带准备时间的自由作业排序问题—最坏性能比分析

本文研究了一类自然的排序问题，带准备时间的自由作业排序。在机器台数任意的情况下，证明了一个简单的贪婪算法的最坏性能比不超过２，并猜想该算法的临界为２－１／ｍ，其中ｍ为机器台数。特别当ｍ＝２时，证明了该算法的最坏性能比恰为３／２。     

订单带多工类工件时的极小迟后范围问题

本文考虑下述由多工类工件组成的订单的单机排序问题：每一个客户提供一个由若干工件组成的订单,总共n个工件又分成k个类．当机器从加工某类中的工件转向加工不同于它的第i类工件时,需一调整时间si．每一订单有一给定的应交工时间,订单的完工时间定义为该定单所含全部工件完工时的时间．我们希望适当排列这n个工件,使得订单的迟后范围最小．相应这一排序问题,文中依不同的背景给出了以下二种模式：同类工件一起连续加工,工件的完工时间为其所属类中全部工件完工时的时间,用GT,Ba来表示；同类工件一起连续加工,工件的完工时间为其本身的完工时间,用GT,Ja来表示．对于这两种模式的排序同题,我们均证明了其NP-hard性并给出了对应的分枝定界算法．     

加工时间和尺寸成正比单机排序和工件运输的最小化最大完工时间问题

在单机排序和工件运输的最小化最大完工时间问题中,工件首先在一台机器上加工,然后被一辆有容量限制的汽车运送到一个顾客．当工件的加工时间和尺寸无关时, Chang和Lee已经证明该问题是强NP困难的．他们也给出了一个启发式算法,它的最差执行比为5／3,并且这个界是紧的．本文考虑工件的加工时间和尺寸成正比的情形,证明了Chang和Lee的算法有更好的最差执行比53／35,并提供了一个新的启发式算法,它的最差执行比是3／2,并且这个界是最好的．     

单可变资源最小化加权完工时间和排序问题的强NP-困难性

Baker和Nuttle提出了下述单可变资源排序问题：扎个工件利用某个单资源进行加工使得工件的完工时间的某个函数达到最小,而资源的可利用率是随着时间而变化的．当最小化的目标函数是工件的加权完工时间和时,Baker和Nuttle猜测该问题是NP-困难的．最近,Yuan、Cheng和Ng证明该问题在一般意义下是NP-困难的,但是问题的精确复杂性仍然是悬而未决的．本文我们证明了该问题是强NP-困难的．     

带有拒绝的单机和同型机排序问题

研究了带有拒绝的单机和同型机排序问题. 对于单机情形, 工件的惩罚费用是对应加工时间的\alpha倍.如果工件有到达时间, 目标为最小化时间表长与惩罚费用之和, 证明了这个问题是可解的.如果所有工件在零时刻到达, 目标为最小化总完工时间与惩罚费用之和, 也证明了该问题是可解的.对于同型机排序问题, 研究了工件分两批在线实时到达的情形, 目标为最小化时间表长与惩罚费用之和.针对机器台数2和m, 分别给出了竞争比为2和4-2/m的在线算法.     

具有不可用区间且工件可拒绝下的单机重新排序问题的近似方案

本文考虑了机器具有不可用区间且工件可拒绝下的单机重新排序问题,在该问题中,给定一个工件集需在一台机器上加工,每个工件有自己的加工时间和权重,且对该工件集目标函数为极小化总加权完工时间的排序计划已给定,根据该排序计划中每个工件的完工时间已确定每个工件的承诺交付时间。然而,在工件正式开始加工前,原计划用于加工的某段时间区间因临时用于检修机器而导致机器在该时间区间不再可用,需要对工件重新排序。为了确保在新的重新排序中,工件的延误成本不致太大,决策者可以选择拒绝部分工件,但需支付相应的拒绝费用。任务是确定接受工件集和拒绝工件集,并将接受的工件在考虑机器具有不可用区间的条件下重新排序使得接受工件集的总加权完工时间,总拒绝费用及赋权最大延误之和最小。该问题是NP-困难的,对此给出了伪多项式时间动态规划精确算法,利用稀疏技术设计了完全多项式时间近似方案。     

问题Pm|rj,B|∑Cj的多项式时间近似算法

本文针对同型机分批排序问题Pm|rj,B|∑Cj进行了研究,给出了该问题在批容量B及机器台数m为常数情况下的多项式时间近似算法(以下简称PTAS);在B为常数时设计出了问题1|rj,B|∑WjCj的计算时间更少的PTAS．     

在线可中断二台机器流水作业问题

本文研究了可中断的二台机器流水作业排序问题,目标函数为最小化最大完工时间,工件实时到达,工件信息在工件到达之前不可知。我们给出了该在线问题的下界,并对问题中只有两个到达时间的特殊情况给出了3/2竞争的在线算法。     

具有特殊工件的平行机在线排序问题

本文研究一类具有特殊工件的平行机在线排序问题,目标是最小化最大完工时间.此模型有两种工件:正常工件和特殊工件.正常工件能够在m台平行机的任何一台机器上加工,而特殊工件仅能够在它唯一被指定的机器上加工.文中所有特殊工件的指定机器为M1.我们提供了竞争比为(2m2-2m 1)/(m2-m 1)的在线近似算法.当m=2时,算法是最好可能的.当m=3时,算法的竞争比为13/7≈1.857,并且提供了竞争比的下界(1 (平方根33))14≈1.686.     

带有退化效应和序列相关运输时间的排序问题

考虑带有退化效应和序列相关运输时间的单机排序问题. 工件的加工时间是其开工时间的简单线性增加函数. 当机器单个加工工件时, 极小化最大完工时间、(加权)总完工时间和总延迟问题被证明是多项式可解的, EDD序对于极小化最大延迟问题不是最优排序, 另外, 就交货期和退化率一致情形给出了一最优算法. 当机器可分批加工工件时, 分别就极小化最大完工时间和加权总完工时间问题提出了多项式时间最优算法.     

A graph coloring approach to scheduling of multiprocessor tasks on dedicated machines with availability constraints

We address a generalization of the classical 1- and 2-processor unit execution time scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these stipulations we show that the problem of optimal scheduling of sparse tree-like instances can be solved in polynomial time. However, if we admit dense instances then the problem becomes NP-hard, even if there are only two machines.     

Minimizing makespan for two parallel machines with job limit on each availability interval

We consider the problem of scheduling jobs on two parallel machines that are not continuously available for processing. The machine is not available after processing a fixed number of jobs in order to make precision adjustment of machines such as in wafer manufacturing, to reload the feeder in printed circuit board production, or to undertake any other maintenance works such as cleaning and safety inspections. The objective of the problem is to minimize the makespan. Two different scheduling horizons are investigated for this problem. For the short-term scheduling horizon, we consider only the time period before the unavailability interval, while for the long-term horizon, machines are allowed to restart processing after the unavailability interval. For both cases, which are strongly NP-hard, exact optimization algorithms based on the branch and bound method are proposed. Although the algorithms have exponential time complexities, computational results show that they can solve optimally the various-sized problems in reasonable computation time.     

Parallel machine scheduling problems with a single server

In this paper, we consider the problem of scheduling jobs on parallel machines with setup times. The setup has to be performed by a single server. The objective is to minimize the schedule length (makespan), as well as the forced idle time. The makespan problem is known to be NP-hard even for the case of two identical parallel machines. This paper presents a pseudopolynomial algorithm for the case of two machines when all setup times are equal to one. We also show that the more general problem with an arbitrary number of machines is unary NP-hard and analyze some list scheduling heuristics for this problem. The problem of minimizing the forced idle time is known to be unary NP-hard for the case of two machines and arbitrary setup and processing times. We prove unary NP-hardness of this problem even for the case of constant setup times. Moreover, some polynomially solvable cases are given.     

A tabu search algorithm for the Open Shop problem

In this paper we consider the minimum makespan Open Shop problem without preemption. It is well-known that the case with only two machines can be optimally solved in linear time, whereas the problem with an arbitrary number of machines is NP-hard in the strong sense. We propose a tabu search algorithm for the solution of the problem which uses simple list scheduling algorithms to build the starting solutions. The algorithm is extensively tested on randomly generated instances.     

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.     

On discrete lot-sizing and scheduling on identical parallel machines

We consider the multi-item discrete lot-sizing and scheduling problem on identical parallel machines. Based on the fact that the machines are identical, we introduce aggregate integer variables instead of individual variables for each machine. For the problem with start-up costs, we show that the inequalities based on a unit flow formulation for each machine can be replaced by a single integer flow formulation without any change in the resulting LP bound. For the resulting integer lot-sizing with start-ups subproblem, we show how inequalities for the unit demand case can be generalized and how an approximate version of the extended formulation of Eppen and Martin can be constructed. The results of some computational experiments carried out to compare the effectiveness of the various mixed-integer programming formulations are presented.     

Scheduling unit-length jobs with precedence constraints of small height

We consider the problem of scheduling unit-length jobs on identical machines subject to precedence constraints. We show that natural scheduling rules fail when the precedence constraints form a collection of stars or a collection of complete bipartite graphs. We prove that the problem is in fact NP-hard on collections of stars when the input is given in a compact encoding, whereas it can be solved in polynomial time with standard adjacency list encoding. On a subclass of collections of stars and on collections of complete bipartite graphs we show that the problem can be solved in polynomial time even when the input is given in compact encoding, in both cases via non-trivial algorithms.     

Online scheduling of parallel jobs on two machines is 2-competitive

We consider online scheduling of parallel jobs on parallel machines. For the problem with two machines and the objective of minimizing the makespan, we show that 2 is a tight lower bound on the competitive ratio. For the problem with m machines, we derive lower bounds using an ILP formulation.     

Improved MILP models for two-machine flowshop with batch processing machines

In this paper, we consider the problem of scheduling jobs in a flowshop with two batch processing machines such that the makespan is minimized. Batch processing machines are frequently encountered in many industrial environments such as heat treatment operations in a steel foundry and chemical processes performed in tanks or kilns. Improved Mixed Integer Linear Programming (MILP) models are presented for the flowshop problem with unlimited or zero intermediate storage. An MILP-based heuristic is also developed for the problem. Computational experiments show that the new MILP models can significantly improve the original ones. Also, the heuristic can obtain the optimal solutions for all the test problem instances.     

Local search algorithms for the multiprocessor flow shop scheduling problem

The multiprocessor flow shop scheduling problem is a generalization of the ordinary flow shop scheduling problem. The problem consists of both assigning operations to machines and scheduling the operations assigned to the same machine. We review the literature on local search methods for flow shop and job shop scheduling and adapt them to the multiprocessor flow shop scheduling problem. Other local search approaches we consider are variable-depth search and simulated annealing. We show that tabu search and variable-depth search with a neighborhood originated by Nowicki and Smutnicki outperform the other algorithms.