Metaheuristic approaches to the hybrid flow shop scheduling problem with a cost-related criterion

In the paper, the flow-shop scheduling problem with parallel machines at each stage (machine center) is studied. For each job its release and due date as well as a processing time for its each operation are given. The scheduling criterion consists of three parts: the total weighted earliness, the total weighted tardiness and the total weighted waiting time. The criterion takes into account the costs of storing semi-manufactured products in the course of production and ready-made products as well as penalties for not meeting the deadlines stated in the conditions of the contract with customer. To solve the problem, three constructive algorithms and three metaheuristics (based one Tabu Search and Simulated Annealing techniques) are developed and experimentally analyzed. All the proposed algorithms operate on the notion of so-called operation processing order, i.e. the order of operations on each machine. We show that the problem of schedule construction on the base of a given operation processing order can be reduced to the linear programming task. We also propose some approximation algorithm for schedule construction and show the conditions of its optimality.

Scheduling a flow-shop with combined buffer conditions

In this paper, No-Wait, No-Buffer, Limited-Buffer, and Infinite-Buffer conditions for the flow-shop problem (FSP) have been investigated. These four different buffer conditions have been combined to generate a new class of scheduling problem, which is significant for modelling many real-world scheduling problems. A new heuristic algorithm is developed to solve this strongly NP-hard problem. Detailed numerical implementations have been analysed and promising results have been achieved.

Adaptive agent-based manufacturing control and its application to flow shop routing control

The manufacturing industry is currently facing unprecedented challenges from changes and disturbances. The sources of these changes and disturbances are of different scope and magnitude. They can be of a commercial nature, or linked to fast product development and design, or purely operational (e.g. rush order, machine breakdown, material shortage etc.). In order to meet these requirements it is increasingly important that a production operation be flexible and is able to adapt to new and more suitable ways of operating. This paper focuses on a new strategy for enabling manufacturing control systems to adapt to changing conditions both in terms of product variation and production system upgrades. The approach proposed is based on two key concepts: (1) An autonomous and distributed approach to manufacturing control based on multi-agent methods in which so called operational agents represent the key physical and logical elements in the production environment to be controlled - for example, products and machines and the control strategies that drive them and (2) An adaptation mechanism based around the evolutionary concept of replicator dynamics which updates the behaviour of newly formed operational agents based on historical performance records in order to be better suited to the production environment. An application of this approach for route selection of similar products in manufacturing flow shops is developed and is illustrated in this paper using an example based on the control of an automobile paint shop.

A new heuristic for three-machine flow shop scheduling

This paper considers the problem of sequencing n jobs in a three-machine flow shop with the objective of minimizing the makespan, which is the completion time of the last job. An O(n log n) time heuristic that is based on Johnson's algorithm is presented. It is shown to generate a schedule with length at most 5/3 times that of an optimal schedule, thereby reducing the previous best available worst-case performance ratio of 2. An application to the general flow shop is also discussed.

Approximation algorithms for two-machine flow shop scheduling with batch setup times

In many practical situations, batching of similar jobs to avoid setups is performed while constructing a schedule. This paper addresses the problem of non-preemptively scheduling independent jobs in a two-machine flow shop with the objective of minimizing the makespan. Jobs are grouped into batches. A sequence independent batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. Besides its practical interest, this problem is a direct generalization of the classical two-machine flow shop problem with no grouping of jobs, which can be solved optimally by Johnson's well-known algorithm. The problem under investigation is known to be NP-hard. We propose two O(n logn) time heuristic algorithms. The first heuristic, which creates a schedule with minimum total setup time by forcing all jobs in the same batch to be sequenced in adjacent positions, has a worst-case performance ratio of 3/2. By allowing each batch to be split into at most two sub-batches, a second heuristic is developed which has an improved worst-case performance ratio of 4/3. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

Minimizing total weighted completion time in a proportionate flow shop

We study the special case of the m machine flow shop problem in which the processing time of each operation of job j is equal to pj; this variant of the flow shop problem is known as the proportionate flow shop problem. We show that for any number of machines and for any regular performance criterion we can restrict our search for an optimal schedule to permutation schedules. Moreover, we show that the problem of minimizing total weighted completion time is solvable in O(n2) time. © 1998 John Wiley & Sons, Ltd.

Proportionate flow shop with controllable processing times

This paper considers a special class of flow-shop problems, known as the proportionate flow shop. In such a shop, each job flows through the machines in the same order and has equal processing times on the machines. The processing times of different jobs may be different. It is assumed that all operations of a job may be compressed by the same amount which will incur an additional cost. The objective is to minimize the makespan of the schedule together with a compression cost function which is non-decreasing with respect to the amount of compression. For a bicriterion problem of minimizing the makespan and a linear cost function, an O(n log n) algorithm is developed to construct the Pareto optimal set. For a single criterion problem, an O(n2) algorithm is developed to minimize the sum of the makespan and compression cost. Copyright © 1999 John Wiley & Sons, Ltd.

Scheduling three-operation jobs in a two-machine flow shop to minimize makespan

This paper considers a variant of the classical problem of minimizing makespan in a two-machine flow shop. In this variant, each job has three operations, where the first operation must be performed on the first machine, the second operation can be performed on either machine but cannot be preempted, and the third operation must be performed on the second machine. The NP-hard nature of the problem motivates the design and analysis of approximation algorithms. It is shown that a schedule in which the operations are sequenced arbitrarily, but without inserted machine idle time, has a worst-case performance ratio of 2. Also, an algorithm that constructs four schedules and selects the best is shown to have a worst-case performance ratio of 3/2. A polynomial time approximation scheme (PTAS) is also presented.

Flow shop scheduling problems under machine–dependent precedence constraints

The paper considers the flow shop scheduling problems to minimize the makespan, provided that an individual precedence relation is specified on each machine. A fairly complete complexity classification of problems with two and three machines is obtained.

Two-machine flow shop scheduling problems with no-wait jobs

In this paper we provide a fairly complete complexity classification of various versions of the two-machine permutation flow shop scheduling problem to minimize the makespan in which some of the jobs have to be processed with no-wait in process. For some version, we offer a fully polynomial-time approximation scheme and a 43-approximation algorithm.

An improved approximation algorithm for the two-machine flow shop scheduling problem with an interstage transporter

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a –approximation algorithm that outputs a two-shipment schedule. We design a –approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables

An approximation algorithm for the two-machine flow shop with a single transporter

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a –approximation algorithm that outputs a two-shipment schedule. We design a –approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables.

Approximation results for flow shop scheduling problems with machine availability constraints

This paper considers two-machine flow shop scheduling problems with machine availability constraints. When the processing of a job is interrupted by an unavailability period of a machine, we consider both the resumable scenario in which the processing can be resumed when the machine next becomes available, and the semi-resumable scenario in which some portion of the processing is repeated but the job is otherwise resumable. For the problem with several non-availability intervals on the first machine under the resumable scenario, we present a fast (3/2)-approximation algorithm. For the problem with one non-availability interval under the semi-resumable scenario, a polynomial-time approximation scheme is developed.