具有老化效应的单机共同工期安排和工件可拒绝排序问题

研究共同工期安排和具有老化效应的单机排序问题。在整个加工过程中,工件的实际加工时间是与其所在位置和工件本身老化率相关的函数,生产商可以通过支付一定的处罚费用而拒绝加工某些工件。鉴于生产过程中出现老化效应,通过采取维修活动来提高生产率。目标是划分接受工件集和拒绝工件集,确定接受工件集中工件的加工次序和维修活动安排的位置,以极小化接受工件的提前、延误、工期与拒绝工件的总处罚费用的加权和。对这一问题,首先将其转化为指派问题并构造了最优多项式时间算法;其次,证明了目标函数满足一定条件下的问题的更一般形式能够在多项式时间内得到最优解;最后,对本文问题的一个特殊情况,设计了具有更低时间复杂度的多项式动态规划算法。     

基于一般学习效应下的单机排序问题

近来具有学习效应的机器排序问题收到广泛的关注.对于机器排序中工件的实际加工来说,与工件加工位置有关的学习模型更具有现实性.本文研究了工件加工位置和与已经加工过的工件之和有关的一般学习效应模型.首先证明文献中与位置和已经加工过的工件加工时间之和有关的学习模型是本模型的特殊情形.其次对于单机排序问题我们提出一般解法.     

具有优先约束的单机随机排序问题

讨论工件的加工时间为常数,机器发生随机故障的单机随机排序问题,目标函数极小化工件的加权完工时间和的数学期望最小.考虑两类优先约束模型.在第一类模型中,设工件间的约束为串并有向图.证明了模块M的ρ因子最大初始集合I中的工件优先于模块中的其它工件加工,并且被连续加工所得的排序为最优排序,从而将Lawler用来求解约束为串并有向图的单机加权总完工时间问题的方法推广到机器发生随机故障的情况.在第二类模型中,设工件间的约束为出树优先约束.证明了最大家庭树中的工件优先于家庭树中其它的工件加工,并且其工件连续加工所得到的排序为最优排序并给出了最优算法.     

Algorithms for single-machine scheduling with stochastic outtree precedence relations to minimize expected weighted flow time or maximum expected lateness

Stochastic single-machine scheduling problems with special tree-like GERT precedence constraints and expected weighted flow time or maximum expected lateness as objective functions are considered. To obtain polynomial algorithms for these problems, Smith's ratio rule and Lawler's rule for the deterministic problems 1¦outtree¦w _v C _v and 1¦prec¦f _max , respectively, are generalized.     

Preemptive Scheduling with Two Minimax Criteria

Two preemptive single-machine bicriteria scheduling problems with release dates and deadlines are considered in this paper. Each criterion is formulated as a maximum cost. In the first problem the cost of both criteria depends on the completion time of the tasks. This problem can be solved by enumerating all the Pareto optimal points with an approach proposed by Hoogeveen (1996) for the nonpreemptive problem without release dates. In the second problem, the costs of one criterion are dependent on the completion times of the tasks and the costs of the other criterion are dependent on the start times. This problem is more difficult but an efficient algorithm is proposed for a sub-problem with heads, tails, release dates and deadlines that appears in the job-shop scheduling problem.     

The Common Cycle Economic Lot Scheduling Problem with Backorders: Benefits of Controllable Production Rates

In this paper, we deal with the production scheduling ofseveral products that are produced periodically, in a fixed sequence, ona single machine. In the literature, this problem is usually referred to asthe Common Cycle Economic Lot Scheduling Problem. We extend thelatter to allow the production rates to be controllable at the beginningof as well as during each production run of a product. Also, we assumethat unsatisfied demand is completely backordered. The objective is todetermine the optimal schedule that satisfies the demand for all theproducts and that realizes the minimum average setup, inventoryholding and backlog cost per unit time. Comparison with previousresults (when production rates are fixed) reveals that averagecosts can be reduced up to 66% by allowing controllable productionrates.     

分支定界算法求解带有释放时间的单机双代理调度问题

本文研究了带有释放时间的单机双代理调度问题,目标函数为极小化最大完工时间和。为了便于利用优化软件求解,建立了混合整数规划模型。考虑到该问题具有NP困难性,因此采用近似与精确算法分别求解不同规模问题。针对大规模问题,提出了优势代理优先启发式算法,并证明了其渐近最优性。针对小规模问题,设计了分支定界法进行最优求解,其中基于释放时间的分支规则和基于加工中断的下界有效地减少了运算时间。最后,通过数值测试验证了分支定界算法的有效性以及启发式算法的收敛性。     

具有指数和位置学习效应的机器排序问题

本文考虑指数学习效应和位置学习效应同时发生的新的排序模型.工件的实际加工时间不仅依赖于已经加工过工件正常加工时间之和的指数函数,而且依赖于该工件所在的位置.单机排序情形下,对于最大完工时间和总完工时间最小化问题给出多项式时间算法.此外某些特殊情况下,总权完工时间和最大延迟最小化问题也给出了多项时间算法.流水机排序情形,对最大完工时间和总完工时间最小化问题在某些特殊情形下给出多项时间算法.     

工件具有加工位置上限最小化加权总误工量的单机排序问题

考虑工件具有加工位置上限最小化总加权误工量的单机排序问题.在此排序问题中,每个工件J_j都具有一个加工位置上限k_j.也就是说,如果工件J_j是一个可行排序中的第x个工件,那么就需要满足x ≤ k_j.证明了（i）当工件具有相同工期时,该排序问题是二元NP-难的并且是拟多项式时间可解的,（ii）当工件具有单位权重时,该排序问题是一元NP-难的.     

Competitive Analysis of a Better On-line Algorithm to Minimize Total Completion Time on a Single-machine

We consider the problem of scheduling jobs on-line on a single machine with the objective of minimizing total completion time. We assume that jobs arrive over time and that release dates are known in advance, but not the processing times. The most important result we are given in this paper is the competitive analysis of a new clairvoyant on-line algorithm for this scheduling problem. We are proving that this deterministic semi-online algorithm, called ST-, is -competitive, which beats the existing lower bound for non-clairvoyant online algorithms.