Grid-Based Hybrid Genetic Approach to Relaxed Flexible Flow Shop with Sequence-Dependent Setup Times

In this paper, a hybrid genetic algorithm implemented in a grid environment to solve hard instances of the flexible flow shop scheduling problem with sequence-dependent setup times is introduced. The genetic algorithm takes advantage of the distributed computing power on the grid to apply a hybrid local search to each individual in the population and reach a near optimal solution in a reduced number of generations. Ant colony systems and simulated annealing are used to apply a combination of iterative and cooperative local searches, respectively. This algorithm is implemented using a master–slave scheme, where the master process distributes the population on the slave process and coordinates the communication on the computational grid elements. The experimental results point out that the proposed scheme obtains the upper bound in a broad set of test instances. Also, an efficiency analysis of the proposed algorithm indicates its competitive use of the computational resources of the grid.

An improved algorithm to minimize the total completion time in a two-machine no-wait flow-shop with uncertain setup times

Since scheduling literature has a wide range of uncertainties, it is crucial to take these into account when solving performance measure problems. Otherwise, the performance may severely be affected in a negative way. In this paper, an algorithm is proposed to minimize the total completion time (TCT) of a two-machine no-wait flowshop with uncertain setup times within lower and upper bounds. The results are compared to the best existing algorithm in scheduling literature: the programming language Python is used to generate random samples with respect to various distributions, and the TCT of the proposed algorithm is compared to that of the best existing one. Results reveal that the proposed one significantly outperforms the best one given in literature for all considered distributions. Specifically, the average percentage improvement of the proposed algorithm over the best existing one is over 90%. A test of hypothesis is conducted to further confirm the results.

Minimizing total tardiness for the order scheduling problem with sequence-dependent setup times using hybrid matheuristics

This paper aims at presenting a customer order scheduling environment in which the setup times are explicit and depend on the production sequence. The considered objective function is the total tardiness minimization. Since the variant under study is NP-hard, we propose a mixed-integer linear programming (MILP) model, an adaptation of the Order-Scheduling Modified Due-Date heuristic (OMDD) (referred to as Order-Scheduling Modified Due-Date Setup (OMMD-S)), an adaptation of the Framinan and Perez-Gonzalez heuristic (FP) (hereinafter referred to as Framinan and Perez-Gonzalez Setup (FP-S)), a matheuristic with Same Permutation in All Machines (SPAM), and the hybrid matheuristic SPAM-SJPO based on Job-Position Oscillation (JPO). The algorithms under comparison have been compared on an extensive benchmark of randomly generated test instances, considering two performance measures: Relative Deviation Index (RDI) and Success Rate (SR). For the small-size evaluated instances, the SPAM is the most efficient algorithm, presenting the better values of RDI and SR. For the large-size evaluated instances, the hybrid matheuristic SPAM-JPO and MILP model are the most efficient methods.

A branch and bound method in a permutation flow shop with blocking and setup times

In this paper it is presented an improvement of the branch and bound algorithm for the permutation flow shop problem with blocking-in-process and setup times with the objective of minimizing the total flow time and tardiness, which is known to be NP-Hard when there are two or more machines involved. With that objective in mind, a new machine-based lower bound that exploits some structural properties of the problem. A database with 27 classes of problems, varying in number of jobs (n) and number of machines (m) was used to perform the computational experiments. Results show that the algorithm can deal with most of the problems with less than 20 jobs in less than one hour. Thus, the method proposed in this work can solve the scheduling of many applications in manufacturing environments with limited buffers and separated setup times.

Single Machine Scheduling Problems With Sequence-dependent Setup Times and Precedence Delays

Sequence-dependent setup times (SDSTs) and delayed precedence (DP) occur commonly in various manufacturing settings. This study investigated the single machine scheduling problem with SDSTs and DP constraints arising in an amplifier assembly company. A mixed-integer linear programming model and a lean iterated greedy (LIG) algorithm is proposed to search for the best job sequence with minimum makespan. Based on the characteristic of delayed precedence constraints of the problem, the proposed LIG algorithm implements a straightforward but effective lean construction mechanism, which can keep the search process within the feasible solution space and quickly converge toward the (near-) global optimum. Computational results reveal that LIG significantly outperforms the state-of-the-art algorithm in terms of solution quality and computational efficiency. This study mainly contributes to providing a simple, effective, and efficient algorithm that can facilitate industrial applications and act as a new benchmark approach for future research.

Explicit Modelling of Multi-Period Setup Times in Proportional Lot-Sizing Problem with Constant Capacity

The planning horizon of small bucket models is often divided into many fictitious micro-periods, with non-zero demand only in the last micro-period of each real (macro-)period. On the one hand, such models ensure schedules with short cycle times and low work-in-process inventory in multilevel systems; on the other, they make setup times that are longer than a single period more likely. This paper presents a new mixed-integer programming model for the case with setup operations that overlap multiple periods. The new model assumes that the capacity is constant in the whole planning horizon and explicitly determines the entire schedule of each changeover. Moreover, a two-level MIP heuristic is presented that uses model-specific cuts to fix a priori some minor decisions. The results of the computational experiments show that the new model and MIP heuristic require a substantially smaller computational effort from a standard MIP solver than the known models.MSC Classification: 90B30 , 90C11