polynomial time, while the optimization versions require pseudo-polynomial time. We also show that changing from standard binary encoding to high-multiplicity encoding does not affect the complexity class of NP-complete problems. Received: April 1996 / Accepted: July 2000?Published online January 17, 2001     

Coordination mechanisms for parallel machine scheduling

We consider coordination mechanisms for the distributed scheduling of n jobs on m parallel machines, where each agent holding a job selects a machine to process his/her own job. Without a central authority to construct a schedule, each agent acts selfishly to minimize his/her own disutility, which is either the completion time of the job or the congestion time (defined as the load of the machine on which the job is scheduled). However, the overall system performance is measured by a central objective which is quite different from the agents’ objective. In the literature, makespan is often considered as the central objective. We, however, investigate problems with other central objectives that minimize the total congestion time, the total completion time, the maximum tardiness, the total tardiness, and the number of tardy jobs. The performance deterioration of the central objective by a lack of central coordination, referred to as the price of anarchy, is typically measured by the maximum ratio of the objective function value of a Nash equilibrium schedule versus that of an optimal, coordinated schedule. In this paper we give bounds for the price of anarchy for the above objectives. For problems with due date related objectives, the price of anarchy may not be defined since the optimal value may be zero. In this case, we consider the maximum difference between the objective function value of an equilibrium schedule and the optimal value. We refer to this metric as the absolute price of anarchy and analyze its lower and upper bounds.     

Single machine stochastic JIT scheduling problem subject to machine breakdowns

In this paper we research the single machine stochastic JIT scheduling problem subject to the machine breakdowns for preemptive-resume and preemptive-repeat.The objective function of the problem is the sum of squared deviations of the job-expected completion times from the due date.For preemptive-resume,we show that the optimal sequence of the SSDE problem is V-shaped with respect to expected processing times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.We discuss the difference between the SSDE problem and the ESSD problem and show that the optimal solution of the SSDE problem is a good approximate optimal solution of the ESSD problem,and the optimal solution of the SSDE problem is an optimal solution of the ESSD problem under some conditions.For preemptive-repeat,the stochastic JIT scheduling problem has not been solved since the variances of the completion times cannot be computed.We replace the ESSD problem by the SSDE problem.We show that the optimal sequence of the SSDE problem is V-shaped with respect to the expected occupying times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.A new thought is advanced for the research of the preemptive-repeat stochastic JIT scheduling problem.     

Single machine scheduling under potential disruption

We provide optimal algorithms to solve a new scheduling problem in which there is a possibility that a disruption will happen at a particular time and last for a period of time with a certain probability. The objective functions are the expected total weighted completion times and the expected maximum tardiness, respectively.     

On scheduling an unbounded batch machine

A batch machine is a machine that can process up to c jobs simultaneously as a batch, and the processing time of the batch is equal to the longest processing time of the jobs assigned to it. In this paper, we deal with the complexity of scheduling an unbounded batch machine, i.e., c=+∞. We prove that minimizing total tardiness is binary NP-hard, which has been an open problem in the literature. Also, we establish the pseudopolynomial solvability of the unbounded batch machine scheduling problem with job release dates and any regular objective. This is distinct from the bounded batch machine and the classical single machine scheduling problems, most of which with different release dates are unary NP-hard. Combined with the existing results, this paper provides a nearly complete mapping of the complexity of scheduling an unbounded batch machine.     

Single machine scheduling under market uncertainty

This paper considers single machine scheduling problems where job processing times are known and deterministic but where the reward received upon completion of a job changes stochastically over time according to Brownian motion. The objectives of maximizing expected net-present-value (NPV), minimizing the variance of NPV and maximizing the probability of achieving a minimum benchmark NPV are considered. For non-preemptive static list policies complexity results and branch and bound procedures are presented. The branch and bound procedures are shown to be effective for problem instances with 20–25 jobs. For the problem of maximizing NPV with non-preemptive dynamic policies the optimal static schedule is shown through empirical testing to be as good as a greedy heuristic and to be near optimal when the variance is not large.     

Schedule-an expert-like system for machine scheduling

The construction of an expert-like system for machine scheduling called SCHEDULE is presented. Essential parts of SCHEDULE were developed by students in a laboratory course Operations Research on Microcomputers at the University of Karlsruhe, Germany. SCHEDULE consists of the components data base, knowledge base, inference engine, explanation facility, dialog component, and knowledge acquisition component. The knowledge base contains an algorithm base for solving different types of scheduling problems. To establish the rules of the knowledge base the well-known three-field classification of deterministic machine scheduling problems and the concept of the reduction digraph are exploited. Experiences gained during building and demonstrating SCHEDULE are reported.     

Single machine earliness and tardiness scheduling

We examine the problem of scheduling a given set of jobs on a single machine to minimize total early and tardy costs without considering machine idle time. We decompose the problem into two subproblems with a simpler structure. Then the lower bound of the problem is the sum of the lower bounds of two subproblems. A lower bound of each subproblem is obtained by Lagrangian relaxation. Rather than using the well-known subgradient optimization approach, we develop two efficient multiplier adjustment procedures with complexity O(nlog n) to solve two Lagrangian dual subproblems. A branch-and-bound algorithm based on the two efficient procedures is presented, and is used to solve problems with up to 50 jobs, hence doubling the size of problems that can be solved by existing branch-and-bound algorithms. We also propose a heuristic procedure based on the neighborhood search approach. The computational results for problems with up to 3 000 jobs show that the heuristic procedure performs much better than known heuristics for this problem in terms of both solution efficiency and quality. In addition, the results establish the effectiveness of the heuristic procedure in solving realistic problems to optimality or near optimality.     

Single machine scheduling with batch deliveries

The single machine batch scheduling problem is studied. The jobs in a batch are delivered to the customer together upon the completion time of the last job in the batch. The earliness of a job is defined as the difference between the delivery time of the batch to which it belongs and its completion time. The objective is to minimize the sum of the batch delivery and job earliness penalties. A relation between this problem and the parallel machine scheduling problem is identified. This enables the establishment of complexity results and algorithms for the former problem based on known results for the latter problem.     

Makespan minimization in online scheduling with machine eligibility

In this paper we provide a survey of online scheduling in parallel machine environments with machine eligibility constraints and the makespan as objective function. We first give a brief overview of the different parallel machine environments and then survey the various types of machine eligibility constraints, including tree-hierarchical processing sets, Grade of Service processing sets, interval processing sets, and nested processing sets. We furthermore describe the relationships between the various different types of processing sets. We proceed with describing two basic online scheduling paradigms, namely online over list and online over time. For each one of the two paradigms we survey all the results that have been recorded in the literature with regard to each type of machine eligibility constraints. We obtain also several extensions in various directions. In the concluding section we describe the most important open problems in this particular area.