Two-machine Permutation Flow Shop Scheduling Research Articles

A distributionally robust approach for the two-machine permutation flow shop scheduling

A distributionally robust approach for the two-machine permutation flow shop scheduling

A branch-and-bound approach to minimise the value-at-risk of the makespan in a stochastic two-machine flow shop

Planning and scheduling approaches in real manufacturing environments entail the need to cope with random attributes and variables to match the characteristics of real scheduling problems where uncertain events are frequent. Moreover, the capability of devising robust schedules, which are less sensitive to the disruptive effects of unexpected events, is a major request in real applications. In this paper, a branch-and-bound approach is proposed to solve the two-machine permutation flow shop scheduling problem with stochastic processing times. The objective is the minimisation of the value-at-risk of the makespan, to support decision-makers in the trade-off between the expected performance and the mitigation of the impact of extreme scenarios. A Markovian Activity Network (MAN) model is adopted to estimate the distribution of the makespan and assess the value-at-risk for both partial and complete schedules. Phase-type distributions are used to enable general distributions for processing times while maintaining the capability to exploit a Markovian approach. The effectiveness and performance of the proposed approach are demonstrated through a set of computational experiments.

Exact method to optimize the total electricity cost in two-machine permutation flow shop scheduling problem under Time-of-use tariff

This study investigates the minimization of total electricity cost in a two-machine permutation flow shop scheduling problem under the most common electricity tariff, Time-of-Use (ToU). We provide a new property and solution approach to enhance existing methods in the literature. First, we provide an overview of the optimal cases for some specific ToU pricing structures that consist of only two pricing intervals. When the electricity price decreases, Johnson’s rule and dynamic programming give rise to an optimal solution. On the other hand, when the electricity price increases, we provide a condition of optimality for Johnson’s rule. Second, we develop a property based on Johnson’s rule to determine the optimal sequence for general ToU pricing structures. Third, we propose a new mixed-integer linear programming. Then, we design an exact method based on “Logic-based Benders decomposition” to solve the problem. Finally, the numerical tests show that our proposed approach significantly improves the quality of existing results in the literature.

Iterated Local Search and Other Algorithms for Buffered Two-Machine Permutation Flow Shops with Constant Processing Times on One Machine.

The two-machine permutation flow shop scheduling problem with buffer is studied for the special case that all processing times on one of the two machines are equal to a constant c. This case is interesting because it occurs in various applications, for example, when one machine is a packing machine or when materials have to be transported. Different types of buffers and buffer usage are considered. It is shown that all considered buffer flow shop problems remain NP-hard for the makespan criterion even with the restriction to equal processing times on one machine. However, the special case where the constant c is larger or smaller than all processing times on the other machine is shown to be polynomially solvable by presenting an algorithm (2BF-OPT) that calculates optimal schedules in O(nlogn) steps. Two heuristics for solving the NP-hard flow shop problems are proposed: (i) a modification of the commonly used NEH heuristic (mNEH) and (ii) an Iterated Local Search heuristic (2BF-ILS) that uses the mNEH heuristic for computing its initial solution. It is shown experimentally that the proposed 2BF-ILS heuristic obtains better results than two state-of-the-art algorithms for buffered flow shop problems from the literature and an Ant Colony Optimization algorithm. In addition, it is shown experimentally that 2BF-ILS obtains the same solution quality as the standard NEH heuristic, however, with a smaller number of function evaluations.

Multi-state two-machine permutation flow shop scheduling optimisation with time-dependent energy costs

This paper studies a multi-state two-machine flowshop scheduling problem with variable electricity tariffs. The objective is to process a set of jobs in the available time slots with different energy costs to minimise the total energy consumption costs. For this purpose, two different 0-1 linear programs are proposed for the problem.Computational experiments are presented and numerical results are discussed and analyzed in order to evaluate their efficiencies.

Genetic factors of chronic pancreatitis in Russian population

The two-machine permutation flow shop scheduling problem with the objective of minimizing total earliness and tardiness is addressed. Unforced idle time can be used to complete jobs closer to their due dates. It is shown that unforced idle time only needs to be considered on the second machine. This result is then used to extend a lower bound and dominance conditions for the single-machine problem to the two-machine permutation flow shop problem. Two branch-and-bound algorithms are developed for the problem utilizing the lower bound and dominance conditions. The algorithms are tested using instances that represent a wide variety of conditions.

Branch-and-bound algorithms for minimizing total earliness and tardiness in a two-machine permutation flow shop with unforced idle allowed

The two-machine permutation flow shop scheduling problem with the objective of minimizing total earliness and tardiness is addressed. Unforced idle time can be used to complete jobs closer to their due dates. It is shown that unforced idle time only needs to be considered on the second machine. This result is then used to extend a lower bound and dominance conditions for the single-machine problem to the two-machine permutation flow shop problem. Two branch-and-bound algorithms are developed for the problem utilizing the lower bound and dominance conditions. The algorithms are tested using instances that represent a wide variety of conditions.

Methods for Scheduling Problems Considering Experience, Learning, and Forgetting Effects

Workers with different levels of experience and knowledge have different effects on job processing times. By taking into account 1) the sum-of-processing-time; 2) the job-position; and 3) the experience of workers, a more general learning model is introduced for scheduling problems. We show that this model generalizes existing ones and brings the consideration of learning and forgetting effects closer to reality. We demonstrate that some single machine scheduling problems are polynomially solvable under this general model. Considering the forgetting effect caused by the idle time on the second machine, we construct a learning-forgetting model for the two-machine permutation flow shop scheduling problem with makespan minimization. A branch-and-bound method and four heuristics are presented to find optimal and approximate solutions, respectively. The proposed heuristics are evaluated over a large number of randomly generated instances. Experimental results show that the proposed heuristics are effective and efficient.

Scheduling on a two-machine permutation flow shop under time-of-use electricity tariffs

We consider a two-machine permutation flow shop scheduling problem to minimise the total electricity cost of processing jobs under time-of-use electricity tariffs. We formulate the problem as a mixed integer linear programming, then we design two heuristic algorithms based on Johnson’s rule and dynamic programming method, respectively. In particular, we show how to find an optimal schedule using dynamic programming when the processing sequence is fixed. In addition, we propose an iterated local search algorithm to solve the problem with problem-tailored procedures and move operators, and test the computational performance of these methods on randomly generated instances.

No-wait two-machine permutation flow shop scheduling problem with learning effect, common due date and controllable job processing times

We consider a two-machine no-wait permutation flow shop common due date assignment scheduling problem where the processing time of a job is given as a function of its position in the sequence and its amount of resource allocated to this job. The common due date (CON) assignment method means that all the jobs are given a common due date. We need to make a decision on the common due date, resource allocation and the sequence of jobs to minimise total earliness, tardiness, common due date cost and total resource cost. We show that the problem remains polynomially solvable under the proposed model.

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 4 3 -approximation algorithm.

A two-machine permutation flow shop scheduling problem with buffers

A two-machine permutation flow shop scheduling problem with buffers

A two-machine permutation flow shop scheduling problem with buffers

Problems with “blocking” (limited intermediate storage space) are used frequently for modelling and scheduling just-in-time and flexible manufacturing systems. In this paper, an approximation algorithm is presented for the problem of finding the minimum makespan in a two-machine permutation flow-shop scheduling problem with the mediating buffer of finite capacity. The algorithm is based on the tabu search approach supported by the reduced neighborhood, search accelerator and technique of back jumps on the search trajectory. Due to some special properties, the proposed algorithm provides makespans very close to optimal in a short time. It has been shown that this algorithm outperforms all known approximation algorithms for the problem stated.