Minimizing makespan with multiple-orders-per-job in a two-machine flowshop

We investigate a new scheduling problem, multiple-orders-per-job (MOJ), in the context of a two-machine flowshop. Lower bounds for the makespan performance measure are provided for combinations of lot-processing and item-processing machines. An optimization model is presented that addresses both job formation and job sequencing. We define a heuristic to minimize the makespan for the MOJ problem for two-machine item-processing flowshops. The heuristic obtains solutions within 2% of a tight lower bound and runs in O(HF) time, where H is the number of orders and F is the restricted number of jobs.     

Evolutionary hybrid approaches for generation scheduling in power systems

Generation scheduling (GS) in power systems is a tough optimisation problem which continues to present a challenge for efficient solution techniques. The solution is to define on/off decisions and generation levels for each electricity generator of a power system for each scheduling interval. The solution procedure requires simultaneous consideration of binary decision and continuous variables. In recent years researchers have focused much attention on developing new hybrid approaches using evolutionary and traditional exact methods for this type of mixed-integer problems. This paper investigates how the optimum or near optimum solution for the GS problem may be quickly identified. A design is proposed which uses a variety of metaheuristic, heuristics and mathematical programming techniques within a hybrid framework. The results obtained for two case studies are promising and show that the hybrid approach offers an effective alternative for solving the GS problems within a realistic timeframe.     

A duality approach to admission and scheduling controls of queues

This paper studies theadmission andscheduling control problem in anM/M/2 queueing system with nonidentical processors. Admission control renders when a newly arrived job should be accepted, whereas scheduling control determines when an available processor should be utilized. The system received a rewardR when a job completes its service and pays a unit holding costC while a job is in the system. The main goal of the paper is to obtain the admission/scheduling policy that maximizes the expected discounted and long-run average profits (reward minus cost). We convert the system into its dual, a stochastically identical system subject toexpulsion/scheduling control, and prove that the individually optimal policy in the dual system is socially optimal in the original system. In contrast with the dynamic programming (DP) technique which considers the system as a whole, we adopt the viewpoint of an individual job and analyze the impact of its behavior on the social outcome. The key properties which simplify the analysis are that under the individually optimal policy the profit of a job under the preemptive last-come first-priority service discipline (LCFP-P) is independent of jobs arrived earlier than itself and that the system is insensitive to service discipline imposed. The former makes possible to bypass complex dynamic programming analyses and the latter serves as a vehicle in connecting the social and individual optimality. We also exploit system operational characteristics under LCFP-P to obtain simple and close approximations of the optimal thresholds.     

Optimal allocation and processing time decisions on non-identical parallel CNC machines: ϵ-constraint approach

When the processing times of jobs are controllable, selected processing times affect both the manufacturing cost and the scheduling performance. A well known example for such a case that this paper specifically deals with is the turning operation on a CNC machine. Manufacturing cost of a turning operation is a nonlinear convex function of its processing time. In this paper, we deal with making optimal machine-job assignments and processing time decisions so as to minimize total manufacturing cost while the makespan being upper bounded by a known value, denoted as ?-constraint approach for a bicriteria problem. We then give optimality properties for the resulting single criterion problem. We provide alternative methods to compute cost lower bounds for partial schedules, which are used in developing an exact (branch and bound) algorithm. For the cases where the exact algorithm is not efficient in terms of computation time, we present a recovering beam search algorithm equipped with an improvement search procedure. In order to find improving search directions, the improvement search algorithm uses the proposed cost bounding properties. Computational results show that our lower bounding methods in branch and bound algorithm achieve a significant reduction in the search tree size that we need to traverse. Also, our recovering beam search and improvement search heuristics achieve solutions within 1% of the optimum on the average while they spent much less computational effort than the exact algorithm.     

两个可解的2×n自由作业排序问题

本文考虑将ｎ个互相独立的每道工序加工时长相等的工件放在两台机器上加工的自由作业排序问题。讨论了目标函数分别是带权完工时间和（Ｏ２／ＵＥＴ／Σｗｉｃｉ）及最大迟后（Ｏ２／ＵＥＴ／Ｌｍａｘ）两个问题，分别得到了计算时间限为Ｏ（ｎｌｏｇｎ）及Ｏ（ｎ２）的两个求解最优时间表的多项式算法。     

Minmax scheduling with job-classes and earliness–tardiness costs

We address scheduling problems with job-dependent due-dates and general (possibly nonlinear and asymmetric) earliness and tardiness costs. The number of distinct due-dates is substantially smaller than the number of jobs, thus jobs are partitioned to classes, where all jobs of a given class share a common due-date. We consider the settings of a single machine and parallel identical machines. Our objective is of a minmax type, i.e., we seek a schedule that minimizes the maximum earliness/tardiness cost among all jobs.     

Minimizing the weighted number of early and tardy jobs in a stochastic single machine scheduling problem

We study a static stochastic single machine scheduling problem in which jobs have random processing times with arbitrary distributions, due dates are known with certainty, and fixed individual penalties (or weights) are imposed on both early and tardy jobs. The objective is to find an optimal sequence that minimizes the expected total weighted number of early and tardy jobs. The general problem is NP-hard to solve; however, in this paper, we develop certain conditions under which the problem is solvable exactly. An efficient heuristic is also introduced to find a candidate for the optimal sequence of the general problem. Our illustrative examples and computational results demonstrate that the heuristic performs well in identifying either optimal sequences or good candidates with low errors. Furthermore, we show that special cases of the problem studied here reduce to some classical stochastic single machine scheduling problems including the problem of minimizing the expected weighted number of early jobs and the problem of minimizing the expected weighted number of tardy jobs which are both solvable by the proposed exact or heuristic methods.     

排序问题中优化准则关于基本参数的正则性及其应用

本文提出了优化准则关于加工时间、准备时间、应交工时间的正则性，利用这种正则性对寻找参数可控排序问题中的有效值、有效解给出了一直观算法，并指出对一些具体的参数可控排序问题，其有效值、有效解的寻找可通过对这一直观算法加以具体化而得．文中还对平均流程问题给出了这样一个具体化算法．     

准时生产制（JIT）排序问题的发展和动态

本文综述十几年来国内外在准时生产制排序领域中取得的研究成果，提出这一领域有特继续研究的一些问题。     

Batching deteriorating items with applications in computer communication and reverse logistics

We study two deterministic scheduling problems that combine batching and deterioration features. In both problems, there is a certain demand for identical good quality items to be produced in batches. In the first problem, each batch is assigned an individual machine that requires a cost and a time to be activated. All the machines are identical, work in parallel, and always produce good quality items. All the items are available at time zero and they deteriorate while waiting for production. Deterioration results in a linear increase of time and cost of production. In the second problem, there is a single machine that produces good quality as well as defective items in batches. Each batch is preceded by a setup time and requires a setup cost. Defective items have to be reworked on the same machine. They deteriorate while waiting for rework. At a time to be decided, the machine switches from production to rework defective items of the current batch. After rework, every defective item has the required good quality. In both problems, the objective is to find batch partitioning such that a linear combination of the production cost and production completion time is minimized. The two problems are observed at computer service providers and also reverse logistics. In computer service providers, machines and items correspond to communication service channels and information transfer tasks, respectively. We reduce both problems to minimizing a function of one variable representing the number of batches. In an optimal solution of either problem, there are at most two different batch sizes. Linear time algorithms are proposed for both problems.