A new heuristic and dominance relations for no-wait flowshops with setups

The two-machine no-wait flowshop problem, where setup times are considered separate from processing times and sequence independent, is addressed with respect to minimizing total flowtime. A local and a global dominance relation are developed and a new heuristic is provided. Furthermore, a lower bound is obtained and used along with the dominance relations in a branch-and-bound algorithm in order to evaluate the efficiency of the heuristic. Computational experience demonstrates the superiority of the local dominance relation and the new heuristic.Scope and purposeNo-wait flowshop problems, where jobs have to be processed without interruption between consecutive machines, represent an important area in scheduling. There are several industries where the no-wait flowshop problem applies including the metal, plastic, and chemical industries. For instance, in the case of steel production, the heated metal must continuously go through a sequence of operations before it is cooled in order to prevent defects in the composition of the material. Another important area arises when setup time is considered separate from processing time. Such a consideration is particularly justified when the ratio of setup to processing time is non-negligible. Many applications warrant separate consideration of setup; examples include the re-tooling of multi-tool equipment. Other applications can be found in textile, plastic, chemical, and semi-conductor industries. This paper develops a new heuristic and dominance relations for the two-machine no-wait separate setup flowshop problem, where the performance criterion is total flowtime.     

Scheduling and Lot Streaming in Flowshops with No-Wait in Process

Lot streaming involves splitting a production lot into a number of sublots, in order to allow the overlapping of successive operations, in multi-machine manufacturing systems. In no-wait flowshop scheduling, sublots are necessarily consistent, that is, they remain the same over all machines. The benefits of lot streaming include reductions in lead times and work-in-process, and increases in machine utilization rates. We study the problem of minimizing the makespan in no-wait flowshops producing multiple products with attached setup times, using lot streaming. Our study of the single product problem resolves an open question from the lot streaming literature. The intractable multiple product problem requires finding the optimal number of sublots, sublot sizes, and a product sequence for each machine. We develop a dynamic programming algorithm to generate all the nondominated schedule profiles for each product that are required to formulate the flowshop problem as a generalized traveling salesman problem. This problem is equivalent to a classical traveling salesman problem with a pseudopolynomial number of cities. We develop and computationally test an efficient heuristic for this problem. Our results indicate that solutions can quickly be found for flowshops with up to 10 machines and 50 products. Moreover, the solutions found by our heuristic provide a substantial improvement over previously published results.     

Minimizing total tardiness in a two-machine re-entrant flowshop with sequence-dependent setup times

We consider a two-machine re-entrant flowshop scheduling problem in which all jobs must be processed twice on each machine and there are sequence-dependent setup times on the second machine. For the problem with the objective of minimizing total tardiness, we develop dominance properties and a lower bound by extending those for a two-machine re-entrant flowshop problem (without sequence-dependent setup times) as well as heuristic algorithms, and present a branch and bound algorithm in which these dominance properties, lower bound, and heuristics are used. For evaluation of the performance of the branch and bound algorithm and heuristics, computational experiments are performed on randomly generated instances, and results are reported.     

An efficient heuristic for a two-stage assembly scheduling problem with batch setup times to minimize makespan

This paper considers a two-stage assembly scheduling problem of N products with setup times to minimize the makespan. In this problem, there is a machining machine which produces components in the first stage. When the required components are available, a single assembly machine can assemble these components into products in the second stage. A setup time is needed whenever the machining machine starts processing components, or the item of component is switched on the machine. The problem is formulated as a mixed integer programming model, and several properties for finding optimal solutions are developed. Moreover, an efficient heuristic based on these optimal properties is proposed. A lower bound is derived to evaluate the performance of the proposed heuristic. Computational results show that the proposed heuristic can obtain a near optimal solution in almost zero time and the average percentage deviation is only 0.478.     

Scheduling two-machine no-wait open shops to minimize makespan

This paper examines the problem of scheduling two-machine no-wait open shops to minimize makespan. The problem is known to be strongly NP-hard. An exact algorithm, based on a branch-and-bound scheme, is developed to optimally solve medium-size problems. A number of dominance rules are proposed to improve the search efficiency of the branch-and-bound algorithm. An efficient two-phase heuristic algorithm is presented for solving large-size problems. Computational results show that the branch-and-bound algorithm can solve problems with up to 100 jobs within a reasonable amount of time. For large-size problems, the solution obtained by the heuristic algorithm has an average percentage deviation of 0.24% from a lower bound value.     

Single machine scheduling to minimize maximum lateness subject to release dates and precedence constraints

This paper considers the problem of finding a nonpreemptive schedule for a single machine to minimize the maximum lateness with release dates and precedence constraints. A branch and bound algorithm is developed. The algorithm uses four different heuristics to find upper bounds at the initial branch node: early release date heuristic, modified Schrage's heuristic, heuristic BLOCK, and a variable neighborhood descent procedure. At each branch node, two branches evolve from a schedule found by heuristic BLOCK using a binary branching rule based on bottleneck and critical jobs, and a lower bound is obtained by optimally solving the relaxed problem with preemption. The algorithm solves 14,984 out of the 15,000 systematically generated instances with up to 1,000 jobs within 1 minute of CPU time.     

An efficient simple metaheuristic for minimizing the makespan in two-machine no-wait job shops

This paper examines the problem of scheduling two-machine no-wait job shops to minimize makespan. The problem is known to be strongly NP-hard. A two-phase heuristic is developed to solve the problem. Phase 1 of the heuristic transforms the problem into a no-wait flow shop problem and solves it using the well known Gilmore and Gomory algorithm. Phase 2 of the heuristic improves the solution obtained in phase 1 using a simple tabu search algorithm. Computational results show that the proposed heuristic performs extremely well in terms of both solution quality and computation time. It finds an optimal solution to about 90% of the problem instances and the average deviation from the lower bond for the other problem instances is infinitesimal.     

Branch and bound algorithms for rate-distortion optimized media streaming

We consider the problem of rate-distortion optimized streaming of packetized multimedia data over a single quality-of-service network using feedback and retransmissions. For a single data unit, we prove that the problem is NP-hard and provide efficient branch and bound algorithms that are much faster than the previously best solution based on dynamic programming. For a group of interdependent data units, we show how to compute optimal solutions with branch and bound algorithms. The branch and bound algorithms for a group of data units are much slower than the current state of the art, a heuristic technique known as sensitivity adaptation. However, in many real-world situations, they provide a significantly better rate-distortion performance.     

多工件类型的无等待机器人制造单元调度研究

首先将加工多工件类型的无等待机器人制造单元调度问题分解为两个相互联系的子问题：（1）多类型工件进入系统的排序问题;（2）机器人搬运作业的排序问题。从解决工件使用工作站和机器人可能发生的冲突入手,以工件进入系统的时间为决策变量,利用禁止区间法建立了问题的数学模型,并开发了一基于图论的动态分枝定界最优算法。最后,通过一自动化印刷电路板（PCB）生产线和随机算例验证了算法的有效性。     

No-wait and separate setup three-machine flowshop with total completion time criterion

This paper considers the three-machine no-wait flowshop problem with the objective of minimizing total completion time where setup times are considered as separate from processing times and sequence independent. We present optimal solutions for certain cases, and a dominance relation for the general case. We also develop and evaluate five heuristic algorithms for small and large number of jobs. Computational experience for up to 100 jobs shows that the proposed heuristics are quite effective and their performance do not depend on the number of jobs. The computational experience has been conducted for the uniform processing time distributions of U (1, 10) and U (1, 100). The best heuristic gives an overall average error of 0.47% for U (1, 10) and it gives an overall average error of 1.23% for U (1, 100).     

离散和声求解带启动时间批量流水线调度问题

分别在有等待和无等待的情况下,深入分析了带有启动时间的批量调度问题,以最小化最大完成时间为目标,提出了两种离散和声搜索算法。针对算法本质连续而问题离散的矛盾,对和声搜索算法进行改进。首先提出了基于工序的编码方式,采用inver-over和重组两种离散算子产生候选解的进化机制;并利用改进的NEH(Nawaz-Enscore-Ham)方法进行初始化,产生的高质量和多样化的初始种群有效地指导了算法的进化方向,提高收敛速度;最后将一种简单而有效的局部邻域搜索方法嵌入到和声搜索算法中以增强其局部搜索能力。仿真实验和比较结果表明了所提算法的有效性。     

Two-stage hybrid flow shop with precedence constraints and parallel machines at second stage

This study deals with the two-stage hybrid flow shop (HFS) problem with precedence constraints. Two versions are examined, the classical HFS where idle time between the operations of the same job is allowed and the no-wait HFS where idle time is not permitted. For solving these problems an adaptive randomized list scheduling heuristic is proposed. Two global bounds are also introduced so as to conservatively estimate the distance to optimality of the proposed heuristic. The evaluation is done on a set of randomly generated instances. The heuristic solutions for the classical HFS in average are provably situated below 2% from the optimal ones, and on the other hand, in the case of the no-wait HFS the average deviation is below 5%.     

The capacitated lot-sizing and scheduling problem with sequence-dependent setup costs and setup times

We consider the single machine capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup costs and non-zero setup times, with the additional feature that setups may be carried over from one period to the next, and that setups are preserved over idle periods. We provide an exact formulation of this problem as a mixed-integer program.It is well known that the CLSP is NP-hard. Therefore, we have also developed a heuristic for solving large problem instances. This is coupled with a procedure for obtaining a lower bound on the optimal solution. We carry out a computational study to test the accuracy of several different lower bounding linear relaxations and the approximate solution obtained by the heuristic. In our study, the average deviation of the heuristic solution from the corresponding exact solution depends on the size of the problem and ranges from 10 to 16%. The heuristic is more effective when there are many more products than there are planning periods. This is a desirable property from a practical viewpoint since most firms are likely to implement such a procedure on a rolling horizon basis, solving the problem repeatedly for a few periods at a time.     

A constructive heuristic for total flowtime minimization in a no-wait flowshop with sequence-dependent setup times

In this paper, we addressed the problem of scheduling jobs in a no-wait flow shop with sequence-dependent setup times with the objective of minimizing the total flow time. As this problem is well-known for being NP-hard, we present a new constructive heuristic, named QUARTS, in order to obtain good approximate solutions in a short CPU time. QUARTS breaks the problem in quartets in order to minimize the total flow time. The method was tested with other literature methods: BAH and BIH by Bianco et al. (1999) [6], TRIPS, by Brown et al. (2004) [7] and the metaheuristic Iterated Greedy with Local Search proposed by Ruiz and Stützle (2007) [25]. The computational results showed that IG_LS obtained the best results and QUARTS presented the best performance regarding other constructive heuristics.     

A tabu search heuristic for a sequence-dependent and time-dependent scheduling problem on a single machine

This paper introduces a tabu search heuristic for a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The problem consists in scheduling a set of dependent jobs, where the transition between two jobs comprises an unrestricted setup that can be performed at any time, and a restricted setup that must be performed outside of a given time interval which repeats daily in the same position. The setup time between two jobs is thus a function of the completion time of the first job. The tabu search heuristic relies on shift and swap moves, and a surrogate objective function is used to speed-up the neighborhood evaluation. Computational experiments show that the proposed heuristic consistently finds better solutions in less computation time than a recent branch-and-cut algorithm. Furthermore, on instances where the branch-and-cut algorithm cannot find the optimal solution, the heuristic always identifies a better solution.     

A branch and price algorithm to minimize makespan on a single batch processing machine with non-identical job sizes

In this paper, we consider the scheduling problem on a single batch processing machine with non-identical job sizes; in which the machine has a limited capacity and can process a group of jobs simultaneously as a batch. The processing time of a batch is the longest processing time of all jobs in the batch. The objective is to minimize the makespan. We formulate the problem using Dantzig–Wolfe decomposition as a set partitioning problem. Based on the set partitioning formulation, we present a tight lower bound using column generation method. A heuristic algorithm is also developed to generate the basic solution in the column generation method. A branch and price algorithm which combines the column generation technique with branch and bound method is then presented to obtain the optimal solution of the problem. The efficiency of the proposed branch and price algorithm is ultimately compared to the branch and bound algorithm from the literature, based on the generated sample problems.     

A 2-phase algorithm for solving the single allocation p-hub center problem

The single allocation p-hub center problem is an NP-hard location–allocation problem which consists of locating hub facilities in a network and allocating non-hub nodes to hub nodes such that the maximum distance/cost between origin–destination pairs is minimized. In this paper we present an exact 2-phase algorithm where in the first phase we compute a set of potential optimal hub combinations using a shortest path based branch and bound. This is followed by an allocation phase using a reduced sized formulation which returns the optimal solution. In order to get a good upper bound for the branch and bound we developed a heuristic for the single allocation p-hub center problem based on an ant colony optimization approach. Numerical results on benchmark instances show that the new solution approach is superior over traditional MIP-solver like CPLEX. As a result we are able to provide new optimal solutions for larger problems than those reported previously in literature. We are able to solve problems consisting of up to 400 nodes in reasonable time. To the best of our knowledge these are the largest problems solved in the literature to date.     

一种求解无等待流水车间调度优化的启发式算法

提出了一种新的启发式算法,用于求解无等待流水车间调度问题的总流水时间指标。该算法命名为标准差启发,基于著名的NEH启发算法。首先阐述了总流水时间指标;其次描述了标准差启发算法的过程;最后用标准差启发算法求解标准实验案例,通过实验并与其他启发式算法比较,验证了标准差启发算法在求解无等待流水车间调度问题总流水时间指标的有效性。     

The total completion time open shop scheduling problem with a given sequence of jobs on one machine

This paper addresses the open shop scheduling problem to minimize the total completion time, provided that one of the machines has to process the jobs in a given sequence. The problem is NP-hard in the strong sense even for the two-machine case. A lower bound is derived based on the optimal solution of a relaxed problem in which the operations on every machine may overlap except for the machine with a given sequence of jobs. This relaxed problem is NP-hard in the ordinary sense, however it can be quickly solved via a decomposition into subset-sum problems. Both heuristic and branch-and-bound algorithm are proposed. Experimental results show that the heuristic is efficient for solving large-scaled problems, and the branch-and-bound algorithm performs well on small-scaled problems.Scope and purposeShop scheduling problems, widely used in the modeling of industrial production processes, are receiving an increasing amount of attention from researchers. To model practical production processes more closely, additional processing restrictions can be introduced, e.g., the resource constraints, the no-wait in process requirement, the precedence constraints, etc. This paper considers the total completion time open shop scheduling problem with a given sequence of jobs on one machine. This model belongs to a new class of shop scheduling problems under machine-dependent precedence constraints. This problem is NP-hard in the strong sense. A heuristic is proposed to efficiently solve large-scaled problems and a branch-and-bound algorithm is presented to optimally solve small-scaled problems. Computational experience is also reported.     

Scheduling jobs on a single serial-batching machine with dynamic job arrivals and multiple job types

This paper investigates a scheduling model with certain co-existing features of serial-batching, dynamic job arrival, multi-types of job, and setup time. In this proposed model, the jobs of all types are first partitioned into serial batches, which are then processed on a single serial-batching machine with an independent constant setup time for each new batch. In order to solve this scheduling problem, we divide it into two phases based on job arrival times, and we also derive and prove certain constructive properties for these two phases. Relying on these properties, we develop a two-phase hybrid algorithm (TPHA). In addition, a valid lower bound of the problem is also derived. This is used to validate the quality of the proposed algorithm. Computational experiments, both with small- and large-scale problems, are performed in order to evaluate the performance of TPHA. The computational results indicate that TPHA outperforms seven other heuristic algorithms. For all test problems of different job sizes, the average gap percentage between the makespan, obtained using TPHA, and the lower bound does not exceed 5.41 %.