Sequence-dependent Setup Times Research Articles

A 3/2-Approximation for the Metric Many-Visits Path TSP

In the Many-visits Path TSP, we are given a set of $n$ cities along with their pairwise distances (or costs) $c(uv)$, and moreover each city $v$ comes with an associated positive integer request $r(v)$. The goal is to find a minimum-cost path, starting at city $s$ and ending at city $t$, that visits each city $v$ exactly $r(v)$ times. We present a $3/2$-approximation algorithm for the metric Many-visits Path TSP that runs in time polynomial in $n$ and polylogarithmic in the requests $r(v)$. Our algorithm can be seen as a generalization of the $3/2$-approximation algorithm for Path TSP by Zenklusen [Proceedings of SODA, 2019, pp. 1539--1549], which answered a long-standing open problem by providing an efficient algorithm which matches the approximation guarantee of Christofides' algorithm from 1976 for metric TSP. One of the key components of our approach is a polynomial-time algorithm to compute a connected, degree-bounded multigraph of minimum cost in an undirected graph with edge costs. We tackle this problem by generalizing a fundamental result of Király, Lau, and Singh [Combinatorica, 32 (2012), pp. 705--720] on the Minimum Bounded Degree Matroid Basis problem, and devise such an algorithm for generalized polymatroids, even allowing element multiplicities. Our result directly yields a $3/2$-approximation to the metric Many-visits TSP, as well as a $3/2$-approximation for the problem of scheduling classes of jobs with sequence-dependent setup times on a single machine so as to minimize the makespan.

A GRASP for a real-world scheduling problem with unrelated parallel print machines and sequence-dependent setup times

We consider a real-world scheduling problem arising in the colour printing industry. The problem consists in assigning print jobs to a heterogeneous set of flexographic printer machines and finding a processing sequence for the jobs assigned to each machine. The machines are characterised by a limited sequence of colour groups and can equip additional components (e.g. embossing rollers and perforating rolls) to process jobs that require specific treatments. The process to equip a machine with an additional component or to clean a colour group takes a long time, with the effect of significantly raising the setup times. The aim is to minimise a weighted sum of total weighted tardiness and total setup time. The problem derives from the activities of an Italian food packaging company. To solve it, we developed a greedy randomised adaptive search procedure equipped with several local search procedures. The excellent performance of the algorithm is proved by extensive computational experiments on real-world instances, for which it produced good-quality solutions within a limited computing time. The algorithm is currently in use at the company to support their weekly scheduling decisions.

Unrelated parallel machine energy-efficient scheduling considering sequence-dependent setup times and time-of-use electricity tariffs

Given that about half of the produced energy in the world is consumed in industries, there has been an increasing concern about optimizing energy consumption in manufacturing sectors. As one of the most effective ways, proper production scheduling to reduce energy consumption is of crucial importance among researchers and manufacturers. This paper addresses an unrelated parallel machine energy-efficient scheduling problem with sequence-dependent setup times by considering different energy consumption tariffs. The setup times are studied in two modes: disjointed from/jointed to processing time. For each one of these problems, two mixed-integer linear programming models have been formulated. The presented models for the problem with setup time disjointed from processing time can solve up to 16 machines and 45 jobs. In contrast, this capability is changed to 20 machines and 40 jobs for processing time jointed to the setup time problem. Furthermore, a fix and relax heuristic algorithm is presented for large-size instances, which can solve instances of up to 20 machines and 100 jobs for each of the two considered problems.

Energy-efficient distributed heterogeneous re-entrant hybrid flow shop scheduling problem with sequence dependent setup times considering factory eligibility constraints

In the face of energy crisis, manufacturers pay more and more attention to energy-saving scheduling. In the paper, we consider the distributed heterogeneous re-entrant hybrid flow shop scheduling problem (DHRHFSP) with sequence dependent setup times (DHRHFSP-SDST) considering factory eligibility constraints under time of use (TOU) price, which means that each job can only be assigned to its available set of factories and all factories have different number of machines and processing capacity, and so on. To deal with DHRHFSP-SDST, a multi-objective Artificial Bee Colony Algorithm (MOABC) is proposed to optimize both the makespan and total energy consumption. For the MOABC, firstly, a hybrid initialization method is presented to initialize the population; then, due to the electricity price shows significant differences vary from periods under TOU price, the energy saving operator based on right-shift strategy is proposed to avoid processing jobs with the high electricity price without affecting the productivity; thirdly, based on the full consideration of distributed heterogeneous and factory eligibility, crossover and mutation operators, three neighborhood search operators and new food sources generation strategy are designed; lastly, extensive experiments demonstrate the effectiveness of the proposed algorithm on solving the DHRHFSP-SDST.

Simulation-optimization of inventory control of multiple products on a single machine with sequence-dependent setup times

This work studies the problem of lot sizing and scheduling of multiple products on a single machine, with stochastic demand and sequence-dependent setup times, called Stochastic Economic Lot Scheduling Problem (SELSP). The present work differs from others in the literature by considering simple inventory control policies and using the simulation–optimization approach to calibrate their parameters. We consider two inventory control policies: (i) fixed cycling (First in Sequence - FIS) and (ii) dynamic scheduling based on inventory levels (Lowest Days of Supply - LDS), combined with an “order-up-to” lot sizing. The problem is solved using AnyLogic simulation software and the OptQuest search engine to minimize total inventory cost (ordering, holding and shortage costs). The experimental design included the following factors: number of items, coefficient of variation of demand, system workload, and degree of setup increment, allowing the comparison of the two inventory control policies in different scenarios. Experiments show that LDS outperforms FIS in all scenarios, achieving up to 4.6% cost savings for cases of more products, higher workload, and greater demand variance. The developed models proved to solve the problem, effectively generating reasonable solutions. Furthermore, as they are user-friendly, we believe they can be adapted, without great difficulties, to real-life scenarios of the process industry.

A hyper-heuristic for distributed parallel machine scheduling with machine-dependent processing and sequence-dependent setup times

Today, because the market is scattered around the world, manufacturing activities are not limited to a single location and have spread globally. As a result, the discussion of scheduling the factory has changed from a classic single to a network scheduling as a need in the real world. In this regard, this study considers the scheduling of multiple factories by taking into account the job transportation time between factories. The main problem here is that each job would be assigned to which factory and machine. In this research, unrelated parallel machines are considered in which the processing time of jobs depends on the machine and setup time. To minimize the makespan, first, a mixed-integer linear model was proposed in which two types of modeling have been combined. Then, a hyper-heuristic algorithm (HHA) was designed to solve the problem in a reasonable time by choosing the best method among four low-level heuristic methods that are precisely designed according to the properties of the problem. Finally, the efficiency of the proposed algorithm has been compared with the imperialist competitive algorithm (ICA) by conducting experiments. The results show that the proposed algorithm performs very well compared to the ICA and, in more than 75% of the test problems, the proposed algorithm was superior. Also, based on the analysis, in comparing the proposed algorithm with the ICA, it can be concluded that there is a significant difference between the results, and in all cases, the HHA was remarkably better. Considering the challenges and rapid changes of today’s market that traditional centralized production planning does not have enough flexibility to respond to them, the results of this research are expected to be useful and attractive for planners in this field.

Impact of Preventive Maintenance and Machine Breakdown on Performance of Stochastic Flexible Job Shop Scheduling with Setup Time

Real-time scheduling problems increase the practical implementation of the manufacturing system. In this study, using a single objective performance measure i.e., Number of Tardy Jobs (NTJ), the influence of 5 input constraints, i.e., reliability level (R_L), percentage of machine failure (%McF), mean time to repair for random machine breakdown (MTR_RMcB), due date tightness factor (Ғ), and routing flexibility level (R_FL) were evaluated for considered stochastic Flexible Job Shop Scheduling Problem (FJSSP). The study integrated reliability-centered preventive maintenance (PMRC) and random machine breakdown (RMcB) environment with sequence-dependent setup time in the considered problem. A statistical response surface methodology was used to assesses NTJ. A second-order regression model was obtained to compute correlation between input constraints and NOTJ at 95% confidence level. The results demonstrate that main effects of R_L, %McF, Ғ, and R_FL; the interaction effects of R_L and Ғ, %McF and R_FL, MTR_RMcB and R­_FL, and Ғ and R_FL; and quadratic effects of Ғ and R_FL, have significant impact on NTJ performance measure. Ғ has emerged as the major factor affecting NTJ. The confirmatory data demonstrate that error is less than 5%, confirming model can be used for future computations. Further, the novelties of the work are shown by the fact that it takes into account the uncertainties in the scheduling issue, as well as the dynamic tasks arrival environment. The aforementioned findings will assist production managers in planning and scheduling flexible job shops in order to satisfy customer demand on time.

Unrelated parallel machines scheduling with dependent setup times in textile industry

The problem tackled in this paper is an unrelated parallel machines scheduling problem with machine and sequence dependent setup times, machine eligibility and different resource types constraints. This subject is inspired from a textile industry partner case. The different characteristics of this problem have never been combined as it is depicted in this paper. Two resolution methods are exposed. A new mathematical programming is proposed to have an exact resolution approach of this complex problem. An improved genetic algorithm (GA) with dedicated operators is also presented in order to solve the industrial case in a reasonable computational time.

Intelligent optimization under blocking constraints: A novel iterated greedy algorithm for the hybrid flow shop group scheduling problem

This paper introduces a new flow shop combinatorial optimization problem, called the blocking hybrid flow shop group scheduling problem (BHFGSP). In the problem, no buffers exist between any adjacent machines, and a set of jobs with different sequence-dependent setup times needs to be scheduled and processed at organized manufacturing cells. We verify the correctness of the mathematical model of BHFGSP by using CPLEX. In this paper, we proposed a novel iterated greedy algorithm to solve the problem. The proposed algorithm has two key techniques. One is the decoding procedure that calculates the makespan of a job sequence, and the other is the neighborhood probabilistic selection strategies with families and blocking-based jobs. The performance of the proposed algorithm is investigated through a large number of numerical experiments. Comprehensive results show that the proposed algorithm is effective in solving BHFGSP.

An effective two-stage iterated greedy algorithm to minimize total tardiness for the distributed flowshop group scheduling problem

This paper aims to minimize the total tardiness for a distributed flowshop group scheduling problem with sequence-dependent setup time, which is an extension of the traditional distributed flowshop scheduling problem and has significant applications in the practical manufacturing environment. A mathematical model is set up and an effective two-stage iterated greedy (TIG) algorithm with an elaborately designed two-stage structure is presented to address the considered problem. A heuristic method combining a problem-specific dispatching rule and a simplified tie-breaking method is designed to generate an initial solution. A novel reconstruction mechanism is developed to explore the most valuable search space to save the evaluation efforts. To validate the effectiveness of the proposed TIG, comprehensive computational and statistical experiments are conducted. Experimental results show that the proposed TIG outperforms the six state-of-the-art algorithms from the closely related literature by a considerable margin in terms of the relative deviation index values at the same maximum elapsed CPU time.

A SIMULATED ANNEALING PROCEDURE TO MINIMIZE TOTAL WEIGHTED TARDINESS ON A SINGLE MACHINE WITH UNEQUAL JOB RELEASE TIME, SEQUENCE DEPENDENT SETUP TIME, AND MACHINE DOWN TIME

ABSTRACT In this study, we explored a scheduling problem with machine down time, unequal job release time, and sequence dependent setup time to minimize the total weighted tardiness on a single machine. The ATCS rule (Apparent Tardiness Cost with Setup time Rule, Lee et al. 1997) was modified first and then presented with a simulated annealing procedure. Experimental results revealed that the performance of the new simulated annealing procedure outperformed the modified Lin''s simulated annealing method (Lin and Ying, 2007) in the total weighted tardiness reduction. Keywords single machine, simulated annealing, dependent setup time, release time, machine down time.

Energy-aware production scheduling in the flow shop environment under sequence-dependent setup times, group scheduling and renewable energy constraints

In this paper, we investigate an energy-aware flow shop scheduling problem under sequence-dependent setup times, group scheduling, and renewable energy constraints. We aim to minimize the total energy cost dependent on time-of-use electricity tariffs. To this end, we develop two mixed-integer linear programming models, including a time-unit index model and a time-interval index model. Besides, we develop a decomposition-based heuristic algorithm to solve efficiently medium-size instances. Using extensive computational experiments, we show that the heuristic algorithm outperforms both developed models, and the time-interval index model indicates superior performance than the time-unit index model. Finally, we provide a set of sensitivity analyses and evaluation of economic performance.

A heuristic and meta-heuristic based on problem-specific knowledge for distributed blocking flow-shop scheduling problem with sequence-dependent setup times

The distributed production scenario with the sequence-dependent setup times (SDST) widely exists in the modern manufacturing system. This paper investigates the distributed blocking flow-shop scheduling problem with sequence-dependent setup times (SDST/DBFSP). Considering the complexity of the distributed scenario and SDSTs, a discrete heuristic and meta-heuristic is proposed by exploring the problem-specific knowledge. First, a knowledge-incorporated construction heuristic is proposed to reduce the blocking times and idle times generated by SDSTs. In the first stage of the meta-heuristic, an insertion-based neighborhood operator of different factories is developed to explore promising regions in the decision space. In the second stage, a local search operator is embedded to enhance the exploitation ability. Additionally, a simulated annealing-like acceptance criterion of the iterated greedy algorithm is employed to keep the diversity of the population. Finally, an insertion operation for critical factories is introduced to further improve the accuracy of the solutions. Moreover, a speedup method for the insertion neighborhood is expanded to reduce the computational complexity of SDST/DBFSP. In the part of the experiment, a deconstruction process is designed to gain insight into the contribution of each component in the proposed meta-heuristic. The proposed meta-heuristic is assessed through comparing with five state-of-the-art algorithms to demonstrate its effectiveness. The experimental results testified that the proposed meta-heuristic outperforms other algorithms regarding the significance of the SDST/DBFSP.

Heuristics for the Hybrid Flow Shop Scheduling Problem with Sequence-Dependent Setup times

This paper considers the hybrid flow shop scheduling problem with two types of sequence-dependent setup times, one depending on the order of jobs and the other depending on both the order of jobs and the machines where the jobs are allocated. Three constructive heuristic algorithms based on the NEH algorithm are developed with the object of minimizing the total energy consumption cost. The first algorithm, called EPRA, obtains the order of jobs using the energy consumption cost based on the processing time. The second algorithm, called ESRA, obtains the order of jobs using the energy consumption cost based on the setup time. The third algorithm, called ESPRA, takes advantage of both EPRA and ESRA by constructing fictitious jobs with ESRA and acquiring the sequence of fictitious jobs with EPRA. Due to the drawback of NEH algorithm for the FFS problem proposed in this paper, all three heuristic algorithms use EST rules to allocate the jobs to the machines. Two lower bounds are developed to evaluate the heuristic algorithms proposed in this paper. A computational experiment based on the split-plot design is developed to carry out the factor analysis, algorithm analysis, lower bounds analysis, and CPU running time analysis. The analysis reveals that all main factor interactions except the algorithm are significant; the ESPRA algorithm is generally outstanding among the three algorithms; LB1 is better than LB2; the CPU running time of ESPRA algorithm is significantly reduced compared to those of EPRA and ESST algorithms.

Enhancement of two-stage flow shop multiprocessor scheduling problems using a target-oriented genetic algorithm

In the recent decades, genetic algorithms (GAs) have often been applied as heuristic techniques at various settings entailing production scheduling. However, early convergence is one of the problems associated with this approach. This study develops an efficient local search rule for the target-oriented rule in traditional GAs. It also addresses the problem of two-stage multiprocessor flow-shop scheduling (FSP) by viewing the due window and sequence-dependent setup times as constraints faced by common flow shops with multiprocessor scheduling suites in the actual production scenario. Using the simulated data, this study verifies the effectiveness and robustness of the proposed algorithm. The results of data testing demonstrate that the proposed method may outperform other algorithms, including a significant hybrid algorithm, in addressing the problems considered.

Flexible Job Shop Scheduling Problem with Fuzzy Times and Due-Windows: Minimizing Weighted Tardiness and Earliness Using Genetic Algorithms

The current requirements of many manufacturing companies, such as the fashion, textile, and clothing industries, involve the production of multiple products with different processing routes and products with short life cycles, which prevents obtaining deterministic setup and processing times. Likewise, several industries present restrictions when changing from one reference to another in the production system, incurring variable and sequence-dependent setup times. Therefore, this article aims to solve the flexible job shop scheduling problem (FJSSP) considering due windows, sequence-dependent setup times, and uncertainty in processing and setup times. A genetic algorithm is proposed to solve the FJSSP by integrating fuzzy logic to minimize the weighted penalties for tardiness/earliness. The proposed algorithm is implemented in a real-world case study of a fabric finishing production system, and it is compared with four heuristics adapted to the FJSSP such as earliest due date, critical reason, shortest processing time, and Monte Carlo simulation. Results show that the performance of the proposed algorithm provides efficient and satisfactory solutions concerning the objective function and computing time since it overperforms (more than 30%) the heuristics used as benchmarks.

Collaborative variable neighborhood search for multi-objective distributed scheduling in two-stage hybrid flow shop with sequence-dependent setup times

Distributed scheduling is seldom investigated in hybrid flow shops. In this study, distributed two-stage hybrid flow shop scheduling problem (DTHFSP) with sequence-dependent setup times is considered. A collaborative variable neighborhood search (CVNS) is proposed to simultaneously minimize total tardiness and makespan. DTHFSP is simplified by incorporating factory assignment into machine assignment of a prefixed stage, and its solution is newly represented with a machine assignment string and a scheduling string. CVNS consists of two cooperated variable neighborhood search (VNS) algorithms, and neighborhood structures and global search have collaborated in each VNS. Eight neighborhood structures and two global search operators are defined to produce new solutions. The current solution is periodically replaced with a member of the archive farthest from it. Experiments are conducted , and the computational results validate that CVNS has good advantages over the considered DTHFSP.

A two-stage cooperative evolutionary algorithm for energy-efficient distributed group blocking flow shop with setup carryover in precast systems

As the main link of the rapidly developing prefabricated construction industry, the production of precast components (PCs) has become a research hotspot. Therefore, the distributed group flow shop scheduling problem with blocking and carryover sequence-dependent setup time constraints (DPGFSP-BCT) in precast systems is considered. To address this problem, first, a mixed integer linear model is presented. Second, a two-stage cooperative coevolutionary algorithm (TS-CCEA) is proposed to minimize both the makespan and total energy consumption (TEC). In TS-CCEA, two acceleration rules are designed to reduce computational efforts. Third, to diversify the population, different initialization methods are established for different populations. Based on the problem-specific knowledge of solution classification, the individuals of the group population and job population execute two neighborhood search algorithms. Subsequently, considering the TEC, a critical path based speed mutation strategy is proposed to further improve the exploitation ability. Furthermore, a reinitialization heuristic is developed to avoid premature convergence. Last, the performance of the TS-CCEA is verified after calibrating the parameters. The experimental results demonstrate the stability and effectiveness of the algorithm.

Solve job shop scheduling problem with sequence dependent setup times using a local search algorithm with different neighborhood search structure

In this study examines job shop scheduling problems with sequence dependent setup times under objective function minimization of makespan (JSSP/SDST/ ). An effective meta-heuristic, local search is a meta-heuristic method for solving computationally hard optimization problems. Local search can be used on problems that can be formulated as finding a solution maximizing or minimizing a criterion among a number of candidate solutions. Local search algorithms move from solution to solution in the space of candidate solutions (the search space) by applying local changes, until a solution deemed optimal is found or a time bound is elapsed. The performance of the local search depends on its neighborhood search structure (NSS). We used five methods from neighborhood search: Swap, Migration Mechanism (MM), Inversion, shift, and a proposed robust neighborhood search method. The results showed that the new PNS method gives less makespan value with different problems size (15x15, 20x15, 20x20, 30x15, 30x20, 50x15, 50x20 and 100x20) taken from the OR- library compared to previous well known neighborhood search methods.

A new technology implementation via mathematical modeling for the sequence-dependent setup times of industrial problems

Scheduling problems with sequence-dependent setup times in industries currently attract the attention of researchers and practitioners. This study aims to develop a mathematical model for optimizing a single-machine environment with such times using an analogy with the traveling salesman problem. Employing a technological and modern modeling language for its computational implementations, firstly, five main formulations of this problem in the literature are evaluated and the best one for addressing the proposed problem is identified. Secondly, an arc-flow completion time and precedence model for a single-machine scheduling problem is assessed. Finally, the proposed model is improved by passing the initial solutions obtained by two heuristics to it. As a result, the mathematical model developed returns lower computational times than state-of-the-art ones (even without improvements to the initial solution) which indicates the success of using an analogy between formulations of the traveling salesman problem and the proposed model.