Flow shop scheduling jobs with position-dependent processing times

The paper is devoted to some flow shop scheduling problems, where job processing times are defined by functions dependent on their positions in the schedule. An example is constructed to show that the classical Johnson's rule is not the optimal solution for two different models of the two-machine flow shop scheduling to minimize makespan. In order to solve the makespan minimization problem in the two-machine flow shop scheduling, we suggest Johnson's rule as a heuristic algorithm, for which the worst-case bound is calculated. We find polynomial time solutions to some special cases of the considered problems for the following optimization criteria: the weighted sum of completion times and maximum lateness. Some furthermore extensions of the problems are also shown.     

An interval approach based on expectation optimization for fuzzy random bilevel linear programming problems

This paper considers a class of bilevel linear programming problems in which the coefficients of both objective functions are fuzzy random variables. The main idea of this paper is to introduce the Pareto optimal solution in a multi-objective bilevel programming problem as a solution for a fuzzy random bilevel programming problem. To this end, a stochastic interval bilevel linear programming problem is first introduced in terms of α-cuts of fuzzy random variables. On the basis of an order relation of interval numbers and the expectation optimization model, the stochastic interval bilevel linear programming problem can be transformed into a multi-objective bilevel programming problem which is solved by means of weighted linear combination technique. In order to compare different optimal solutions depending on different cuts, two criterions are given to provide the preferable optimal solutions for the upper and lower level decision makers respectively. Finally, a production planning problem is given to demonstrate the feasibility of the proposed approach.     

Two-machine flow shop no-wait scheduling with machine maintenance

We study a two-machine flow shop scheduling problem with no-wait in process, in which one of the machines is subject to mandatory maintenance. The length of the maintenance period is defined by a non-decreasing function that depends on the starting time of that maintenance. The objective is to minimize the completion time of all activities. We present a polynomial-time approximation scheme for this problem. Received: November 2004 / Received version: March 2005 AMS classification: 90B35, 90B30, 90C59 The research was partly supported by INTAS (Project 03-51-5501) All correspondence to: Vitali A. Strusevich     

Two machine open shop scheduling problem to minimize an arbitrary machine usage regular penalty function

The paper present a linear-time algorithm for solving the two machine open shop scheduling problem to minimize an arbitrary regular penalty function depending on the lengths of periods during which the machines are used. Both the preemptive and the nonpreemptive cases of the problem are considered.     

Genetic algorithm-based subproblem solution procedures for a modified shifting bottleneck heuristic for complex job shops

In this paper, we consider a modified shifting bottleneck heuristic for complex job shops. The considered job shop environment contains parallel batching machines, machines with sequence-dependent setup times and reentrant process flows. Semiconductor wafer fabrication facilities (Wafer Fabs) are typical examples for manufacturing systems with these characteristics. Our primary performance measure is total weighted tardiness (TWT). The shifting bottleneck heuristic uses a disjunctive graph to decompose the overall scheduling into scheduling problems for single tool groups. The scheduling algorithms for these scheduling problems are called subproblem solution procedures (SSPs). In previous research, only subproblem solution procedures based on dispatching rules have been considered. In this paper, we are interested in how much we can gain in terms of TWT if we apply more sophisticated subproblem solution procedures like genetic algorithms for parallel machine scheduling. We conduct simulation experiments in a dynamic job shop environment in order to assess the performance of the suggested subproblem solution procedures. It turns out that using near to optimal subproblem solution procedures leads in many situations to improved results compared to dispatching-based subproblem solution procedures.     

Minimizing maximum completion time in a proportionate flow shop with one machine of different speed

A flow shop with identical machines is called a proportionate flow shop. In this paper, we consider the variant of the n-job, m-machine proportionate flow shop scheduling problem in which only one machine is different and job processing times are inversely proportional to machine speeds. The objective is to minimize maximum completion time. We describe some optimality conditions and show that the problem is NP-complete. We provide two heuristic procedures whose worst-case performance ratio is less than two. Extensive experiments with various sizes are conducted to show the performance of the proposed heuristics.     

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.     

机器具有优势关系下的工件加工时间可控的流水作业排序问题

本文主要研究机器具有优势关系下的工件加工时间可控的流水作业排序问题.我们主要对以下两种情形进行了讨论:工件加工时间为线性恶化和线性学习.对于每一种加工模型,我们分别研究了几类不同的优势机器,并且对每种情况均给出了多项式时间算法.     

Survey on fuzzy shop scheduling

The real life scheduling problems often have several uncertainties. The solutions of these problems can provide deeper insights to the decision maker than those of deterministic problems. Fuzzy set theory as most important tool to model uncertainty represents an attractive tool to aid research in the production management. Since to the best of our knowledge, there is not a comprehensive review on the fuzzy scheduling literature, the goal of this paper is to provide an extensive review for the fuzzy machine scheduling which it covers more than 140 papers. For this purpose, first, this paper classifies and reviews the literature according to shop environments, including single machine, parallel machines, flowshop, job shop and open shop. Then the reviewed literature is quantified and measured. At the end the paper concludes by presenting some problems receiving less attention than the others and proposing some research opportunities in the field.     

Scheduling open shops with parallel machines

The parallel shop and the open shop are two machine environments that have received much attention in the literature of scheduling theory. A common generalization—the open shop with parallel machines—is considered in this paper. Polynomial-time algorithms are presented for obtaining minimum-length preemptive schedules for three cases. Open shops with single-operation machines of equal speed are scheduled with essentially no more difficulty than an ordinary open shop. Open shops with multiple-operation machines of equal speed are scheduled with the aid of a sequence of network flow computations. The general open shop problem with parallel machines of arbitrary speeds can be solved by linear programming, in much the same way as an optimal preemptive schedule can be found for unrelated parallel machines.     

Flow shop scheduling problems with deteriorating jobs on no-idle dominant machines

In this paper, we study the permutation flow shop scheduling problems with deteriorating jobs on no-idle dominant machines. The objective is to minimize one of the two regular performance criteria, namely, makespan and total completion time. For each objective, the following dominant machines constraint: idm, ddm, idm–ddm and ddm–idm are considered. We present a polynomial time solution algorithm for each of the four cases.     

A branch and bound algorithm for hybrid flow shop scheduling problem with setup time and assembly operations

A hybrid flow shop scheduling problem (HFSP) with assembly operations is studied in this paper. In the considered problem, a number of products of the same kind are produced. Each product is assembled using a set of several parts. At first, the parts are produced in a hybrid flow shop and then they are assembled in an assembly stage to produce products. The considered objective is to minimize the completion time of all products (makespan). This problem has been proved strongly NP-hard, so in order to solve it, a hierarchical branch and bound algorithm is presented. Also, some lower and upper bounds are developed to increase the efficiency of the proposed algorithm. The numerical experiments are used to evaluate the performance of the proposed algorithm.     

Local search algorithms for the multiprocessor flow shop scheduling problem

The multiprocessor flow shop scheduling problem is a generalization of the ordinary flow shop scheduling problem. The problem consists of both assigning operations to machines and scheduling the operations assigned to the same machine. We review the literature on local search methods for flow shop and job shop scheduling and adapt them to the multiprocessor flow shop scheduling problem. Other local search approaches we consider are variable-depth search and simulated annealing. We show that tabu search and variable-depth search with a neighborhood originated by Nowicki and Smutnicki outperform the other algorithms.     

Flexible flow shop scheduling with uniform parallel machines

We consider the multistage flexible flow shop scheduling problem with uniform parallel machines in each stage and the objective of minimizing makespan. We develop a general class of heuristics for this strongly NP-hard problem that extend several well-known heuristics for the corresponding embedded serial flow shop problem, and obtain absolute performance guarantees for heuristics in this class by building on similar absolute performance guarantees for the corresponding serial flow shop heuristics. Our approach is quite robust, since it can extend any heuristic for the serial flow shop problem (with an absolute performance guarantee) to a similar one for the flexible flow shop problem with uniform parallel machines.     

A variable neighbourhood search for hybrid flow-shop scheduling problem with rework and set-up times

This paper deals with hybrid flow-shop scheduling problem with rework. In this problem, jobs are inspected at the last stage, and poorly processed jobs were returned and processed again. Thus, a job may visit a stage more than once, and we have a hybrid flow-shop with re-entrant flow. This kind of a shop may occur in many industries, such as final inspection system in automotive manufacturing. The criterion is to minimize the makespan of the system. We developed a 0–1 mixed-integer program of the problem. Since the hybrid flow-shop scheduling problem is NP-hard, an algorithm for finding an optimal solution in polynomial time does not exist. So we generalized some heuristic methods based on several basic dispatching rules and proposed a variable neighbourhood search (VNS) for the problem with sequence-dependent set-up times and unrelated parallel machines. The computational experiments show that VNS provides better solutions than heuristic methods.     

A note on the two-stage assembly flow shop scheduling problem with uniform parallel machines

We study the problem of minimizing the makespan in a two-stage assembly flow shop scheduling problem with uniform parallel machines. This problem is a generalization of the assembly flow shop problem with concurrent operations in the first stage and a single assembly operation in the second stage. We propose a heuristic with an absolute performance bound which becomes asymptotically optimal as the number of jobs becomes very large. We show that our results slightly improve earlier results for the simpler assembly flow shop problem (without uniform machines) and for the two-stage hybrid flow shop problem with uniform machines.     

A penalty-shift-insertion-based algorithm to minimize total flow time in no-wait flow shops

This paper proposes a penalty-shift-insertion (PSI)-based algorithm for the no-wait flow shop scheduling problem to minimize total flow time. In the first phase, a penalty-based heuristic, derived from Vogel’s approximation method used for the classic transportation problem is used to generate an initial schedule. In the second phase, a known solution is improved using a forward shift heuristic. Then the third phase improves this solution using a job-pair and a single-job insertion heuristic. Results of the computational experiments with a large number of randomly generated problem instances show that the proposed PSI algorithm is relatively more effective and efficient in minimizing total flow time in a no-wait flow shop than the state-of-the-art procedures. Statistical significance of better results obtained by the proposed algorithm is also reported.     

NP-hard cases in scheduling deteriorating jobs on dedicated machines

In this paper problems of time-dependent scheduling on dedicated machines are considered. The processing time of each job is described by a function which is dependent on the starting time of the job. The objective is to minimise the maximum completion time (makespan). We prove that under linear deterioration the two-machine flow shop problem is strongly NP-hard and the two-machine open shop problem is ordinarily NP-hard. We show that for the three-machine flow shop and simple linear deterioration there does not exist a polynomial-time approximation algorithm with the worst case ratio bounded by a constant, unless P=NP. We also prove that the three-machine open shop problem with simple linear deterioration is ordinarily NP-hard, even if the jobs have got equal deterioration rates on the third machine.     

A hierarchical scheduling problem with a well-solvable second stage

In the hierarchical scheduling model to be considered, the decision at the aggregate level to acquire a number of identical machines has to be based on probabilistic information about the jobs that have to be scheduled on these machines at the detailed level. The objective is to minimize the sum of the acquisition costs and the expected average completion time of the jobs. In contrast to previous models of this type, the second part of this objective function corresponds to a well-solvable scheduling problem that can be solved to optimality by a simple priority rule. A heuristic method to solve the entire problem is described, for which strong asymptotic optimality results can be established.     

二层决策问题的灵敏度分析(2)

二层决策系统包含着两个最优化决策问题,其中上层决策问题的目标值是由下层决策的解所隐含地确定的.本文研究了二层决策问题的另一方面的灵敏度分析问题,讨论了上层决策者的价值系数发生变化而二层决策问题的最优解不变所产生的灵敏度分析问题.为了确定二层决策问题价值系数发生变化的范围,首先我们给出了灵敏度分析的基本方法,结合“k th-best”算法我们又给出了灵敏度分析的操作步骤.在所确定的变化范围内,价值系数的变化,不会引起二层决策问题的全局最优解的变化,从而为决策者提供了相对稳定的决策方案.最后我们给出了数值实例,它表明本文所给出的灵敏度分析的方法是正确的.