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Constructive Heuristics for the Unrelated Parallel Machines Scheduling Problem with Machine Eligibility and Setup Times
Abstract
This work considers a scheduling problem identified in a factory producing customised Heating, Ventilation and Air Conditioning (HVAC) equipment. More specifically, the metal folding section is modelled as unrelated parallel machines with machine eligibility and sequence-dependent setup times. The objective under consideration is the minimisation of the total tardiness. The problem is known to be NP-hard so approximate methods are needed to solve real-size instances. In order to embed the scheduling procedure into a decision support system providing high-quality solutions in nearly real time, the goal of this paper is to develop fast, efficient constructive heuristics for the problem. Due to the lack of methods for this specific problem, some existing heuristics and one metaheuristic are selected from related problems and adapted. In addition, a set of heuristics with novel repair and improvement phases are proposed. The performance of the methods adapted and the proposals are compared with the optimal/approximate solutions obtained by a solver for an MILP in two sets of instances with small and medium sizes. Additionally, big-size instances (representing more realistic cases for our company) have been solved using the proposed constructive heuristics, providing efficient solutions in negligible computational times. Even if the adaptation of heuristics performs reasonably well, these are outperformed by the new heuristic proposed in this paper. In addition, when the new heuristic is embedded in the metaheuristic adapted from a related the problem, the results obtained are excellent in terms of the quality of the solution, even if the computational effort is somewhat higher.
... PMSPs that consider eligible machines are well-known in the literature and have been studied in several publications (e.g. Afzalirad and Rezaeian 2016;Perez-Gonzalez et al. 2019). Similarly, problems with varying machine efficiency have been previously described as Unrelated PMSP (UPMSP) (e.g. ...
... The corresponding changeover times between jobs have been referred to as sequence-dependent setup times in previous publications (e.g. Vallada and Ruiz 2011;Perez-Gonzalez et al. 2019). ...
... To show the robustness of our method we compare to the approach from Perez-Gonzalez et al. (2019) that was proposed recently for a similar problem. The problem specification provided by Perez-Gonzalez et al. (2019) uses the same set of constraints of the problem that we investigate in this paper and also aims to minimise total tardiness. However, the authors do not consider the minimisation of the total makespan. ...
In this paper, we study an important real-life scheduling problem that can be formulated as an unrelated parallel machine scheduling problem with sequence-dependent setup times, due dates, and machine eligibility constraints. The objective is to minimise total tardiness and makespan. We adapt and extend a mathematical model to find optimal solutions for small instances. Additionally, we propose several variants of simulated annealing to solve very large-scale instances as they appear in practice. We utilise several different search neighbourhoods and additionally investigate the use of innovative heuristic move selection strategies. Further, we provide a set of real-life problem instances as well as a random instance generator that we use to generate a large number of test instances. We perform a thorough evaluation of the proposed techniques and analyse their performance. We also apply our metaheuristics to approach a similar problem from the literature. Experimental results show that our methods are able to improve the results produced with state-of-the-art approaches for a large number of instances.
... The authors propose a two step heuristic in which the jobs are assigned to machines to minimise the total cost (with the property of being preemptive) and then in the second stage the jobs are scheduled without preemption using an insertion heuristic. A problem with setup times, machine eligibility constraints and total tardiness minimisation was considered in [87]. The authors first propose several heuristic methods that are adapted for the considered problem. ...
... Cmax [24], [25], [26], [28], [29], [30], [32], [33], [39], [40], [41], [42], [43], [44], [45], [47], [48], [49], [50], [51], [52], [55], [57], [58], [59], [62], [63], [64], [65], [70], [71], [74], [75], [77], [79], [80], [81], [84], [85], [88], [89], [90], [91], [93], [94], [95], [97], [100], [105], [106], [107], [109], [111], [113], [117], [118], [119], [122], [123], [127], [130], [131], [132], [133], [134], [135], [136], [140], [142], [145], [146], [147], [149], [152], [153], [154], [158], [159], [160], [161], [163], [167], [168], [169], [170], [171], [172], [173], [175], [176], [177], [179], [180], [182], [183], [185], [186], [188], [189], [193], [195], [196], [197], [198], [199], [200], [201], [202], [204], [205], [207], [209], [210], [213], [214], [215], [216], [218], [219], [220], [221], [222], [225], [226], [228], [229], [230], [231], [232], [235], [237], [240], [242], [243], [244], [245], [246], [248], [250], [252], [255], [256], [257], [258], [259], [260], [261], [262], [263], [264] Etwt [58], [63], [73], [82], [98], [104], [120], [123], [131], [173], [174], [181], [206], [209], [211], [212], [239], [241], [252] F t [27], [39], [44], [46], [48], [54], [58], [62], [63], [64], [65], [72], [83], [115], [125], [178], [190], [194], [205], [206], [213], [234], [244], [253], [255] F wt [31], [35], [36], [50], [58], [63], [80], [94], [126], [128], [129], [138], [143], [148], [150], [155], [158], [161], [162], [165], [166], [185], [186], [191], [203], [208], [239], [224] Fmax [58], [63] M L [27], [39], [58], [63], [95], [98], [213] T T [69], [72], [87], [92], [95], [102], [108], [113], [114], [121], [137], [151], [157], [164], [170], [172], [187], [213], [227], [231], [242], [254], [265] T W T [37], [38], [42], [50], [53], [58], [62], [63], [64], [65], [66], [67], [68], [76], [80], [94], [96], [99], [109], [112], [124], [128], [129], [138], [141], [143], [156], [158], [161], [163], [184], [185], [186], [191], [193], [203], [205], [208], [223], [233], [236], [238], [239], [244], [247], [249] Tmax [58], [63], [90], [103] U t [27], [34], [51], [72], [78], [125] U wt [43], [58], [62], [63], [64], [65], [101], [116], [144], [205], [244] [260], COST [42], [56], [74], [99], [163], [209], [210], [211], [217], [251], [253], [257] N jit [139] Ru [46], [250] T l [192] T EC [86], [184], [200], [225], [227], [238], [260], [261], [264], [265] T s ...
... [83] s [27], [31], [35], [36], [37], [38], [42], [43], [46], [51], [53], [68], [72], [74], [76], [77], [78], [79], [83], [54], [87], [92], [93], [98], [101], [102], [103], [105], [106], [108], [109], [113], [114], [115], [116], [117], [118], [119], [120], [121], [122], [125], [128], [129], [133], [136], [137], [138], [143], [142], [144], [145], [146], [147], [149], [152], [153], [154], [155], [161], [163], [164], [166], [167], [168], [169], [170], [171], [172], [173], [174], [175], [176], [179], [180], [181], [182], [187], [189], [190], [191], [192], [194], [195], [196], [201], [202], [203], [206], [207], [208], [210], [213], [214], [216], [218], [219], [220], [223], [226], [230], [231], [232], [233], [235], [237], [238], [239], [240], [243], [247], [250], [252], [256], [257], [258], [259], [262], [263], [264] brkdwn [68], [70], [96], [143], [191], [208], [210], [251], [257] M j [38], [43], [51], [68], [72], [75], [78], [79], [87], [96], [101], [102], [103], [115], [123], [131], [143], [159], [160], [172], [173], [180], [190], [191], [192], [195], [203], [204], [206], [208], [210], [211], [233], [257], [260], [261] M ded [83], [212] r j [33], [43], [47], [50], [51], [53], [56], [57], [58], [59], [62], [63], [64], [65], [66], [67], [68], [73], [96], [101], [108], [114], [124], [125], [140], [141], [143], [144], [151], [161], [179], [180], [184], [191], [192], [193], [194], [195], [197], [203], [205], [206], [208], [209], [210], [213], [232], [234], [236], [239], [244], [247], [257], [258] batch [35], [36], [37], [52], [57], [59], [76], [78], [79], [81], [92], [96], [111], [124], [143], [159], [170], [191], [197], [208], [209], [210], [215], [217], [221], [234] R [46], [77], [81], [84], [85], [102], [103], [152], [153], [154], [155], [160], [161], [170], [195], [198], [199], [200], [204], [210], [213], [222], [228], [232], [237], [250], [253] [254], [257], [258], [264] d [101], [121], [166] pc [160], [194], [204], [215], [238] j f [43], [124] prec [45], [68], [71], [125], [151], [157], [192], [195], [203], [255] rwrk [47], [180], [249] [163], [211], [251] Mm [188], [211], [215], [220], [231], [246], [251] js [57], [59], [197], [209], [210], [221], [234] Q k [57], [59], [197], [209], [210], [221], [234] Ms [200], [225], [265] studies will focus even more on optimising problems with several different constraints, and that even more new constraint variants will be defined. Finally, Table IV shows the application of different methods in the reviewed papers. ...
Today scheduling problems have an immense effect on various areas of human lives, be it from their application in manufacturing and production industry, transportation, or workforce allocation. The unrelated parallel machines scheduling problem (UPMSP), which is only one of the many different problem types that exist, found its application in many areas like production industries or distributed computing. Due to the complexity of the problem, heuristic and metaheuristic methods are gaining more attention for solving it. Although this problem variant did not receive much attention as other models, recent years saw the increase of research dealing with this problem. During that time, many different problem variants, solution methods, or other interesting research directions were considered. However, no study has until now tried to systematise the research in which heuristic methods are applied for the UPMSP. The goal of this study is to provide an extensive literature review on the application of heuristic and metaheuristic methods for solving the UPMSP. The research was systematised and classified into several categories to enable an easy overview of the different problem and solution variants. Additionally, current trends and possible future research directions are also shortly outlined.
... Many variants of Parallel Machine Scheduling Problem, e.g., (Allahverdi et al. 2008;Allahverdi 2015), have been studied extensively in the literature. Previous publications have considered eligibility of machines, e.g., (Afzalirad and Rezaeian 2016;Perez-Gonzalez et al. 2019;Bektur and Saraç 2019), machine dependent processing time, e.g., (Vallada and Ruiz 2011a;Avalos-Rosales et al. 2013;Allahverdi 2015), and sequence dependent setup times, e.g., (Vallada and Ruiz 2011a;Perez-Gonzalez et al. 2019;Fanjul-Peyro et al. 2019;Gedik et al. 2018). ...
... Many variants of Parallel Machine Scheduling Problem, e.g., (Allahverdi et al. 2008;Allahverdi 2015), have been studied extensively in the literature. Previous publications have considered eligibility of machines, e.g., (Afzalirad and Rezaeian 2016;Perez-Gonzalez et al. 2019;Bektur and Saraç 2019), machine dependent processing time, e.g., (Vallada and Ruiz 2011a;Avalos-Rosales et al. 2013;Allahverdi 2015), and sequence dependent setup times, e.g., (Vallada and Ruiz 2011a;Perez-Gonzalez et al. 2019;Fanjul-Peyro et al. 2019;Gedik et al. 2018). ...
We deal with a challenging scheduling problem on parallel machines with sequence-dependent setup times and release dates from a real-world application of semiconductor work-shop production. There, jobs can only be processed by dedicated machines, thus few machines can determine the makespan almost regardless of how jobs are scheduled on the remaining ones. This causes problems when machines fail and jobs need to be rescheduled. Instead of optimising only the makespan, we put the individual machine spans in non-ascending order and lexicographically minimise the resulting tuples. This achieves that all machines complete as early as possible and increases the robustness of the schedule. We study the application of Answer-Set Programming (ASP) to solve this problem. While ASP eases modelling, the combination of timing constraints and the considered objective function challenges current solving technology. The former issue is addressed by using an extension of ASP by difference logic. For the latter, we devise different algorithms that use multi-shot solving. To tackle industrial-sized instances, we study different approximations and heuristics. Our experimental results show that ASP is indeed a promising KRR paradigm for this problem and is competitive with state-of-the-art CP and MIP solvers. Under consideration in Theory and Practice of Logic Programming (TPLP).
... Many variants of Parallel Machine Scheduling Problem, e.g., (Allahverdi et al. 2008;Allahverdi 2015), have been studied extensively in the literature. Previous publications have considered eligibility of machines, e.g., (Afzalirad and Rezaeian 2016;Perez-Gonzalez et al. 2019;Bektur and Saraç 2019), machine dependent processing time, e.g., (Vallada and Ruiz 2011b;Avalos-Rosales, Alvarez, andÁngel-Bello 2013;Allahverdi 2015), and sequence dependent setup times, e.g., (Vallada and Ruiz 2011b;Perez-Gonzalez et al. 2019;Fanjul-Peyro, Ruiz, and Perea 2019;Gedik et al. 2018). ...
... Many variants of Parallel Machine Scheduling Problem, e.g., (Allahverdi et al. 2008;Allahverdi 2015), have been studied extensively in the literature. Previous publications have considered eligibility of machines, e.g., (Afzalirad and Rezaeian 2016;Perez-Gonzalez et al. 2019;Bektur and Saraç 2019), machine dependent processing time, e.g., (Vallada and Ruiz 2011b;Avalos-Rosales, Alvarez, andÁngel-Bello 2013;Allahverdi 2015), and sequence dependent setup times, e.g., (Vallada and Ruiz 2011b;Perez-Gonzalez et al. 2019;Fanjul-Peyro, Ruiz, and Perea 2019;Gedik et al. 2018). ...
We deal with a challenging scheduling problem on parallel-machines with sequence-dependent setup times and release dates from a real-world application of semiconductor work-shop production. There, jobs can only be processed by dedicated machines, thus few machines can determine the makespan almost regardless of how jobs are scheduled on the remaining ones. This causes problems when machines fail and jobs need to be rescheduled. Instead of optimising only the makespan, we put the individual machine spans in non-ascending order and lexicographically minimise the resulting tuples. This achieves that all machines complete as early as possible and increases the robustness of the schedule. We study the application of Answer-Set Programming (ASP) to solve this problem. While ASP eases modelling, the combination of timing constraints and the considered objective function challenges current solving technology. The former issue is addressed by using an extension of ASP by difference logic. For the latter, we devise different algorithms that use multi-shot solving. To tackle industrial-sized instances, we study different approximations and heuristics. Our experimental results show that ASP is indeed a promising KRR paradigm for this problem and is competitive with state-of-the-art CP and MIP solvers.
... In a final stage, they developed a branch-and-bound algorithm to handle complex instances. Concerning [42], they investigated the unrelated-parallel machines problem with machine eligibility and sequence-dependent setup times. In order to minimize total tardiness, they put forward a mixed integer linear programming model. ...
Mathematical programming, and above all, the multi-objective scheduling problems stand as remarkably versatile tools, highly useful for optimizing the health care services. In this context, the present work is designed to put forward two-fold multi-objective mixed integer linear programs, simultaneously integrating the objectives of minimizing the patients? total waiting and flow time, while minimizing the doctors' work-load variations. For this purpose, the three major health-care system intervening actors are simultaneously considered, namely, the patients, doctors and machines. To the best of our knowledge, such an issue does not seem to be actually addressed in the relevant literature. To this end, we opt for implementing an appropriate lexicographic method, whereby, effective solutions enabling to minimize the performance of two-objective functions could be used to solve randomly generated small cases. Mathematical models of our study have been resolved using the CPLEX software. Then, results have been comparatively assessed in terms of both objectives and CPU times. A real laser-treatment case study, involving a set of diabetic retinopathy patients in the ophthalmology department in Habib Bourguiba Hospital in Sfax, Tunisia, helps in illustrating the effective practicality of our advanced approach. To resolve the treated problem, we use three relevant heuristics which have been compared to the first-come first-served rule. We find that the program based on our second formulation with time-limit provided the best solution in terms of total flow time.
... The scheduling problem of parallel machines may not only be considered in single-stage manufacturing environments but may also be a critical stage in complex manufacturing environments. Unrelated parallel machines often appear in real manufacturing environments, such as customized heating, ventilation and air conditioning (HVAC) equipment [2], ceramic plants [3], packaging industry [4], electronic assembly industry [5], additive manufacturing [6], and printed circuit board assembly [7]. ...
This study considers order acceptance and scheduling problems in unrelated parallel machines with several practical constraints, including order release times, sequence-dependent setup times, machines’ unequal ready times, and preventive maintenance. In a make-to-order production environment, issues with order acceptance and scheduling are mainly caused by the limited production capacity of a factory, which makes it impossible to accept all orders. Consequently, some orders must be rejected in order to maximize profits and the accepted orders must be completed by the due date or no later than the deadline. An iterated population-based metaheuristic is proposed to solve the problems. The algorithm begins with an efficient initial solution generator to generate an initial solution, and then uses the destruction and construction procedure to generate a population with multiple solutions. Then, a solution is selected from the population, and a variable neighborhood descent search algorithm with several new reduced-size neighborhood structures is applied to improve the selected solution. Following the completion of the local search, a method for updating the members of the population was devised to enhance its diversity. Finally, the metaheuristic allows the populations to evolve for several generations until the termination condition is satisfied. To evaluate the performance of the proposed metaheuristic, a heuristic rule and an iterated local search algorithm are examined and compared. The computational experimental results indicate that the presented metaheuristic outperforms the other heuristics.
... Although the problem including a single server considered in this study is interesting and new, it was not considered further in any study. Perez-Gonzalez et al. (2019) consider a problem with setup times, machine eligibility constraints and total tardiness minimisation. The authors apply CLONALG with GRASP and VND, and compare their performance to certain heuristic methods, against which it achieved a good performance. ...
Scheduling has an immense effect on various areas of human lives, be it though its application in manufacturing and production industry, transportation, workforce allocation, or others. The unrelated parallel machines scheduling problem (UPMSP), which is one of the various problem types that exist, found its application in many areas like manufacturing and distributed computing. Due to the complexity of the problem, heuristic and metaheuristic methods have dominantly been applied for solving it. Although this problem variant did not receive much attention as other models, recent years saw the increase of research dealing with the UPMSP. During that time, different problem variants, solution methods, and interesting research directions were considered. However, no study provided a systematic overview of the research in which heuristic methods are applied for solving the UPMSP. This comes as a problem since it is becoming difficult to keep track of all the relevant research directions and solution methods considered for this problem. Therefore, the goal of this study is to provide an extensive literature review on the application of heuristic and metaheuristic methods for solving the UPMSP. Each reviewed study is briefly described based on the considered problem and solution method. Additionally, studies dealing with similar problems are grouped together to outline the evolution of the research, and possible areas where further research can be carried out. All studies were systematised and classified into several categories to allow for an easy overview of different problem and solution variants. Finally, recent research trends and possible future directions are also outlined.
... As machines are of different capabilities in processing jobs, it usually refers to the unrelated parallel machine environment. Perez-Gonzalez et al. (2019) address an unrelated parallel machine scheduling problem with machine eligibility constraint and sequence-dependent setup times. For the objective of minimum total tardiness, several heuristics with novel repair and improvement phases are proposed. ...
This work investigates an unrelated parallel machine scheduling problem in the shared manufacturing environment. Based on practical production complexity, five job and machine-related factors, including job splitting, setup time, learning effect, processing cost and machine eligibility constraint, are integrated into the considered problem. Parallel machines with uniform speed but non-identical processing capabilities are shared on a sharing service platform, and jobs with different types can only be processed by the machines with matching eligibilities. The platform pays an amount of processing cost for using any machine to process the jobs. To balance the processing cost paid and the satisfaction of customers, we aim to minimize the weighted sum of total processing cost and total completion time of jobs in the considered problem. We establish a mixed integer linear programming model, and provide a lower bound by relaxing the machine eligibility constraint. The CPLEX solver is employed to generate optimal solutions for small-scale instances. For large-scale instances, we propose an efficient heuristic algorithm. Experimental results demonstrate that for various instance settings, the proposed algorithm can always produce near optimal solutions. We further present several managerial insights for the shared manufacturing platform.
... This paper considers four performance evaluation metrics: the average tardiness time of the workpiece (T), the tardiness ratio of workpieces (%T), the average flow time of the workpiece (F), and the completion rate of the urgent workpiece (%Q). This paper uses the Relative Deviation Index (RDI) (Paz et al. 2019) to evaluate the difference between the optimal and worst control results in 9 different environments. Where the smaller the RDI value, the better the control pattern. ...
The production control for the mass individualisation paradigm of R&D-stage products is challenging due to the mix-flow and frequently-disturbed environment. With the convergence of the sustainable development goals and the increasing individualised demands in products, resilient manufacturing is envisioned in Industry 5.0 proposition. Concerning that conventional centralised production control methods suffer from low stability and inefficiency of decisions under frequent disruptions, this paper establishes a blockchained smart contract pyramid-driven multi-agent autonomous process control (BSCP-MAAPC) approach for improving the timeliness and adaptability of control towards resilient individualised manufacturing. Firstly, a blockchain-based multi-agent system architecture is designed based on agent encapsulation of manufacturing units. Blockchained smart contracts are used as the enabler of the multi-agent system for peer-to-peer negotiation and coordination of tasks. Secondly, a quad-play blockchained smart contract pyramid together with a series of decentralised control patterns are designed to enable the initial task dispatching of various individualised demands, as well as rapid dynamic adjustment of schedule in response to internal random disruptions. Finally, a blockchained smart contract pyramid-driven multi-agent autonomous process control system prototype is built in the ManuChain system, and experiments are conducted to analyze the proposed BSCP-MAAPC approach in different environments.
HIGHLIGHTS
• A blockchained smart contract pyramid-driven multi-agent autonomous process control (BSCP-MAAPC) approach.
• A quad-play blockchained smart contract pyramid together with a series of decentralized control patterns.
• Blockchained smart contracts as the enabler of the multi-agent system for peer-to-peer negotiation and coordination of tasks.
... Gokhale and Mathirajan addressed parallel machines with sequence-dependent setup times, unequal release times, and machine eligibility restrictions to minimize total weighted flow time [19]. Perez-Gonzalez et al. modeled unrelated parallel machines with machine eligibility and sequence-dependent setup times to minimize the total tardiness [20]. They selected and adapted some existing heuristics and a metaheuristic from related problems, as well as proposed a set of heuristics with novel repair and improvement phases as solution approaches. ...
Inspired by a real industrial case, this study deals with the problem of scheduling jobs on uniform parallel machines with past-sequence-dependent setup times to minimize the total earliness and tardiness costs. The paper contributes to the existing literature of uniform parallel machines problems by the novel idea of considering position-based learning effects along with processing set restrictions. The presented problem is formulated as a Mixed Integer linear programming (MILP) model. Then, an exact method is introduced to calculate the accurate objective function in the just-in-time (JIT) environments for a given sequence of jobs. Furthermore, three meta-heuristic approaches, (1) a genetic algorithm (GA), (2) a simulated annealing algorithm (SA), and (3) a particle swarm optimization algorithm (PSO) are proposed to solve large size problems in reasonable computational time. Finally, computational results of the proposed meta-heuristic algorithms are evaluated through extensive experiments and tested using ANOVA followed by t-tests to identify the most effective meta-heuristic.
... Skutella and Woeginger (2000) proved tardiness minimization with sequence-dependent setups (i.e., P |ST sd | T j and Q|ST sd | T j ) is N P-hard, which is special case of our problem with deterministic processing times. Several approaches were developed to address variants of parallel machine scheduling problems with different objectives and considerations without setup times in (Şen and Bülbül, 2015;Wang and Ye, 2019;Kovalyov et al., 2019;Naderi and Roshanaei, 2019) and with setup times using heuristics in (Behnamian et al., 2009;Dastidar and Nagi, 2005;Ekici et al., 2019;Bektur and Saraç, 2019;Perez-Gonzalez et al., 2019). ...
This paper studies a machine scheduling problem that minimizes the worst-case total tardiness for unrelated parallel machines with sequence-dependent setup and uncertain processing times. We propose a robust optimization reformulation of the related machine scheduling problem and discuss several important properties of the mathematical model and the reformulation approach. The proposed model generalizes robust parallel machine scheduling problems by including sequence-dependent setup times and ellipsoidal uncertainty sets. Another key contribution of the paper is to show that scheduling problems usually have alternative optimal solutions for the worst-case tardiness objective, whose performance under nominal processing times may vary or vice a versa. This issue has been addressed by studying the Pareto efficient extensions of the proposed robust optimization models to provide solutions that are immune to changes in processing times. A branch-and-price algorithm has been developed to solve realistically sized instances in less than one hour, which a commercial solver cannot achieve. Numerical results show the effectiveness of the proposed approach since realistically sized instances such as (4 machines, 32 jobs) and (150 machines, 300 jobs) can be solved to optimality within the time limit, and the (average) objective function value improvement made by the robust approach can get as high as 56% compared with the (nominal) optimal solutions that ignore uncertainty in problem data.
... Since the problem was an NP-hard problem, a hybrid Artificial Bee Colony and Tabu Search (ABC-TS) was practiced for medium-and large-sized problems. Perez-Gonzalez (2019) [18] studied a real-world example unrelated PMS problem. The problem statement was adapted from a customized heating, ventilation, and air conditioning (HAVC) factory, metal folding section. ...
In this paper, we studied a real-world example of an unrelated parallel machine scheduling problem in which the Just-in-Time (JIT) inventory system, including Work-in-Process and Finished Goods inventories, is the center of interest. The presented Simulated Annealing Algorithm tackling the combinatorial problem is a part of the expert and intelligent production system that assists a Decision Maker in perceiving his/her decision’s outcome in advance. Precisely noted, the problem statement is novel since the integration of inventory systems (Work-in-Process and Finished Goods), and renewable and non-renewable resources engaged in manufacturing are taken into account. The undertaken manufacturing system could be attributed to the direct influence of the management strategy of the JIT inventory system not only to reduce the inventory level but also to minimize the earliness and tardiness cost responding to due dates. Moreover, the conventional parameters are reflected in the problem description and solution methodology. In conclusion, the results are remarkable in two terms, the first is to obtain better production planning in considerably less time, and secondly, a cost-benefit analysis tool to contrast the JIT approach with the earliest possible completion time criterion. Finally, possible research directions are suggested for future studies.
... First, the PBPMS includes classical time related scheduling objectives such as minimisation of the makespan, tardiness and total completion time (see, e.g. Thomasson et al. 2018;Perez-Gonzalez et al. 2019;Zhang, Yao, and Li 2020). On the other hand, different than the PBPMS literature, the objective of the ASBSP is to maximise the total profit. ...
This paper introduces the airport shuttle bus scheduling problem (ASBSP) as a new practical scheduling variant. In this problem, a number of identical vehicles that have a specific number of available seats provides transfer service between the airport and the city centre. After making a transfer in one direction, the vehicle can either make a new transfer in the opposite direction depending on the availability and the schedule of the passengers or make an empty return to make a new transfer in the same direction. The vehicles can wait in either location until their next transfer. The passengers have certain time windows for the transfer in relation to their flight times and operational rules to satisfy customer satisfaction. This is a profit-seeking service where transfer requests can also be rejected. The ASBSP aims to prepare a daily schedule for the available vehicles and to assign passengers to these vehicles with the objective of maximising the total profit. This paper presents two alternative mixed integer programming formulations and proposes two valid inequalities to get better bounds. Furthermore, it develops a hybrid metaheuristic that integrates multi-start, simulated annealing and large neighbourhood search for its solution. Extensive computational experiments on real-life benchmark instances have been made to test the performances of the formulations and the hybrid metaheuristic. Furthermore, the impacts of several problem parameters including the number of vehicles, vehicle capacity, transfer fee, transportation time and allowable passenger waiting times on the problem complexity and results have been investigated.
... Moreover, Kayvanfar et al. [17,18] developed a Mixed Integer Programming (MIP) mathematical model to solve a multi-criteria scheduling problem with the goals of minimizing the maximum completion time, the earliness and the tardiness penalties simultaneously. In addition, a new constructive heuristic algorithm is embedded in the metaheuristic to solve the unrelated parallel machines with machine eligibility and sequence-dependent setup times by P. Perez-Gonzalez et al. [19]. Meanwhile, G. Bektur, T. Saraç [20], addressed the unrelated parallel machine scheduling problem with sequence-dependent setup times and machine eligibility restrictions. ...
The first objective of this study is to update a capacity constraint to the mixed integer programming model of the unrelated parallel machines scheduling problem. Then, a new proposed algorithm is developed based on the combination between the genetic algorithm with the so-called ISETP heuristics (Initial Sequence based on Earliness-Tardiness criterion on Parallel machine). The new Genetic Algorithm with Initial Sequence based on Earliness-Tardiness criterion on Parallel machine (GAISETP) generates job sequences and allocates them to the machines subject to capacity constraint. A case of automobile component manufacturing company is investigated to test the performance of the proposed method for both small-sized and large-sized problems. The obtained results are very promising both in terms of makespan and earliness-tardiness.
... A variety of approximate methods for unrelated PMSP has been proposed during the past decades, such as heuristics, meta-heuristics, matheuristics, decomposition, etc. Heuristics are problem-dependent techniques, which are often too greedy and get trapped in a local optimum. Heuristics have been widely applied to unrelated PMSP to minimize makespan Villa, Vallada, and Fanjul-Peyro (2018) and minimize total tardiness Perez-Gonzalez, Fernandez-Viagas, García, and Framinan (2019). Meta-heuristics are problem-independent techniques, which allowed to explore the solution space more thoroughly and thus to hopefully get a better solution. ...
... In the scheduling literature, more focus has been given recently to flexible shop scheduling problems in which a given operation can be processed on more than one machine. Examples include the two-stage flow shop scheduling problem with unrelated parallel machines (Figielska, 2018), the flexible job shop scheduling problem (Caldeira and Gnanavelbabu, 2019), the multiprocessor job shop scheduling problem (Fan, Wang, Zhai and Li, 2019) and the unrelated parallel machine scheduling problem (Perez-Gonzalez, Fernandez-Viagas, Garca and Framinan, 2019). The studied problem can be denoted as O(R)||C max according to the three field notation of Graham, Lawler, Lenstra and Rinnooy Kan (1979) with the extension of Vignier, Billaut and Proust (1999). ...
Maintenance and health care diagnostic systems are generally composed of different workstations pertaining to technologically different processes. A workstation is composed of one or more parallel machines. In such systems, the multiprocessor open shop scheduling problem is commonly encountered. It is concerned with assigning processing intervals for each job on machines that need to be selected in each requested workstation. Meanwhile, jobs do not require a specific order for visiting workstations. This paper considers a static, deterministic version of the problem in which jobs do not have to visit all workstations, the workstations do not necessarily have identical machines, and the processing times depend on both the job and the machine. The objective is to minimize the maximum completion time (makespan) which is commensurate with maximizing the utilization of the available machines. To the best of our knowledge, this problem structure has not been considered in the literature before despite its existence in real-life applications. Since it is NP-hard problem, efficient heuristics are needed to generate near optimal solutions in practically acceptable computational times. In this paper, two neighborhood search functions and two solution combination functions are developed and used within a scatter search with path relinking metaheuristic, along with a new distance definition between solutions. Computational experiments are conducted first to select the best levels of the metaheuristic parameters. Then, computational experiments are conducted on specially designed instances that take into consideration different settings of the studied problem. This is followed by computational experiments on a set of benchmark instances of the proportionate multiprocessor open shop scheduling problem which is a special case of the studied problem for which other metaheuristics have been developed in the literature. Results show that the developed metaheuristic is capable of generating optimal or near-optimal solutions for different configurations of the studied problem. In addition, it generates competitive results for the proportionate case compared to the available metaheuristics with 18 new upper bounds; among them seven are optimal.
... Skutella and Woeginger (2000) proved tardiness minimization with sequence-dependent setups (i.e., P |ST sd | T j and Q|ST sd | T j ) is N P-hard, which is special case of our problem with deterministic processing times. Several approaches were developed to address variants of parallel machine scheduling problems with different objectives and considerations without setup times in (Şen and Bülbül, 2015;Wang and Ye, 2019;Kovalyov et al., 2019;Naderi and Roshanaei, 2019) and with setup times using heuristics in (Behnamian et al., 2009;Dastidar and Nagi, 2005;Ekici et al., 2019;Bektur and Saraç, 2019;Perez-Gonzalez et al., 2019). ...
We focus on rapid needs assessment operations conducted immediately after a disaster to identify the urgent needs of the affected community groups, and address the problem of selecting the sites to be visited by the assessment teams during a fixed assessment period and constructing assessment routes under travel time uncertainty. Due to significant uncertainties in post-disaster transportation network conditions, only rough information on travel times may be available during rapid needs assessment planning. We represent uncertain travel times simply by specifying a range of values, and implement robust optimization methods to ensure that each constructed route is feasible for all realizations of the uncertain parameters that lie in a predetermined uncertainty set. We present a tractable robust optimization formulation with a coaxial box uncertainty set due to its advantages in handling uncertainty in our selective assessment routing problem, in which the dimension of the uncertainty (number of arcs traversed) is implicitly determined. To solve the proposed model efficiently, we develop a practical method for evaluating route feasibility with respect to the robust route duration constraints, and embed this feasibility check procedure in a tabu search heuristic. We present computational results to evaluate the effectiveness of our solution method, and illustrate our approach on a case study based on a real-world post-disaster network.
İlişkisiz paralel makine çizelgeleme, hem sanayide hem de literatürde sıklıkla yer alan bir problemdir. Bu problemi ele alan çalışmalarda yaygın olarak kullanılan amaç fonksiyonlarından birisi toplam gecikmenin enküçüklenmesidir. İşlerin gecikmesinin önlenmesi, müşterilere ödenmesi gereken cezalar ve prestij kaybı gibi olumsuzlukların önlenmesi anlamına geldiğinden oldukça önemlidir. Teslim zamanları, gecikme sürelerini belirleyen parametredir. Müşterilerin üretim planlarının değişimine bağlı olarak siparişlerin teslim zamanlarının değişebilmesi, özellikle yan sanayi konumundaki firmaların karşılaşabildiği bir durum olduğundan, daha gerçekçi çizelgeler oluşturulması için teslim zamanlarının stokastik ele alınması gerekmektedir. Bu çalışmada ele alınan ilişkisiz paralel makine çizelgeleme probleminde (UPM) teslim zamanları stokastiktir. Bu çalışma kapsamında, iki aşamalı stokastik programlama modeli ve bir genetik algoritma (GA) geliştirilmiştir. Rassal türetilen test problemleri kullanılarak yapılan testler sonucunda geliştirilen GA ile önerilen modellerden daha başarılı çözümlere daha kısa sürede ulaşıldığı görülmüştür. Elde edilen sonuçlar, özellikle değişkenliği ve boyutu büyük olan problemleri stokastik ele almanın gerekliliğini ortaya koymuştur.
We deal with a challenging scheduling problem on parallel machines with sequence-dependent setup times and release dates from a real-world application of semiconductor work-shop production. There, jobs can only be processed by dedicated machines, thus few machines can determine the makespan almost regardless of how jobs are scheduled on the remaining ones. This causes problems when machines fail and jobs need to be rescheduled. Instead of optimising only the makespan, we put the individual machine spans in non-ascending order and lexicographically minimise the resulting tuples. This achieves that all machines complete as early as possible and increases the robustness of the schedule. We study the application of answer-set programming (ASP) to solve this problem. While ASP eases modelling, the combination of timing constraints and the considered objective function challenges current solving technology. The former issue is addressed by using an extension of ASP by difference logic. For the latter, we devise different algorithms that use multi-shot solving. To tackle industrial-sized instances, we study different approximations and heuristics. Our experimental results show that ASP is indeed a promising knowledge representation and reasoning (KRR) paradigm for this problem and is competitive with state-of-the-art constraint programming (CP) and Mixed-Integer Programming (MIP) solvers.
Özdeş olmayan paralel makine çizelgeleme problemi son zamanlarda işletmelerin ilgisini çeken konulardan birisi olmuştur. İşletmeye gelene bir işin son derece etkin ve hızlı şekilde yapılabilmesi çizelgelemeye bağlıdır. Makinelerin işlem süreleri, ürün geçişlerinde yapılan hazırlık süreler gibi fazladan harcanan her süre üretim hızı ve kapasitesini etkilemektedir. Yapılan bu çalışmada sıra bağımlı hazırlık süreli özdeş olmayan paralel makine çizelgeleme problemi ele alınmıştır. Çalışma oluklu mukavva üretimi gerçekleştiren işletmede uygulamalı olarak gerçekleştirilmiştir. Çalışmanın amacı toplam tamamlanma zamanı (Cmax) minimizasyonudur. Firmada aynı operasyonlarda kullanılan fakat sahip oldukları özelliklere göre özdeş olmayan iki adet paralel makine bulunmaktadır. Makine farklılıkları ise hız, kapasite, ürün geçişlerindeki hazırlık süreleri ve teknik özellikleridir. İşletmeden 112 adet sipariş- ürün bilgisi ve makinelerde yapılan hazırlık sürelerinin bilgisi alınmıştır. Alınan bilgiler doğrultusunda gelen siparişlerin işlem süreleri ve ürün geçişleri esnasında yapılan hazırlıkların hazırlık süreleri matrisi hesaplanmıştır. Bu hesaplanan veriler oluşturulan matematiksel modele aktarılarak, ILOG Cplex Optimization programı ile çözülmüştür. Çözüm sonucunda işletme için uygun iki haftalık üretim çizelgesi elde edilmiştir.
This paper addresses an unrelated parallel machine scheduling problem with job-machine-dependent delivery times and eligibility constraints motivated by a distributed manufacturing environment. The objective is total weighted tardiness minimization. We present a mixed integer linear programming (MILP) formulation and conduct an analysis of the scheduling problem to derive precedence properties that can be integrated in local search procedures to increase computational efficiency. We implement a variable neighborhood search (VNS) algorithm for the problem at hand and examine the effect of integrating the properties on the performance. The tests show that the theoretical findings can reduce computational effort significantly. Furthermore, we propose another heuristic approach based on the Apparent Tardiness Cost rule and a memetic biased random-key genetic algorithm. In experiments, we compare the MILP and (meta-)heuristics on a large set of randomly generated problem instances. The VNS procedure outperforms the other algorithms.
Under the background of the emerging of shared manufacturing economics, this work addresses a new production order scheduling problem on unrelated parallel machines. Customer orders with release times are of various types depending on their specific product demands. Unrelated machines may be rented for processing orders via one cloud manufacturing service platform. It occurs a uniform processing cost once any machine is rented (via contract) for a given length time duration to process the orders. Each machine is generally able to process some but not all types of orders, i.e., machine eligibility is considered. Orders can be split into sub-orders and processed on their eligible machines simultaneously. For the objective of minimizing the weighted sum of total completion time of orders and total processing cost of machines being used, we establish a mixed integer linear programming model. We provide a lower bound of the considered problem by constraint relaxation, and present the pseudocode of an approach to obtain the lower bound. CPLEX is employed to generate optimal solutions for small-scale instances. For large-scale instances, two heuristic algorithms named Type-Based Greedy and Improved Differential Evolution are developed. The former algorithm selects a smallest set of machines to process the jobs and makes use of job splitting as much as possible, while the latter one is to acquire a best local optimal solution via finite times random global search in the feasible region. Computational experiments are carried out to demonstrate the efficiency and effectiveness of the proposed heuristics.
This chapter describes a single-objective, multi-facility, location model for a logistics network, whose aim is to support the economical aspect. In this work, a new variant of the facility location model is presented to ask the optimum positions of the new facilities with the target that the aggregate logistics cost from the endure facilities to the new facilities along with the fixed-charge cost will be reduced. A new approximation approach is incorporated for solving the proposed model for extracting results. An experimental design is consolidated to demonstrate the proficiency and viability of the proposed consideration in connection with reality. The novel contributions of this study have introduced a way to connect the facility location problem and fixed-charge transportation problem using a new approximation approach with minimizing the conveyance cost. The chapter ends with conclusions and perspectives on future studies.
In the last few years, a lot of researchers addresses scheduling problems considering unrelated parallel machines to bridge theoretical problems and real-world manufacture environments. Most of these works consider objective function’s characteristics to assist the algorithms in exploiting the search space. This assistance usually leads to a better convergence of the algorithms, but it tends to leave these algorithms restricted only to the own optimization criterion studied. This feature hinders to extend these works to optimization criteria with less theoretical visibility. This work proposes an immuno-inspired algorithm for the resolution of scheduling problems under unrelated parallel environments, evaluating the hypothesis that it is possible to construct a robust approach that is extensible to different optimization criteria, achieving results similar to the state-of-art approaches in the literature for specific criteria. Four case studies are proposed, each one addressing an optimization criterion, which is a benchmark for sequencing problems. The criteria are Total Weighted Tardiness, Makespan, Total Tardiness, and Total Weighted Completion Time. The experiments indicate that the results achieved by the proposed approach are compatible and, in many cases, superior to the state-of-art approaches for the optimization criteria studied, using computational resources compatible with those presented by these approaches.
We present and solve a joint production and qualification planning problem for a manufacturing environment with high process flexibility. Various factors contribute to the complexity of the problem, one of which is product‐machine mapping: Each machine may be qualified to produce multiple products and each product can be produced on multiple machines. To meet a build‐plan, the factory needs to not only determine a multi‐machine‐multi‐product production schedule that accounts for sequence‐dependent setup time, but also a qualification schedule which prescribes whether and when a machine should undergo a qualification process such that it is ready to produce a product. We consider processing characteristics including sequence‐dependent setups, job splitting, and machine eligibility in addition to qualification. We formulate the mathematical model as an MILP problem that minimizes the total weighted delay. In this paper, we describe two heuristic solution approaches developed for this complex decision setting and the application at Intel. We compare our approach with Intel’s current approach which is a spread‐sheet based manual approach that relies on the experience of the factory planner. The results indicate that our approach, which we call the GS approach, dominates in terms of minimizing the delay. Our approach performs well when capacity is tight and additional qualifications are considered while the Intel approach may perform better on reducing the setup and qualification time in certain problem instances, particularly those with loose capacity. As a result, an integrated approach which selects the better solution from both approaches is proposed, which shows significant reduction over the current approach in both the weighted delay and the setup and qualification time.
In this paper, a scheduling problem on non-identical parallel machines with auxiliary resources and sequence-dependent and machine-dependent setup times is studied. This problem can be found in various manufacturing contexts, and in particular in workshops of wafer manufacturing facilities. Three different criteria are defined and analyzed: The number of products completed before the end of a given time horizon, the weighted sum of completion times and the number of auxiliary resource moves. The first criterion is maximized, while the two others are minimized. The first and the third criteria are not classical in scheduling theory, but are justified in industrial settings. The complexity of the problem with each of the new criteria is characterized. Integer linear programming models are also proposed and numerical experiments are conducted to analyze their behavior.
The existing papers on unrelated parallel machine scheduling problem with sequence and machine-dependent setup times (UPMSP-SMDST) ignore the worker resources and learning effect. Given the influence and potential of human factors and learning effect in real production systems to improve production efficiency and decrease production cost, we propose a UPMSP-SMDST with limited worker resources and learning effect (NUPMSP). In the NUPMSP, the workers have learning ability and are categorized to different skill levels, i.e., a worker’s skill level for a machine is changing with his accumulating operation times on the same machine. A combinatorial evolutionary algorithm (CEA) which integrates a list scheduling (LS) heuristic, the shortest setup time first (SST) rule and an earliest completion time first (ECT) rule is presented to solve the NUPMSP. In the experimental phase, 72 benchmark instances of NUPMSP are constructed to test the performance of the CEA and facilitate future study. The Taguchi method is used to obtain the best combination of key parameters of the CEA. The effectiveness of the LS, SST and ECT is verified based on 15 benchmark instances. Extensive experiments conducted to compare the CEA with some well-known algorithms confirm that the proposed CEA is superior to these algorithms in terms of solving accuracy and efficiency.
Industry 4.0 portrays the pattern toward mechanization and information trade in manufacturing innovations and procedures which incorporate cyber-physical systems, the Internet of Things, the Industrial Internet of Things, cloud computing, cognitive processing, and artificial intelligence. For all purposes, we require multioperating units of reliable machining systems, which should function uninterruptedly. In this chapter, we propose the mathematical study of the stochastic model involved in preventive, corrective, and predictive maintenance policies that require for well-functioning of the machining system. We present a machine repair problem of standbys provisioning in a Markovian environment with unreliable service and vacation interruption. Sensitivity and optimal analysis are done for reliability characteristics and the expected total cost incurred, respectively. The substantial recommendation is proposed for the decision-makers for the optimal design of the machining systems.
This study investigates an energy-efficiency scheduling problem of multi-cell manufacturing system with eligibility constraints, in which each manufacturing cell is configured as a flexible flow shop. The purpose of the energy-efficiency scheduling is to optimize energy consumption, total handling distance and makespan. Firstly, a new mathematical model is established for the investigated problem. Secondly, in order to effectively reduce energy consumption and balance the load of the machines, a novel decoding scheme is proposed. Thirdly, an improved multi-objective evolution algorithm based on decomposition which uses a local search strategy to improve the neighborhoods solutions of the sub-problem with the least non-dominated solutions is proposed to solve the established model. Finally, a large number of experiments are carried out to verify the effectiveness of the proposed approach. The results demonstrate that the proposed model and approach have feasibility in energy efficiency improvement, and the proposed approach has better performance than the existing methods.
This paper investigates the problem of manufacturing processes by bar-turning machine. The scenario is modeled as a problem of scheduling jobs to non-related parallel machines with sequence dependent setup times applying batch splitting. In order to optimize this problem, we propose a mixed integer linear programming model (MILP). However, as shown in numerical result, it is limited to solve only small instances. Hence, a two-step approach is presented to solve real-size instances. This method uses a relaxed version of the MILP model proposed, however, allowing solutions with sub-tour. Afterwards, a heuristic algorithm is presented to adjust these solutions. The numerical results analyze 20 instances with different sizes, compositions of demand and set of machines. Some general rules to characterize good solutions were presented after investigating the results. These rules associate the quantity of pieces for each demand and the type of machine used, and the complexity of the piece demanded for the type of machine.
This paper focuses on two components of idle time and waiting time, namely core idle time, ∑CITi, and core waiting time, ∑CWTj. Both measures are relevant indicators of the efficiency of production systems, since they are directly related to machine utilization and to the flow of jobs, and they can be used as scheduling criteria if no-idle and no-wait constraints do not have to be strictly enforced. However, they have been scarcely considered in the literature, and their relationship with other objectives in the permutation flowshop literature (makespan or Cmax and total completion time or ∑Cj), has not been studied. To bridge this gap, the alignment between ∑CITi and ∑CWTj, and the classical scheduling criteria is studied. First, it is shown that ∑CWTj (∑CITi) is tantamount to ∑Cj (Cmax) for some special cases. Secondly, the general case with randomly generated processing times is computationally analysed using exact methods. Results show alignment between ∑CWTj and ∑Cj and between ∑CITi and Cmax, being the alignment stronger for the first pair of objectives. Based on the analysis, conclusions about the possibilities for the permutation flowshop problem with these new objectives are established.
The chapter focuses on treating a particular problem of intelligent threats. We consider a least cost attack in a network-interdiction framework with a single source and a single destination. We suppose that a network is disabled if all links of a full cut set fail. That is, no flow can reach its destination node. We propose an exact solution under a budget constraint accounting for a threshold of success probability of the attack on targeted cut sets. We investigate the efficiency of the suggested solution through some illustrations. We extend the results to the case of networks with multiple sources/destinations.
Predicting and understanding the machining system performance is a constant challenge
in the process industries like manufacturing and production systems, computer and communication systems, just-in-time (JIT) service systems. The reliability modeling supports the decision-making process from early to the optimal state-of-the-art design of the machining system. Reliability measures account the performance of different preventive, predictive, corrective, zero-hours and periodic maintenance strategies. For all strategies, the most anterior arrangement is the availability of the service facility as and when required to maintain the high grade or efficient quality of service (QoS). The permanent service facility may increase cost, idleness, deterioration in quality. To reduce the wastage of valuable resources like time, money, quality, etc., vacation is a prominent idea for the service facility. The vacation time is a period of time of not doing the usual service or activities. In this time, the server may take rest to rejuvenate, to reduce idle time at the station, to diminish the expected cost incurred in service. The long vacation time also wastes the valuable resources substantially due to the long waiting queue of failed machines. The vacation time period is a critical issue and needs to analyze judgementally. In this chapter, a comparative study of different vacation policies on the reliability characteristics of the machining system is presented. For that purpose, the queueing-theoretic approach is employed and the Markovian models are developed for various types of vacation policy namely N-policy, single vacation, multiple vacations, Bernoulli vacation, working vacation, vacation interruption, etc. For all vacation policies, the reliability and mean-time-to-failure (MT T F) of the system are compared and
results are depicted in the graphs for quick insights. From this study, readers get a glance
to understand about vacation, researchers get a concrete platform to choose appropriate assumptions for their research in machining/service system, or system analyst may opt suitable vacation policy as per limitation of the system.
In this paper we consider a problem of scheduling n single-operation jobs on m uniform parallel machines. It is assumed that each machine has a resource consumption per unit time when processing the job. Our goal is to find a schedule that minimizes the makespan, subject to the constraint that the total resource consumption cannot exceed a given number. For solving this problem, a fuzzy simplified swarm optimization (SSO) algorithm, accompanied by a specific legalizing method, which is presented to legalize the infeasible solution, is employed. In order to verify the effectiveness and efficiency of this algorithm, we compare its performance with those of a genetic algorithm (GA) and a particle swarm optimization with genetic local search (PSOLS) both adapted from the literature. Considering the parameter values of algorithms have a great influence on the quality of the output solution, we first use Taguchi method to determine suitable levels for the design factors. Afterwards, three different job-scale simulated experiments (i.e., small, medium and large experiments) are separately conducted. Finally, to further analyze the level of difference between SSO and the other two algorithms, the Wilcoxon signed-rank test is carried out. Experimental results indicate that SSO performs better than GA and PSOLS.
In this paper, we study a production scheduling and vehicle routing problem with job splitting and delivery time windows in a company working in the metal packaging industry. In this problem, a set of jobs has to be processed on unrelated parallel machines with job splitting and sequence-dependent setup time (cost). Then the finished products are delivered in batches to several customers with heterogeneous vehicles, subject to delivery time windows. The objective of production is to minimize the total setup cost and the objective of distribution is to minimize the transportation cost. We propose mathematical models for decentralized scheduling problems, where a production schedule and a distribution plan are built consecutively. We develop a two-phase iterative heuristic to solve the integrated scheduling problem. We evaluate the benefits of coordination through numerical experiments.
Computer-based manufacturing scheduling tools can play a key role in the management of industrial operations, as obtaining economic and reliable schedules is at the core of excellence in customer service and of efficiency in manufacturing companies. As a consequence, this topic has been receiving an increasing interest in the last decades, resulting in a number of case studies and descriptions of implementation of these tools. However, to the best of our knowledge, there is no review of these cases in order to classify existing references and to identify relevant issues still not properly addressed. Therefore, in this paper we carry out a systematic review of case studies of manufacturing scheduling tools. In order to provide a coherent taxonomy for the analysis of these tools, we develop a classification based on the functionalities of the manufacturing scheduling tools. Using this framework, existing contributions are classified and discussed, and a number of conclusions and open issues are identified. We hope that our work can establish a coherent picture of the topic so it serves as a starting point for future research.
Since Johnson׳s seminal paper in 1954, scheduling jobs in a permutation flowshop has been receiving the attention of hundreds of practitioners and researchers, being one of the most studied topics in the Operations Research literature. Among the different objectives that can be considered, minimising the total tardiness (i.e. the sum of the surplus of the completion time of each job over its due date) is regarded as a key objective for manufacturing companies, as it entails the fulfilment of the due dates committed to customers. Since this problem is known to be NP-hard, most research has focused on proposing approximate procedures to solve it in reasonable computation times. Particularly, several constructive heuristics have been proposed, with NEHedd being the most efficient one, serving also to provide an initial solution for more elaborate approximate procedures. In this paper, we first analyse in detail the decision problem depending on the generation of the due dates of the jobs, and discuss the similarities with different related decision problems. In addition, for the most characteristic tardiness scenario, the analysis shows that a huge number of ties appear during the construction of the solutions done by the NEHedd heuristic, and that wisely breaking the ties greatly influences the quality of the final solution. Since no tie-breaking mechanism has been designed for this heuristic up to now, we propose several mechanisms that are exhaustively tested. The results show that some of them outperform the original NEHedd by about 25% while keeping the same computational requirements.
This study considers the problem of scheduling independent jobs on unrelated parallel machines with machine- and sequence-dependent setup times for the objective of minimizing the total tardiness, i.e., R
m
│S
ijk
│∑T
j
. Since the parallel machines are unrelated, sequence-dependent setup times must depend on machines. To the best of the authors’ knowledge, the simulated annealing and the iterated greedy algorithms are two existing ones for the new class of scheduling problem with an additional constraint of strict due date constraints for some jobs, i.e., deadlines. In this study, we suggest a tabu search algorithm that incorporates various neighborhood generation methods. A computational experiment was done on the instances generated by the method used in the two previous research articles, and the results show that the tabu search algorithm outperforms the simulated annealing algorithm significantly. In particular, it gave optimal solutions for more than 50 % of small-sized test instances. Also, an additional test was done to compare the performances of the tabu search and the existing iterated greedy algorithms, and the result shows that the tabu search algorithm gives quicker solutions than the iterated greedy algorithm although it gives less quality solutions.
In this paper, we address a scheduling problem for minimizing total weighted flowtime, observed in automobile gear manufacturing. Specifically, the bottleneck operation of the pre-heat treatment stage of gear manufacturing process has been dealt with in scheduling. Many real-life scenarios like unequal release times, sequence dependent setup times, and machine eligibility restrictions have been considered. A mathematical model taking into account dynamic starting conditions has been proposed. The problem is derived to be NP-hard. To approach the problem, a few heuristic algorithms have been proposed. Based on planned computational experiments, the performance of the proposed heuristic algorithms is evaluated: (a) in comparison with optimal solution for small-size problem instances and (b) in comparison with the estimated optimal solution for large-size problem instances. Extensive computational analyses reveal that the proposed heuristic algorithms are capable of consistently yielding near-statistically estimated optimal solutions in a reasonable computational time.
We study a problem of optimal scheduling and lot-sizing a number of products on m un-related parallel machines to satisfy given demands. A sequence dependent setup time is required between lots of different products. The products are assumed to be all continuously divisible or all discrete. The criterion is to minimize the time, at which all the demands are satisfied, C max , or the maximum lateness of the product completion times from the given due dates, L max . The problem is motivated by the real-life scheduling applications in multi-product plants. We derive properties of optimal solutions, NP-hardness proofs, enumeration and dynamic programming algorithms for various special cases of the problem. The major contribution is an NP-hardness proof and pseudo-polynomial algorithms linear in m for the case, in which the number of products is a given constant. The results can be adapted for solving a production line design problem.
In this work a genetic algorithm is presented for the unrelated parallel machine scheduling problem in which machine and job sequence dependent setup times are considered. The proposed genetic algorithm includes a fast local search and a local search enhanced crossover operator. Two versions of the algorithm are obtained after extensive calibrations using the Design of Experiments (DOE) approach. We review, evaluate and compare the proposed algorithm against the best methods known from the literature. We also develop a benchmark of small and large instances to carry out the computational experiments. After an exhaustive computational and statistical analysis we can conclude that the proposed method shows an excellent performance overcoming the rest of the evaluated methods in a comprehensive benchmark set of instances.
In the present work, a case study focusing on online and dynamic scheduling of parallel heat treatment furnaces at a real manufacturing company is presented. The problem under consideration in this study involves release times, eligibility constraints, due dates, sequence-dependent setup times due to heating up or cooling down the furnaces, breakdowns and maintenance periods. Moreover, dynamic events, for instance, arrivals of rush orders, cancellations of already handled jobs, changes in due dates or in lot sizes exist in the nature of the problem considered here. Such dynamic factors make the introduced problem more challenging. One more difficulty is the vast variety of products at the firm. Generating a large-scaled setup matrix is neither practical nor reliable. Therefore, based on the distinctive attributes of the products, an implicit clustering is employed. As a solution approach, a multi-start and constructive search algorithm is proposed for this problem. Finally, as a dynamic scheduling module for the heat treatment furnaces, the proposed algorithm is embedded into the enterprise resource planning system of the company that is built on JAVA. The current system contributes to the firm by online scheduling of the heat treatment furnaces, generating online Gantt Charts for managers, online transmission of work orders and digitalized performance analysis reports. Thus, as demonstrated by numeric data presented in the present paper, a decrease in energy consumption and an increase in annual income are expected.
The problem investigated in this study involves an unrelated parallel machine scheduling problem with sequence-dependent setup times, different release dates, machine eligibility and precedence constraints. This problem has been inspired from a realistic scheduling problem in the shipyard. The optimization criteria are to simultaneously minimize mean weighted flow time and mean weighted tardiness. To formulate this complicated problem, a new mixed-integer programming model is presented. Considering the NP-complete characteristic of this problem, two famous meta-heuristics including a non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective ant colony optimization (MOACO) which is a modified and adaptive version of BicriterionAnt algorithm are developed. Obviously, the precedence constraints increase the complexity of the scheduling problem in strong sense in order to generate feasible solutions, especially in parallel machine environment. Therefore a new corrective algorithm is proposed to obtain the feasibility in all stages of the algorithms. Due to the fact that appropriate design of parameter has a significant effect on the performance of algorithms, we calibrate the parameters of these algorithms by using new approach of Taguchi method. The performances of the proposed meta-heuristics are evaluated by a number of numerical examples. The results indicated that the suggested MOACO statistically outperformed the proposed NSGA-II in solving the test problems. In addition, the application of the proposed algorithms is justified by a real block erection scheduling problem in the shipyard.
This study addresses an unrelated parallel machine scheduling problem with resource constrains, sequence-dependent setup times, different release dates, machine eligibility and precedence constraints. This problem has been inspired from the block erection scheduling problem in a shipyard. Majority of the traditional scheduling problems in parallel machine environment deal with machine as the only resource. However, other resources such as labors, tools, jigs, fixtures, pallets, dies and industrial robots are not only required for processing jobs but also are often restricted. To formulate this complicated problem, a new pure integer mathematical modeling is proposed and makespan is employed as the objective function. Since the problem is strongly NP-hard, exact approaches are intractable for large size problems. Thus, two new meta-heuristic algorithms including genetic algorithm (GA) and artificial immune system (AIS) are developed to find optimal or near optimal solutions. In addition, the parameters of these algorithms are calibrated by using Taguchi method. The performances of the proposed meta-heuristics are evaluated by a number of numerical examples. The computational results demonstrated that in small scale problems both algorithms are effective and efficient, but in large scale problems the suggested AIS statistically outperformed the proposed GA.
In this paper we present a new heuristic algorithm to minimize the makespan for scheduling jobs on unrelated parallel machines with machine eligibility restrictions (R m / M j / C max). To the best of our knowledge, the problem has not been addressed previously in the literature. The multi-phase heuristic algorithm incorporates new concepts from the multi-depot vehicle routing in the constructive heuristic. A computational study includes problems with two or four machines, up to 105 jobs, and three levels of a machine selection parameter. The heuristic algorithm solution values are compared to optimal solution values. The results show that the heuristic algorithm can yield solutions within a few percent of the optimal solutions with performance improving as the number of jobs to be scheduled increases.
This paper addresses the problem of scheduling jobs on unrelated parallel machines with eligibility constraints, where job-processing times are controllable through the allocation of a nonrenewable common resource, and can be modeled by a linear resource consumption function. The objective is to assign the jobs to machines and to allocate resources, so that the makespan is minimized. We provide an exact formulation of the addressed problem as a mixed integer programming model. In view of the computational complexity associated with the formulation makes it difficult for standard solvers to deal with large-sized problems in reasonable solution time, two ant-colony optimization algorithms based on distinct procedures, respectively, are also presented and analyzed. Numerical results show that both the proposed algorithms are capable of solving industrial-dimensioned problems within reasonable computation time and accuracy.
The book is devoted to the problem of manufacturing scheduling, which is the efficient allocation of jobs (orders) over machines (resources) in a manufacturing facility. It offers a comprehensive and integrated perspective on the different aspects required to design and implement systems to efficiently and effectively support manufacturing scheduling decisions. Obtaining economic and reliable schedules constitutes the core of excellence in customer service and efficiency in manufacturing operations. Therefore, scheduling forms an area of vital importance for competition in manufacturing companies. However, only a fraction of scheduling research has been translated into practice, due to several reasons. First, the inherent complexity of scheduling has led to an excessively fragmented field in which different sub problems and issues are treated in an independent manner as goals themselves, therefore lacking a unifying view of the scheduling problem. Furthermore, mathematical brilliance and elegance has sometimes taken preference over practical, general purpose, hands-on approaches when dealing with these problems. Moreover, the paucity of research on implementation issues in scheduling has restricted translation of valuable research insights into industry. "Manufacturing Scheduling Systems: An Integrated View on Models, Methods and Tools" presents the different elements constituting a scheduling system, along with an analysis the manufacturing context in which the scheduling system is to be developed. Examples and case studies from real implementations of scheduling systems are presented in order to drive the presentation of the theoretical insights. The book is intended for an ample readership including industrial engineering/operations post-graduate students and researchers, business managers, and readers seeking an introduction to the field.
This study addresses a resource-constrained unrelated parallel machine scheduling problem with machine eligibility restrictions. Majority of the traditional scheduling problems in parallel machine environment deal with machine as the only resource. However, other resources such as labors, tools, jigs, fixtures, pallets, dies, and industrial robots are not only required for processing jobs but also are often restricted. Considering other resources makes the scheduling problems more realistic and practical to implement in manufacturing environments. First, an integer mathematical programming model with the objective of minimizing makespan is developed for this problem. Noteworthy, due to NP-hardness of the considered problem, application of meta-heuristic is avoidable. Furthermore, two new genetic algorithms including a pure genetic algorithm and a genetic algorithm along with a heuristic procedure are proposed to tackle this problem. With regard to the fact that appropriate design of the parameters has a significant effect on the performance of algorithms, hence, we calibrate the parameters of these algorithms by using the response surface method. The performance of the proposed algorithms is evaluated by a number of numerical examples. The computational results demonstrated that the proposed genetic algorithm is an effective and appropriate approach for our investigated problem.
We propose a three-phase heuristic for the problem of minimizing the total weighted tardiness on a single machine in the presence of sequence-dependent setup times. In the first phase a number of parameters characterizing the problem instance at hand are calculated. In the second phase we develop a schedule by using a new priority rule whose parameters are calculated based on the results of the first phase. Computational experiments show that this rule significantly outperforms the only other rule so far developed in the literature. The third phase consists of a local improvement procedure to improve the schedule obtained in the second phase. The procedure we suggest has been successfully implemented in an industrial scheduling system.
This study involves an unrelated parallel machine scheduling problem in which sequence-dependent set-up times, different release dates, machine eligibility and precedence constraints are considered to minimize total late works. A new mixed-integer programming model is presented and two efficient hybrid meta-heuristics, genetic algorithm and ant colony optimization, combined with the acceptance strategy of the simulated annealing algorithm (Metropolis acceptance rule), are proposed to solve this problem. Manifestly, the precedence constraints greatly increase the complexity of the scheduling problem to generate feasible solutions, especially in a parallel machine environment. In this research, a new corrective algorithm is proposed to obtain the feasibility in all stages of the algorithms. The performance of the proposed algorithms is evaluated in numerical examples. The results indicate that the suggested hybrid ant colony optimization statistically outperformed the proposed hybrid genetic algorithm in solving large-size test problems.
This paper proposes an immune-inspired algorithm to the problem of minimising the makespan on unrelated parallel machines, with sequence dependent setup times. The initial population is generated through the construction phase of the Greedy Randomised Adaptive Search Procedure (GRASP). An evaluation function is proposed to help the algorithm escape from local optima. A Variable Neighbourhood Descent (VND) local search heuristic, which makes significant use of the characteristics of the problem, is proposed as a somatic hypermutation operator to accelerate the convergence of the algorithm. A population re-selection operator, which strategically keeps good quality solutions with a high level of dispersion in the search space, is also proposed. The experiments performed show that the proposed algorithm enables better results than those reported in recent literature studies.
This paper dealt with an unrelated parallel machines scheduling problem with machine eligibility restrictions, sequence and machine dependent setup times and possibility of producing imperfect items. Rework processes are considered to improve and regain defective items to an acceptable quality level. In order to formulate this problem, a new optimization model is developed and makespan is employed as the objective function. Since the problem is strongly NP-hard, exact algorithms are inefficient for medium and large-sized problems. Thus, some meta-heuristic algorithms including genetic algorithm (GA) and bees algorithms (BA1 & BA2) are implemented to find optimal/near optimal solutions. To achieve better robustness of algorithms, parameter setting process is performed for all three mentioned algorithms in each one of small, medium and large scales, separately. For small size yet complex problems, the results from these algorithms are compared to the optimal solutions. The result obtained in all of these problems is that the algorithms can find solutions as good as exact algorithms but in drastically shorter computational time.
We present a genetic algorithm for the solution of an industrial scheduling problem in an Alcan aluminium foundry situated in Québec. We seek the best processing sequence for n orders on a m parallel machines. The set-up times are sequence dependent and we must deal with multiple criteria. There are also a number of structural constraints that distinguish this situation from the classical model. The performance of the solution approach is compared with the results of the scheduling process used by the firm according to three criteria: meeting due dates, number and duration of required set-ups and metal flow.
We consider the problem of scheduling sequence-dependent jobs on identical parallel machines. Each job has to be processed without interruption on one of the machines. A machine changeover time must be respected between job processing on each machine. This changeover time is dependent on the job sequence. Our objective is to minimize the maximum completion time of the jobs or the mean completion time of the jobs. This problem is a vehicle routeing problem and is NP hard. We propose an assignment algorithm to solve it. Our heuristic is an extension of the Hungarian method to the multiple use of resources and has been developed during past years to solve routeing problems. This paper models the scheduling problem, presents the solution tool and shows the heuristic result quality for 24 problem sizes.
The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. In this paper we survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory. Special cases considered are single machine scheduling, identical, uniform and unrelated parallel machine scheduling, and open shop, flow shop and job shop scheduling. We indicate some problems for future research and include a selective bibliography.
The problem addressed in this paper is the non-preemptive unrelated parallel machine scheduling problem with the objective
of minimizing the makespan. Machine-dependent and job sequence-dependent setup times are considered, all jobs are available
at time zero, and all times are deterministic. This is a NP-hard problem and in this paper, optimal solutions are found for
small problems only. For larger problems, a new meta-heuristic, Meta-RaPS, is introduced and its performance is evaluated
by comparing its solutions to the solutions of an existing heuristic for the same problem. The results show that Meta-RaPS
found all optimal solutions for the small problems and outperformed the solutions obtained by the existing heuristic for larger
problems.
This paper addresses the non-preemptive unrelated parallel machine scheduling problem with machine-dependent and sequence-dependent
setup times. All jobs are available at time zero, all times are deterministic, and the objective is to minimize the makespan.
An Ant Colony Optimization (ACO) algorithm is introduced in this paper and is applied to this NP-hard problem; in particular,
the proposed ACO tackles a special structure of the problem, where the ratio of the number of jobs to the number of machines
is large (i.e., for a highly utilized set of machines). Its performance is evaluated by comparing its solutions to solutions
obtained using Tabu Search and other existing heuristics for the same problem, namely the Partitioning Heuristic and Meta-RaPS.
The results show that ACO outperformed the other algorithms.
KeywordsScheduling-Unrelated parallel machine-Sequence-dependent setup times-Ant Colony Optimization
We consider the problem of scheduling N jobs on M unrelated parallel machines to minimize maximum tardiness. Each job has
a due date and requires a single stage of processing. A setup for dies is incurred if the type of the job scheduled is different
from the previous one on that machine. For each die type, the number of dies is restricted. Because of the mechanical structure
of the machines and the fitness of dies to each machine, the processing time depends on both the job and the machine. In this
paper, an efficient heuristic based on guided search, record-to-record travel, and tabu lists is presented to minimize maximum
tardiness. Computational characteristics of the proposed heuristic are evaluated through extensive experiments, which show
that the proposed heuristic outperforms a simulated annealing method tested and is able to prescribe the optimal solutions
for problems in small scales.
This study considers the problem of scheduling jobs on unrelated parallel machines with machine-dependent and job sequence-dependent
setup times. In this study, a restricted simulated annealing (RSA) algorithm which incorporates a restricted search strategy
is presented to minimize the makespan. The proposed RSA algorithm can effective reduce the search effort required to find
the best neighborhood solution by eliminating ineffective job moves. The effectiveness and efficiency of the proposed RSA
algorithm is compared with the basic simulated annealing and existing meta-heuristics on a benchmark problem dataset used
in earlier studies. Computational results indicate that the proposed RSA algorithm compares well with the state-of-the-art
meta-heuristic for small-sized problems, and significantly outperforms basic simulated annealing algorithm and existing algorithms
for large-sized problems.
KeywordsScheduling-Unrelated parallel machines-Meta-heuristic-Simulated annealing
The unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times in the presence of due
date constraints represents an important but relatively less-studied scheduling problem in the literature. In this study,
a simple iterated greedy (IG) heuristic is presented to minimize the total tardiness of this scheduling problem. The effectiveness
and efficiency of the proposed IG heuristic are compared with existing algorithms on a benchmark problem dataset used in earlier
studies. Extensive computational results indicate that the proposed IG heuristic is capable of obtaining significantly better
solutions than the state-of-the-art algorithms on the same benchmark problem dataset with similar computational resources.
KeywordsUnrelated parallel machines–Total tardiness–Sequence-dependent setup times–Machine-dependent setup times–Due date constraints
A scheduling problem with unrelated parallel machines, sequence and machine-dependent setup times, due dates and weighted jobs is considered in this work. A branch-and-bound algorithm (B&B) is developed and a solution provided by the metaheuristic GRASP is used as an upper bound. We also propose a set of instances for this type of problem. The results are compared to the solutions provided by two mixed integer programming models (MIP) with the solver CPLEX 9.0. We carry out computational experiments and the algorithm performs extremely well on instances with up to 30 jobs.
In this study, we address a rescheduling problem in parallel machine environments under machine eligibility constraints. We consider total flow time as efficiency measure and the number of jobs processed on different machines in the initial and revised schedules as a stability measure. We present an optimizing algorithm for minimizing the stability measure subject to the constraint that the efficiency measure is at its minimum level. We then propose several heuristic procedures to generate a set of approximate efficient schedules relative to efficiency and stability measures.