具有机器适用限制的分布式置换流水车间问题的模型与算法

考虑具有机器适用限制的多个不同置换流水车间的调度问题. 机器适用限制指的是每个工件只能分配到其可加工工厂集合. 所有置换流水车间拥有的机器数相同但是具有不同的加工能力. 首先, 针对该问题建立了基于位置的混合整数线性规划模型; 进而, 对一般情况和三种特殊情况给出了具有较小近似比的多项式时间算法. 其次, 基于NEH方法提出了启发式算法NEHg, 并给出了以NEHg为上界的分支定界算法. 最后, 通过例子说明了NEHg启发式算法和分支定界算法的计算过程, 并进行大量的实验将NEHg与NEH算法结果进行比较, 从而验证了NEHg算法的有效性.     

The flow shop problem with no-idle constraints: A review and approximation

The makespan minimization problem in flow shops with no-idle constraints on machines is considered. The latter means that each machine, once started, must process all its operations without intermediate idle time until all those operations are completed. The problem is known to be strongly NP-hard already for three machines. While being based on a geometrical approach, we propose several polynomial time heuristics (for the general case and for special cases of 3 and 4 machines) which provide asymptotically optimal solutions for the increasing number of jobs. A comprehensive review of relevant results is also presented.     

An approximation algorithm for the m-machine permutation flow shop scheduling problem with controllable processing times

The paper deals with the m-machine permutation flow shop scheduling problem in which job processing times, along with a processing order, are decision variables. It is assumed that the cost of processing a job on each machine is a linear function of its processing time and the overall schedule cost to be minimized is the total processing cost plus maximum completion time cost. A algorithm for the problem with m = 2 is provided; the best approximation algorithm until now has a worst-case performance ratio equal to . An extension to the m-machine (m ≥2) permutation flow shop problem yields an approximation algorithm with a worst-case bound equal to

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, where is the worst-case performance ratio of a procedure used, in the proposed algorithm, for solving the (pure) sequencing problem. Moreover, examples which achieve this bound for = 1 are also presented.     

On non-permutation solutions to some two machine flow shop scheduling problems

In this paper, we study two versions of the two machine flow shop scheduling problem, where schedule length is to be minimized. First, we consider the two machine flow shop with setup, processing, and removal times separated. It is shown that an optimal solution need not be a permutation schedule, and that the problem isNP-hard in the strong sense, which contradicts some known results. The tight worst-case bound for an optimal permutation solution in proportion to a global optimal solution is shown to be 3/2. An O(n) approximation algorithm with this bound is presented. Secondly, we consider the two machine flow shop with finite storage capacity. Again, it is shown that there may not exist an optimal solution that is a permutation schedule, and that the problem isNP-hard in the strong sense.     

The hybrid flow shop scheduling problem

The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the hybrid flow shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution. The paper briefly discusses and reviews several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.     

Heuristic solution methods for the stochastic flow shop problem

We investigate the stochastic flow shop problem with m machines and general distributions for processing times. No analytic method exists for solving this problem, so we looked instead at heuristic methods. We devised three constructive procedures with modest computational requirements, each based on approaches that have been successful at solving the deterministic counterpart. We compared the performance of these procedures experimentally on a set of test problems and found that all of them achieve near-optimal performance.     

Approximating a two-machine flow shop scheduling under discrete scenario uncertainty

This paper deals with the two machine permutation flow shop problem with uncertain data, whose deterministic counterpart is known to be polynomially solvable. In this paper, it is assumed that job processing times are uncertain and they are specified as a discrete scenario set. For this uncertainty representation, the min-max and min-max regret criteria are adopted. The min-max regret version of the problem is known to be weakly NP-hard even for two processing time scenarios. In this paper, it is shown that the min-max and min-max regret versions of the problem are strongly NP-hard even for two scenarios. Furthermore, the min-max version admits a polynomial time approximation scheme if the number of scenarios is constant and it is approximable with performance ratio of 2 and not (4/3 − ?)-approximable for any ? > 0 unless P = NP if the number of scenarios is a part of the input. On the other hand, the min-max regret version is not at all approximable even for two scenarios.     

Minimizing makespan in a two-stage hybrid flow shop scheduling problem with open shop in one stage

This paper considers a scheduling problem in two-stage hybrid flow shop, where the first stage consists of two machines formed an open shop and the other stage has only one machine. The objective is to minimize the makespan, i.e., the maximum completion time of all jobs. We first show the problem is NP-hard in the strong sense, then we present two heuristics to solve the problem. Computational experiments show that the combined algorithm of the two heuristics performs well on randomly generated problem instances.     

The two-machine open shop problem: To fit or not to fit, that is the question

We consider the open shop scheduling problem with two machines. Each job consists of two operations, and it is prescribed that the first (second) operation has to be executed by the first (second) machine. The order in which the two operations are scheduled is not fixed, but their execution intervals cannot overlap. We are interested in the question whether, for two given values D₁ and D₂, there exists a feasible schedule such that the first and second machine process all jobs during the intervals [0,D₁] and [0,D₂], respectively.We formulate four simple conditions on D₁ and D₂, which can be verified in linear time. These conditions are necessary and sufficient for the existence of a feasible schedule. The proof of sufficiency is algorithmical, and yields a feasible schedule in linear time. Furthermore, we show that there are at most two non-dominated points (D₁,D₂) for which there exists a feasible schedule.     

Bounding strategies for the hybrid flow shop scheduling problem

In this paper, we investigate new lower and upper bounds for the multiple-center hybrid flow shop scheduling problem. We propose a family of center-based lower bounds as well as a destructive lower bound that is based on the concept of revised energetic reasoning. Also, we describe an optimization-based heuristic that requires iteratively solving a sequence of parallel machine problems with heads and tails. We present the results of extensive computational experiments that provide evidence that the proposed bounding procedures consistently improve the best existing ones.     

Two-machine flow shop scheduling problem with an outsourcing option

We consider a two-machine flow shop problem in which each job is processed through an in-house system or outsourced to a subcontractor. A schedule is established for the in-house jobs, and performance is measured by the makespan. Jobs processed by subcontractors require paying an outsourcing cost. The objective is to minimize the sum of the makespan and total outsourcing costs. We show that the problem is NP-hard in the ordinary sense. We consider a special case in which each job has a processing requirement, and each machine a characteristic value. In this case, the time a job occupies a machine is equal to the job’s processing requirement plus a setup time equal to the characteristic value of that machine. We introduce some optimality conditions and present a polynomial-time algorithm to solve the special case.     

Heuristic constructive algorithms for open shop scheduling to minimize mean flow time

In this paper, we consider the problem of scheduling n jobs on m machines in an open shop environment so that the sum of completion times or mean flow time becomes minimal. For this strongly NP-hard problem, we develop and discuss different constructive heuristic algorithms. Extensive computational results are presented for problems with up to 50 jobs and 50 machines, respectively. The quality of the solutions is evaluated by a lower bound for the corresponding preemptive open shop problem and by an alternative estimate of mean flow time. We observe that the recommendation of an appropriate constructive algorithm strongly depends on the ratio n/m.     

Approximability of flow shop scheduling

Shop scheduling problems are notorious for their intractability, both in theory and practice. In this paper, we construct a polynomial approximation scheme for the flow shop scheduling problem with an arbitrary fixed number of machines. For the three common shop models (open, flow, and job), this result is the only known approximation scheme. Since none of the three models can be approximated arbitrarily closely in the general case (unless P = NP), the result demonstrates the approximability gap between the models in which the number of machines is fixed, and those in which it is part of the input of the instance. The result can be extended to flow shops with job release dates and delivery times and to flow shops with a fixed number of stages, where the number of machines at any stage is fixed. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.A preliminary version of this paper appeared in theProceedings of the 36th Annual IEEE Symposium on the Foundations of Computer Science, 1995.Research supported by NSF grant DMI-9496153.     

On the optimality of static policy in stochastic open shop

Consider n jobs and two machines. Each job has to be processed on both machines. The order in which it is dome is immaterial. However, the decision maker has to decide in advance which jobs will be processes first on machine 1 (2). We assume that processing times on each machine are identically exponentially distributed random variables. We prove that assigning equal number of jobs to be first processed by machine 1 (2) stochastically minimizes the makespan.     

一种求解延迟工件数最小的混合流水车间调度问题的模拟退火算法

针对延迟工件数最小的混合流水车间调度问题,给出了一种改进的模拟退火求解算法. 该算法首先给出一个启发式算法来获得初始解,然后用模拟退火算法对初始解改进. 通过交换工件在第一阶段的排序来获得一个新的解,采用最先空闲设备分配规则和先到先被加工规则,对工件在剩余各级的工序进行调度. 实验仿真表明算法是可行有效的.     

A problem expanding parametric programming method for solving the job shop scheduling problem

A new zero-one integer programming model for the job shop scheduling problem with minimum makespan criterion is presented. The algorithm consists of two parts: (a) a branch and bound parametric linear programming code for solving the job shop problem with fixed completion time; (b) a problem expanding algorithm for finding the optimal completion time. Computational experience for problems having up to thirty-six operations is presented. The largest problem solved was limited by memory space, not computation time. Efforts are under way to improve the efficiency of the algorithm and to reduce its memory requirements.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie-Mellon University, under Contract No. N00014-82-K-0329 NR 047-048 with the U.S. Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

Hybrid flow shop scheduling with sequence dependent family setup time and uncertain due dates

This paper studies the scheduling problem in hybrid flow shop (HFS) environment. The sequence dependent family setup time (SDFST) is concerned with minimization of makespan and total tardiness. Production environments in real world include innumerable cases of uncertainty and stochasticity of events and a suitable scheduling model should consider them. Hence, in this paper, due date is assumed to be uncertain and its data follow a normal distribution. Since the proposed problem is NP-hard, two metaheuristic algorithms are presented based on genetic algorithm, namely: Non-dominated Sorting Genetic Algorithm (NSGAII) and Multi Objective Genetic Algorithm (MOGA). The quantitative and qualitative results of these two algorithms have been compared in different dimensions with multi phase genetic algorithm (MPGA) used in literature review. Experimental results indicate that the NSGAII performs very well when compared against MOGA and MPGA in a considerably shorter time.     

On the adjustment problem for linear programs

We propose a generalization of the inverse problem which we will call the adjustment problem. For an optimization problem with linear objective function and its restriction defined by a given subset of feasible solutions, the adjustment problem consists in finding the least costly perturbations of the original objective function coefficients, which guarantee that an optimal solution of the perturbed problem is also feasible for the considered restriction. We describe a method of solving the adjustment problem for continuous linear programming problems when variables in the restriction are required to be binary.