Multi-objective scheduling of two-job families on a single machine

This paper presents a preliminary analysis of the typical scheduling environment in semiconductor manufacturing involving multiple job families, and where more than one objective such as cycle time, machine utilization and the due-date accuracy needs to be simultaneously considered. In this study, the NP-hard problem of scheduling N independent jobs on a single testing machine with due dates and sequence-dependent setup times is addressed, where the multiple objectives are to minimize average cycle time, to minimize average tardiness, and to maximize machine utilization. A Pareto optimal solution, which is not inferior to any other feasible solutions in terms of all objectives, is generated combining the analytically optimal and conjunctive simulated scheduling approach. First, the machine-scheduling problem is modeled using the discrete event simulation approach and the problem is divided into simulation clock based lot selection sub-problems. Then, a Pareto optimal lot is selected using the compromise programming technique for multiobjective optimization at each decision instant in simulated time. With the help of a broad experimental design, this developed solution is then compared with common heuristic-dispatching rules such as SPT and EDD, which show better results for all the objectives over a wide range of problems. The developed scheduling method shows approximately 16.7% reduction in average cycle time, 25.6% reduction in average tardiness, and 21.6% improvement in machine utilization over the common dispatching rules, SPT and EDD.     

中小呼叫中心月度排班优化模型与算法

国内中小呼叫中心制定坐席人员月度排班表时,通常考虑劳动法规合同约束和体现企业自身用工管理诉求。构建坐席人员月度排班优化问题的二次整数规划模型。鉴于问题模型难解性,依据调研企业需求和模型逻辑结构分析,把问题分解成三个子问题。通过构建整数规划模型和提出启发式算法来求出子问题解,从而生成排班问题优化解。问题实例计算表明,模型算法能够有效控制人力成本和兼顾员工同班次管理目标。与周排班方法比较,该方法能够充分体现月度排班人力灵活性来实现人力优化配置。     

Flexible reasoning using sensible agent-based systems: A case study in job flow scheduling

Planning and control systems for highly dynamic and uncertain manufacturing environments require adaptive flexibility and decision-making capabilities. Modern distributed manufacturing systems assess the utility of planning and executing solutions for both system goals (e.g. minimize manufacturing production time for all parts or minimize WIP) and local goals (e.g. expedite part A production schedule or maximize machine X utilization). Sensible Agents have the ability to alter their autonomy levels to choose among a set of decision models in order to handle the differences between local and system goals. In this paper, Sensible Agents are applied to a production planning and control problem in the context of job shop scheduling and decision model theory. Sensible Agents provide for trade-off reasoning mechanisms among system and local utilities that are flexible and responsive to an agent's abilities, situational context and position in the organizational structure of the system.     

PRODUCTION SCHEDULING OF CONTINUOUS FLOW LINES: MULTIPLE PRODUCTS WITH SETUP TIMES AND COSTS

The problem of production planning and setup scheduling of multiple products on a single facility is studied in this paper. The facility can only produce one product at a time. A setup is required when the production switches from one type of product to another. Both setup times and setup costs are considered. The objective is to determine the setup schedule and production rate for each product that minimize the average total costs, which include the inventory, backlog, and setup costs. Under the assumption of a constant production rate, we obtain the optimal cyclic rotation schedule for the multiple products system. Besides the decision variables studied in the classical economic lot scheduling problem (ELSP), the production rate is also a decision variable in our model. We prove that our solutions improve the results of the classical ELSP.     

A tardiness-augmented approximation scheme for rejection-allowed multiprocessor rescheduling

In the multiprocessor scheduling problem to minimize the total job completion time, an optimal schedule can be obtained by the shortest processing time rule and the completion time of each job in the schedule can be used as a guarantee for scheduling revenue. However, in practice, some jobs will not arrive at the beginning of the schedule but are delayed and their delayed arrival times are given to the decision-maker for possible rescheduling. The decision-maker can choose to reject some jobs in order to minimize the total operational cost that includes three cost components: the total rejection cost of the rejected jobs, the total completion time of the accepted jobs, and the penalty on the maximum tardiness for the accepted jobs, for which their completion times in the planned schedule are their virtual due dates. This novel rescheduling problem generalizes several classic NP-hard scheduling problems. We first design a pseudo-polynomial time dynamic programming exact algorithm and then, when the tardiness can be unbounded, we develop it into a fully polynomial time approximation scheme. The dynamic programming exact algorithm has a space complexity too high for truthful implementation; we propose an alternative to integrate the enumeration and the dynamic programming recurrences, followed by a depth-first-search walk in the reschedule space. We implemented the alternative exact algorithm in C and conducted numerical experiments to demonstrate its promising performance.

     

The permutation flow shop problem with just in time production considerations

This research presents a variation to the permutation flow shop problem where Just In Time (JIT) production requirements are taken into account. The model developed in this research employs dual objectives. In addition to the traditional objective of minimizing the production makespan, minimization of Miltenburg's material usage rate is also incorporated. In this model, multiple units of any product are permitted in the production sequence. However, the minimization of material usage rates attempts to prevent batch scheduling of products and allows unit flow of products as required in demand flow manufacturing. A solution method is proposed for determining an optimal production sequence via an efficient frontier approach and Simulated Annealing (SA). Test problems and specific performance criteria are used to assess the solutions generated by the proposed method. Experimental results presented in this paper show that the use of the efficient frontier and SA provide solutions that approach the optimal solution for the performance measures used in this research.     

基于改进遗传算法的置换装配线调度问题研究

企业的置换装配线调度问题（Permutation Assembly-line Scheduling Problem,PASP）是一类典型的NP-hard型生产调度问题,是现代集成制造系统CIMS极为关心的问题。该问题可以具体描述为n个工件要在m台机器上加工,每个工件需要经过m道工序,每道工序要求不同的机器,这n个工件通过m台机器的顺序相同,它们在每台机器上的加工顺序也相同,问题的主要目标是找到n个工件在每台机器上的最优加工顺序,使得最大完工时间最小。由于PASP问题的NP-hard性质,本文使用遗传算法对其进行求解。尽管遗传算法常用以求解调度问题,但其选择与交叉机制易导致局部最优及收敛慢。因此,本文提出基于区块挖掘与重组的改进遗传算法用于求解置换装配线调度问题。首先通过关联规则挖掘出不同的优秀基因,然后将具有较优结果的基因组合为优势区块,产生具优势的人工解,并引入高收敛性的局部搜索方法,提高搜索到最优解的机会与收敛效率。本文以OR-Library中Taillard标准测试例来验证改进遗传算法的求解质量与效率,结果证明：本文所提算法与其它求解调度问题的现有5种知名算法相比,不仅收敛速度较快,同时求解质量优于它们。     

SCHEDULING PARALLEL PROCESSORS WITH SETUP COSTS AND RESOURCE LIMITATIONS

An integer linear programming model is presented for the scheduling of n products on m identical machines. The particular problem studied is one that occurs frequently in the fiberglass and textile industries. The model incorporates setup costs, lost production costs, and overtime costs. Due to the structure of the model, integer solutions can be obtained by explicitly restricting only a small number of the integer variables. This allows those responsible for scheduling to solve realistically sized problems in an efficient manner. Computational results are provided for a set of generated test problems.     

A mathematical model for job shop scheduling with multiple process plan consideration per job

In this paper, a mixed integer programming model is formulated for scheduling a set of jobs through a shop when each job is supplied or provided with multiple process plans or process routings. Simultaneous selection of a process plan for each job and the sequencing of the jobs through the machines in the shop based on the set of selected process plans is addressed. The procedure developed seeks to integrate the selection of machines for each job and the sequencing of jobs on each machine based on the objective of minimizing production makespan. the application of the procedure is demonstrated with an example problem. The following conclusions were drawn as a result of the research: (1) the procedure developed produces optimal or near optimal solution; (2) the benefit from the developed approach is that it allows a shop to adaptively select process plans for jobs to optimize on production makespan. By combining solution quality with scheduling flexibility and efficiency, the productivity of a shop can be greatly enhanced.     

Flow shop scheduling with deteriorating jobs under dominating machines

This paper addresses no-wait or no-idle flow shop scheduling problems with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their starting time. A simple linear deterioration function is assumed and some dominating relationships between machines can be satisfied. It is shown that for the problems to minimize makespan or weighted sum of completion time, polynomial algorithms still exist, although these problems are more complicated than the classical ones. When the objective is to minimize maximum lateness or maximum tardiness, the solutions of a classical version may not hold.     

Optimum common cycle for scheduling a single-machine multiproduct system with a budgetary constraint

This paper deals with the single machine multi-product lot size scheduling problem, and has two objectives. The first objective is to minimize the maximum aggregate inventory for the common cycle (CC) scheduling policy. A simple and easy-to-apply rule has been developed which determines the optimal production sequence that achieves this objective. The second objective is to find an optimal common cycle for minimizing the average production and inventory costs per unit time, subject to a given budgetary constraint. A method has been presented that achieves this objective     

Minimization of maximum lateness under linear deterioration

This paper considers a single-machine scheduling problem to minimize the maximum lateness. The processing time of each job is a linear function of the time when the job starts processing. This problem is known to be -hard in the literature. In this paper, we design a branch-and-bound algorithm for deriving exact solutions by incorporating several properties concerning dominance relations and lower bounds. These properties produce synergic effects in accelerating the solution finding process such that the algorithm can solve problems of 100 jobs within 1 min on average. To compose approximate solutions, we revise a heuristic algorithm available in the literature and propose several hybrid variants. Numerical results evince that the proposed approaches are very effective in successfully reporting optimal solutions for most of the test cases.     

Equal Processing Time Bicriteria Scheduling on Parallel Machines

We consider the problem of scheduling jobs on parallel, identical machines so as to minimize a primary and a secondary criteria. All the jobs are assumed to have identical processing times. Polynomial time algorithms, that generate optimal solutions, are presented for various combinations of primary and secondary criteria.     

Traffic regulation with single- and dual-homed ISPs under a percentile-based pricing policy

We investigate how a customer (an enterprise or a large organization), when facing a percentile-based pricing policy, can optimally balance the Internet access cost and the traffic buffering delay penalty by traffic regulation. The problem is referred to as the Optimal Traffic Regulation (OTR) problem. Solutions to various cases of the OTR problem are provided. For a customer with a single-homed ISP, we present optimal solutions to the OTR problem based on dynamic programming for the offline case with a known traffic demand pattern. A real-time traffic scheduling algorithm is proposed to deal with the online case where the traffic demands are different from a given demand pattern. We further extend the dynamic programming model to the case of dual-homed ISPs. Experimental results on the data from an Internet trace confirm the effectiveness of our solutions. Part of the results has been presented in the First International Conference on Scalable Information Systems.     

Single-machine scheduling with production and rejection costs to minimize the maximum earliness

In this paper, we consider the single-machine scheduling problem with production and rejection costs to minimize the maximum earliness. If a job is accepted, then this job must be processed on the machine and a corresponding production cost needs be paid. If the job is rejected, then a corresponding rejection cost has to be paid. The objective is to minimize the sum of the maximum earliness of the accepted jobs, the total production cost of the accepted jobs and the total rejection cost of the rejected jobs. We show that this problem is equivalent to a single-machine scheduling problem to minimize the maximum earliness with two distinct rejection modes. In the latter problem, rejection cost might be negative in the rejection-award mode which is different from the traditional rejection-penalty mode in the previous literatures. We show that both of two problems are NP-hard in the ordinary sense and then provide two pseudo-polynomial-time algorithms to solve them. Finally, we also show that three special cases can be solved in polynomial time.     

The Retail Planning Problem Under Demand Uncertainty

We consider the retail planning problem in which the retailer chooses suppliers and determines the production, distribution, and inventory planning for products with uncertain demand to minimize total expected costs. This problem is often faced by large retail chains that carry private‐label products. We formulate this problem as a convex‐mixed integer program and show that it is strongly NP‐hard. We determine a lower bound by applying a Lagrangian relaxation and show that this bound outperforms the standard convex programming relaxation while being computationally efficient. We also establish a worst‐case error bound for the Lagrangian relaxation. We then develop heuristics to generate feasible solutions. Our computational results indicate that our convex programming heuristic yields feasible solutions that are close to optimal with an average suboptimality gap at 3.4%. We also develop managerial insights for practitioners who choose suppliers and make production, distribution, and inventory decisions in the supply chain.     

Minmax common flow-allowance problems with convex resource allocation and position-dependent workloads

We study minmax due-date based on common flow-allowance assignment and scheduling problems on a single machine, and extend known results in scheduling theory by considering convex resource allocation. The total cost function of a given job consists of its earliness, tardiness and flow-allowance cost components. Thus, the common flow-allowance and the actual jobs’ processing times are decision variables, implying that the due-dates and actual processing times can be controlled by allocating additional resource to the job operations. Consequently, our goal is to optimize a cost function by seeking the optimal job sequence, the optimal job-dependent due-dates along with the actual processing times. In all addressed problems we aim to minimize the maximal cost among all the jobs subject to a constraint on the resource consumption. We start by analyzing and solving the problem with position-independent workloads and then proceed to position-dependent workloads. Finally, the results are generalized to the method of common due-window. For all studied problems closed form solutions are provided, leading to polynomial time solutions.

     

混合离散差分进化算法在单机批处理调度中的应用

本文研究单机批处理调度问题,批处理机有批次容量限制,批处理时间由每个批次所含作业中的最长作业处理时间决定。每个作业具有不同的大小、处理时间、提前拖期惩罚权重,所有作业具有公共交货期,且交货期无限晚。目标函数为最小化所有作业的加权提前拖期惩罚之和。该问题已被证明为NP难题,本研究找到了其最优解具有的一些性质,在此基础上利用它们提出了一种动态规划(DP)与差分进化(DE)算法相结合的混合离散差分进化(HDDE)算法来求解该问题,通过与传统的遗传算法、模拟退火算法和迭代贪婪算法进行对比,HDDE算法显示了更加强大的全局搜索能力。     

On the Robust Single Machine Scheduling Problem

The single machine scheduling problem with sum of completion times criterion (SS) can be solved easily by the Shortest Processing Time (SPT) rule. In the case of significant uncertainty of the processing times, a robustness approach is appropriate. In this paper, we show that the robust version of the (SS) problem is NP-complete even for very restricted cases. We present an algorithm for finding optimal solutions for the robust (SS) problem using dynamic programming. We also provide two polynomial time heuristics and demonstrate their effectiveness.     

A review of quantitative approaches in just-in-time manufacturing

The objectives of this survey are four-fold: (1) to describe the principle of just-in-time production, (2) to provide an overview of the problems and research issues in scheduling, lot sizing and determining the number of kanbans, (3) to describe prior studies which use quantitative approaches to study JIT production and its variant systems including simulation, stochastic process, and mathematical programming, and (4) to identify fertile opportunities for further research in the quantitative analysis of JIT production.