Showing papers on "Flow shop scheduling published in 2019"
TL;DR: This paper explores the future research direction in SDS and discusses the new techniques for developing future new JSP scheduling models and constructing a framework on solving the JSP problem under Industry 4.0.
Abstract: Traditional job shop scheduling is concentrated on centralized scheduling or semi-distributed scheduling. Under the Industry 4.0, the scheduling should deal with a smart and distributed manufacturing system supported by novel and emerging manufacturing technologies such as mass customization, Cyber-Physics Systems, Digital Twin, and SMAC (Social, Mobile, Analytics, Cloud). The scheduling research needs to shift its focus to smart distributed scheduling modeling and optimization. In order to transferring traditional scheduling into smart distributed scheduling (SDS), we aim to answer two questions: (1) what traditional scheduling methods and techniques can be combined and reused in SDS and (2) what are new methods and techniques required for SDS. In this paper, we first review existing researches from over 120 papers and answer the first question and then we explore a future research direction in SDS and discuss the new techniques for developing future new JSP scheduling models and constructing a framework on solving the JSP problem under Industry 4.0.
308 citations
TL;DR: A digital twin-driven methodology for rapid individualised designing of the automated flow-shop manufacturing system using physics-based system modelling and distributed semi-physical simulation to provide engineering solution analysis capabilities and generates an authoritative digital design of the system at pre-production phase is presented.
Abstract: Under a mass individualisation paradigm, the individualised design of manufacturing systems is difficult as it involves adaptive integrating both new and legacy machines for the formation of part f...
233 citations
TL;DR: A survey on the applications of optimal control to scheduling in production, supply chain and Industry 4.0 systems with a focus on the deterministic maximum principle to derive major contributions, application areas, limitations, as well as research and application recommendations for the future research.
Abstract: This paper presents a survey on the applications of optimal control to scheduling in production, supply chain and Industry 4.0 systems with a focus on the deterministic maximum principle. The first objective is to derive major contributions, application areas, limitations, as well as research and application recommendations for the future research. The second objective is to explain control engineering models in terms of industrial engineering and production management. To achieve these objectives, optimal control models, qualitative methods of performance analysis and computational methods for optimal control are considered. We provide a brief historic overview and clarify major mathematical fundamentals whereby the control engineering terms are brought into correspondence with industrial engineering and management. The survey allows the grouping of models with only terminal constraints with application to master production scheduling, models with hybrid terminal–logical constraints with applications to ...
212 citations
TL;DR: This paper investigates the joint problem of partial offloading scheduling and resource allocation for MEC systems with multiple independent tasks, and proposes iterative algorithms for the joint issue of POSP.
Abstract: Mobile edge computing (MEC) is a promising technique to enhance computation capacity at the edge of mobile networks. The joint problem of partial offloading decision, offloading scheduling, and resource allocation for MEC systems is a challenging issue. In this paper, we investigate the joint problem of partial offloading scheduling and resource allocation for MEC systems with multiple independent tasks. A partial offloading scheduling and power allocation (POSP) problem in single-user MEC systems is formulated. The goal is to minimize the weighted sum of the execution delay and energy consumption while guaranteeing the transmission power constraint of the tasks. The execution delay of tasks running at both MEC and mobile device is considered. The energy consumption of both the task computing and task data transmission is considered as well. The formulated problem is a nonconvex mixed-integer optimization problem. In order to solve the formulated problem, we propose a two-level alternation method framework based on Lagrangian dual decomposition. The task offloading decision and offloading scheduling problem, given the allocated transmission power, is solved in the upper level using flow shop scheduling theory or greedy strategy, and the suboptimal power allocation with the partial offloading decision is obtained in the lower level using convex optimization techniques. We propose iterative algorithms for the joint problem of POSP. Numerical results demonstrate that the proposed algorithms achieve near-optimal delay performance with a large energy consumption reduction.
210 citations
TL;DR: A new time division multiple access (TDMA) based workflow model is proposed, which allows parallel transmissions and executions in the UAV-assisted system, and an alternative algorithm is developed to set the initial point closer to the optimal solution.
Abstract: This paper considers a UAV-enabled mobile edge computing (MEC) system, where a UAV first powers the Internet of things device (IoTD) by utilizing Wireless Power Transfer (WPT) technology. Then each IoTD sends the collected data to the UAV for processing by using the energy harvested from the UAV. In order to improve the energy efficiency of the UAV, we propose a new time division multiple access (TDMA) based workflow model, which allows parallel transmissions and executions in the UAV-assisted system. We aim to minimize the total energy consumption of the UAV by jointly optimizing the IoTDs association, computing resources allocation, UAV hovering time, wireless powering duration and the services sequence of the IoTDs. The formulated problem is a mixed-integer non-convex problem, which is very difficult to solve in general. We transform and relax it into a convex problem and apply flow-shop scheduling techniques to address it. Furthermore, an alternative algorithm is developed to set the initial point closer to the optimal solution. Simulation results show that the total energy consumption of the UAV can be effectively reduced by the proposed scheme compared with the conventional systems.
160 citations
TL;DR: An evolutionary multiobjective robust scheduling algorithm is suggested, in which solutions obtained by a variant of single-objective heuristic are incorporated into population initialization and two novel crossover operators are proposed to take advantage of nondominated solutions.
Abstract: In various flow shop scheduling problems, it is very common that a machine suffers from breakdowns. Under this situation, a robust and stable suboptimal scheduling solution is of more practical interest than a global optimal solution that is sensitive to environmental changes. However, blocking lot-streaming flow shop (BLSFS) scheduling problems with machine breakdowns have not yet been well studied up to date. This paper presents, for the first time, a multiobjective model of the above problem including robustness and stability criteria. Based on this model, an evolutionary multiobjective robust scheduling algorithm is suggested, in which solutions obtained by a variant of single-objective heuristic are incorporated into population initialization and two novel crossover operators are proposed to take advantage of nondominated solutions. In addition, a rescheduling strategy based on the local search is presented to further reduce the negative influence resulted from machine breakdowns.The proposed algorithm is applied to 22 test sets, and compared with the state-of-the-art algorithms without machine breakdowns. Our empirical results demonstrate that the proposed algorithm can effectively tackle BLSFS scheduling problems in the presence of machine breakdowns by obtaining scheduling strategies that are robust and stable.
149 citations
TL;DR: Issues in the context of urgent need for energy-conservation as well as the advent of globalized and multi-factory manufacture motivate the attempts to address a stochastic multi-objective distributed permutation flow shop scheduling problem by considering total tardiness constraint via minimizing the makespan and the total energy consumption.
143 citations
TL;DR: The results demonstrate that the IGA is more effective than the genetic algorithm (GA), simulating annealing algorithm (SA) and migrating birds optimisation algorithm (MBO) and within no more than 10% of the running time of the best MILP model.
Abstract: This paper investigates an energy-conscious hybrid flow shop scheduling problem with unrelated parallel machines (HFSP-UPM) with the energy-saving strategy of turning off and on We first analyse t
99 citations
TL;DR: This is the first attempt to solve either the Parallel Blocking flow shop problem or the Distributed Blocking Flow Shop problem with the goal of minimizing total tardiness, and the performance of the proposed algorithm is compared against other benchmark algorithms proposed for the DPFSP.
Abstract: This paper proposes an iterated greedy algorithm for scheduling jobs in F parallel flow shops (lines), each consisting of a series of m machines without storage capacity between machines. This constraint can provoke the blockage of machines if a job has finished its operation and the next machine is not available. The criterion considered is the minimization of the sum of tardiness of all the jobs to schedule, i.e., minimization of the total tardiness of jobs. Notice that the proposed method is also valid for solving the Distributed Permutation Blocking Flow Shop Scheduling Problem (DBFSP), which allows modelling the scheduling process in companies with more than one factory when each factory has an identical flow shop configuration. Firstly, several constructive procedures have been implemented and tested to provide an efficient solution in terms of quality and CPU time. This initial solution is later improved upon with an iterated greedy algorithm that includes a variable neighbourhood search for interchanging or reassigning jobs from the critical line to other lines. Next, two strategies have been tested for selecting the critical line; the one with a higher total tardiness of jobs and the one with a job that has the highest tardiness. The experimental design chooses the best combination of initial solution and critical line selection. Finally, we compare the performance of the proposed algorithm against other benchmark algorithms proposed for the DPFSP, which have been adapted to the problem being considered here since, to the best of our knowledge, this is the first attempt to solve either the Parallel Blocking Flow Shop problem or the Distributed Blocking Flow Shop problem with the goal of minimizing total tardiness. This comparison has allowed us to confirm the good performance of the proposed method.
78 citations
TL;DR: An estimation of distributed algorithm with Pareto dominate concept which uses a probabilistic model to generate offspring to solve a multiobjective distributed no-wait flow-shop scheduling problem with sequence-dependent setup time.
Abstract: Influenced by the economic globalization, the distributed manufacturing has been a common production mode. This paper considers a multiobjective distributed no-wait flow-shop scheduling problem with sequence-dependent setup time (MDNWFSP-SDST). This scheduling problem exists in many real productions such as baker production, parallel computer system, and surgery scheduling. The performance criteria are the makespan and the total weight tardiness. In the MDNWFSP-SDST, several identical factories are considered with the related flow-shop scheduling problem with no-wait constraints. For solving the MDNWFSP-SDST, a Pareto-based estimation of distribution algorithm (PEDA) is presented. Three probabilistic models including the probability of jobs in empty factory, two jobs in the same factory, and the adjacent jobs are constructed. The PWQ heuristic is extended to the distributed environment to generate initial individuals. A sampling method with the referenced template is presented to generate offspring individuals. Several multiobjective neighborhood search methods are developed to optimize the quality of solutions. The comparison results show that the PEDA obviously outperforms other considered multiobjective optimization algorithms for addressing MDNWFSP-SDST. Note to Practitioners —This paper is motivated by the process cycles in multiproduction factories (or lines) of baker production, surgery scheduling, and parallel computer systems. In these process cycles, jobs are assigned to multiproduction factories (or lines), and no interruption exists between consecutive operations. This paper models this process as a multiobjective distributed no-wait flow-shop scheduling with SDST. Scheduling becomes more challenging when facing distributed factories. This paper provides an estimation of distributed algorithm with Pareto dominate concept which uses a probabilistic model to generate offspring. Experiment results suggest that the proposed algorithm can find superior solutions of large-scale instances. This scheduling model can be extended to practical problems by considering other constraints, such as assembly process, mixed no-wait, and transporting times. Besides, the proposed algorithm can be applied to solve other distributed scheduling problems and industrial cases, once their constraints are known, i.e., the processing time of operations, the setup time of machines.
78 citations
TL;DR: Comparisons show that dynamic mating strategy and local intensification are effective in improving performances and the proposed algorithm is more effective than the existing algorithms.
Abstract: With the increasing attention on environment issues, green scheduling in manufacturing industry has been a hot research topic. As a typical scheduling problem, permutation flow shop scheduling has ...
TL;DR: A consolidated survey of assembly flow shop models with their solution methodology is provided and some problems receiving less attention are presented and several salient research opportunities are proposed.
Abstract: The past few years have witnessed a resurgence of interest in assembly flow shop scheduling as evidenced by increasing number of published articles in this field. A basic assembly flow shop consist...
TL;DR: This paper addresses the energy-efficient distributed no-idle permutation flow-shop scheduling problem (EEDNIPFSP) to minimize makespan and total energy consumption simultaneously by using a collaborative optimization algorithm (COA).
Abstract: Facing the energy crisis, manufacturers is paying much attention to the energy-efficient scheduling by taking both economic benefits and energy conservation into account. Meanwhile, with the economic globalization, it is significant to facilitate the advanced manufacturing and scheduling in the distributed way. This paper addresses the energy-efficient distributed no-idle permutation flow-shop scheduling problem (EEDNIPFSP) to minimize makespan and total energy consumption simultaneously. By analyzing the characteristics of the problem, several properties are derived. To solve the problem effectively, a collaborative optimization algorithm (COA) is proposed by using the properties and some collaborative mechanisms. First, two heuristics are collaboratively utilized for population initialization to guarantee certain quality and diversity. Second, multiple search operators collaborate in a competitive way to enhance the exploration adaptively. Third, different local intensification strategies are designed for the dominated and non-dominated individuals to enhance the exploitation. Fourth, a speed adjusting strategy for the non-critical operations is designed to improve total energy consumption. The effect of key parameters is investigated using the design-of-experiment with full factorial setting. Comparisons based on extensive numerical tests are carried out, which demonstrate the effectiveness of the proposed algorithm in solving the EEDNIPFSP.
TL;DR: It is demonstrated that the consideration of different objectives leads to various optimal decisions on jobs assignment, jobs batching, and batches sequencing, which generates a new insight to investigate batching scheduling problems with learning effect under single-machine and parallel-machine settings.
Abstract: This paper introduces the serial batching scheduling problems with position-based learning effect, where the actual job processing time is a function of its position. Two scheduling problems respectively for single-machine and parallel-machine are studied, and in each problem the objectives of minimizing maximum earliness and total number of tardy jobs are both considered respectively. In the proposed scheduling models, all jobs are first partitioned into serial batches, and then all batches are processed on the serial-batching machine. We take some practical production features into consideration, i.e., setup time before processing each batch increases with the time, regarded as time-dependent setup time, and we formalize it as a linear function of its starting time. Under the single-machine scheduling setting, structural properties are derived for the problems with the objectives of minimizing maximum earliness and number of tardy jobs respectively, based on which optimization algorithms are developed to solve them. Under the parallel-machine scheduling setting, a hybrid VNS–GSA algorithm combining variable neighborhood search (VNS) and gravitational search algorithm (GSA) is proposed to solve the problems with these two objectives respectively, and the effectiveness and efficiency of the proposed VNS–GSA are demonstrated and compared with the algorithms of GSA, VNS, and simulated annealing (SA). This paper demonstrates that the consideration of different objectives leads to various optimal decisions on jobs assignment, jobs batching, and batches sequencing, which generates a new insight to investigate batching scheduling problems with learning effect under single-machine and parallel-machine settings.
TL;DR: A new multiphase iterated local search algorithm (ILS) is developed to determine a three-dimensional Pareto front regarding three objectives: makespan, total energy costs and peak load, which is proven to be suitable in purposeful search in the solution space, which allows practical decision support.
TL;DR: A hybrid biogeography-based optimization with variable neighborhood search (HBV) is implemented for solving the no-wait flow shop scheduling problem (NWFSP) with the makespan criterion and the computational results and comparisons show that the efficiency and performance of HBV for solving NWFSP are shown to be good.
Abstract: The no-wait flow shop scheduling problem (NWFSP) plays an essential role in the manufacturing industry. Inspired by the overall process of biogeography theory, the standard biogeography-based optimization (BBO) was constructed with migration and mutation operators. In this paper, a hybrid biogeography-based optimization with variable neighborhood search (HBV) is implemented for solving the NWFSP with the makespan criterion. The modified NEH and the nearest neighbor mechanism are employed to generate a potential initial population. A hybrid migration operator, which combines the path relink technique and the block-based self-improvement strategy, is designed to accelerate the convergence speed of HBV. The iterated greedy (IG) algorithm is introduced into the mutation operator to obtain a promising solution in exploitation phase. A variable neighbor search strategy, which is based on the block neighborhood structure and the insert neighborhood structure, is designed to perform the local search around the current best solution in each generation. Furthermore, the global convergence performance of the HBV is analyzed with the Markov model. The computational results and comparisons with other state-of-art algorithms based on Taillard and VRF benchmark show that the efficiency and performance of HBV for solving NWFSP.
TL;DR: An improved artificial bee colony (IABC) algorithm for addressing the distributed flow shop considering the distance coefficient found in precast concrete production system, with the minimisation of the makespan is proposed.
Abstract: This paper proposes an improved artificial bee colony (IABC) algorithm for addressing the distributed flow shop considering the distance coefficient found in precast concrete production system, wit...
TL;DR: In this paper, a discrete multi-objective fireworks algorithm (DMOFWA) is proposed to address the MOFSP-SDST problem with sequence-dependent setup times.
Abstract: Multi-objective flow shop scheduling problem with sequence-dependent setup times (MOFSP-SDST) is a class of important production scheduling problem with strong industry background. In this paper, a MOFSP-SDST mathematic model with the objectives of total production cost, makespan, mean flow time and mean idle time of machines is developed. To solve this multi-objective model, a novel multi-objective approach based on fuzzy correlation entropy analysis is proposed firstly. In this multi-objective approach, two types of objective function value sequences, namely the referenced function value sequence and comparable function value sequence, are constructed and mapped into two types of fuzzy sets by a modified relative membership function. The fuzzy correlation entropy coefficient between the two types of fuzzy sets is used to select better solutions in a multi-objective problem. A discrete multi-objective fireworks algorithm (DMOFWA) is proposed to address the MOFSP-SDST. In the DMOFWA, a new multi-objective approach is adopted to handle the multiple objectives and guide the search of the algorithm. Two kinds of machine learning strategies are adopted, namely opposition-based learning (OBL) and clustering analysis (CA). The OBL is employed to learn from the current search space and improve the exploration ability of DMOFWA, and the CA based on fuzzy correlation entropy coefficient is proposed to cluster firework individuals. Computational and statistical results show that the novel multi-objective approach, OBL and CA strategies can effectively improve the performance of DMOFWA. Furthermore, the results indicate that DMOFWA performs better than four state-of-the-art comparison algorithms.
TL;DR: A new Pareto dominance is defined to deal with the relative importance of objectives and a two-level imperialist competitive algorithm (TICA) is presented, in which two levels consist of the strongest empire and other empires, respectively.
Abstract: Energy-efficient hybrid flow shop scheduling problem (EHFSP) has been investigated in recent years; however, the relative importance of objectives is seldom considered in the previous works. In this study, EHFSP with total tardiness, makespan and total energy consumption is addressed, in which the third objective has lower importance than other ones. A new Pareto dominance is defined to deal with the relative importance and a two-level imperialist competitive algorithm (TICA) is presented, in which two levels consist of the strongest empire and other empires, respectively. To generate high quality solutions, assimilation and revolution are executed differently in empires in the different search stages, the strongest empire is excluded from imperialist competition, memory is often combined with the strongest empire and a member of memory is added into the winning empire to avoid the inclusion of the weakest colony of the weakest empire. Extensive experiments are conducted and the computational results show that TICA provides promising results for the considered EHFSP.
TL;DR: Results showed that makespan was the objective function most adopted by the researchers, with 62% of the total covered, followed by multi-objective based (12%), total flow time-based (11%), due date- based (7%), stochastic based functions (6%) and cycle time (3%).
Abstract: This paper presents a literature review on the m-machine flow shop scheduling problem with blocking conditions. In total, 139 papers are reviewed and classified, ranging from 1969 up to early 2019. Results showed that makespan was the objective function most adopted by the researchers, with 62% of the total covered, followed by multi-objective based (12%), total flow time-based (11%), due date-based (7%), stochastic based functions (6%) and cycle time (3%). Regarding the purpose of the paper, approximately 92% of the papers proposed solution methods, where 76% of the papers developed heuristic methods and 16% of exact methods, and 8% of the papers considered the analysis of the problem and literature reviews. Directions for future researches include the proposition of solution methods for mono-objective functions as total flow time-based and due date-based, development of solution methods for the m-machine flow shop with RCb and RCb* constraints and adoption of more than one additional constraint to the problem.
TL;DR: In this paper, a comprehensive exploration review on the FFS scheduling problem is presented, which guides the reader by considering and understanding different environmental assumptions, system constraints and objective functions for future research works.
Abstract: Article history: Received December 26 2017 Received in Revised Format February 18 2018 Accepted April 14 2018 Available online April 14 2018 The Flexible flow shop (FFS) is defined as a multi-stage flow shops with multiple parallel machines. FFS scheduling problem is a complex combinatorial problem which has been intensively studied in many real world industries. This review paper gives a comprehensive exploration review on the FFS scheduling problem and guides the reader by considering and understanding different environmental assumptions, system constraints and objective functions for future research works. The published papers are classified into two categories. First is the FFS system characteristics and constraints including the problem differences and limitation defined by different studies. Second, the scheduling performances evaluation are elaborated and categorized into time, job and multi related objectives. In addition, the resolution approaches that have been used to solve FFS scheduling problems are discussed. This paper gives a comprehensive guide for the reader with respect to future research work on the FFS scheduling problem.
TL;DR: An energy efficient dynamic flexible flow shop scheduling model using the peak power value with consideration of new arrival jobs with a priority based hybrid parallel Genetic Algorithm with a predictive reactive complete rescheduling strategy is developed.
TL;DR: This paper extends three constructive heuristics based on a new job assignment rule and proposes two simple meta-heuristics including iterated local search (ILS) and variable neighborhood search (VNS) which demonstrates the high effectiveness of the proposed ILS and VNS.
Abstract: Due to the complexity of a real-practice manufacturing process, various complex constraints should be considered to make the conventional model more suitable for the realistic production. This paper proposes a distributed assembly no-idle flow shop scheduling problem (DANIFSP) with the objective of minimizing the makespan at the assembly stage. The DANIFSP consists of two stages, i.e., production and assembly. The production stage contains several identical flow shops working in parallel, in which all jobs with series of operations that should be allocated to one of these factories and all operations of jobs should be performed in the allocated factories. To satisfy the no-idle constraint, each machine must process jobs without any interruption from the start of processing the job to the completion of processing the last job. In the second assembly stage, the processed jobs are assembled by a single machine. For addressing the DANIFSP, this paper extends three constructive heuristics based on a new job assignment rule and proposes two simple meta-heuristics including iterated local search (ILS) and variable neighborhood search (VNS). A comprehensive calibration and analysis for the proposed algorithms through a design of experiments are carried out. The comparison with recently published algorithms demonstrates the high effectiveness of the proposed ILS and VNS.
TL;DR: A novel multi-objective discrete water wave optimization (MODWWO) algorithm to solve a multi-Objective BFSP (MOBFSP) that minimizes both makespan and total flow time is proposed and compared with several state-of-the-art multi- objective scheduling optimization approaches.
Abstract: The blocking flow-shop scheduling problem (BFSP) has been aroused general attention due to its broad industrial applications. However, most researches about it mainly focus on optimization of single objective. Multiple objectives are less considered simultaneously. Actually, in the practical production, the consideration of multiple objectives simultaneously could give more realistic solutions to the decision maker. Therefore, in this paper, we propose a novel multi-objective discrete water wave optimization (MODWWO) algorithm to solve a multi-objective BFSP (MOBFSP) that minimizes both makespan and total flow time. In the proposed algorithm, a decomposition-based initialization strategy is developed to generate a population with high quality and diversity. Then, a ranking-based propagation operator is designed to guide the global exploration and local exploitation of algorithm. Afterwards, a local intensification-based breaking operator is applied to improve the quality of the new created waves. Furthermore, a problem-specific refraction operator is incorporated to avoid being trapped in local optimum. The proposed algorithm is evaluated based on the benchmark instances, and compared with several state-of-the-art multi-objective scheduling optimization approaches. The comparison results show that the proposed MODWWO is a high-performing method for the considered MOBFSP.
TL;DR: The size of the space of semiactive schedules achieved by the different solution representations and the issue of the quality of the schedules that can be achieved by these representations are established using the optimal solutions given by several MILP models and complete enumeration.
TL;DR: This work undertakes a study of truck scheduling in a parallel dock cross-docking center, and proposes a hybrid method based on a Lagrangian relaxation technique through the volume algorithm that outperforms current results.
28 May 2019
TL;DR: A Robust Mixed-Integer Linear Programming (RMILP) model is proposed to accommodate the problem with the real-world conditions and the obtained results show the effects of the robustness in optimizing the model under uncertainty condition.
Abstract: Scheduling is known as a great part of production planning in manufacturing systems. Flow Shop Scheduling (FSS) problem deals with the determination of the optimal sequence of jobs processing on ma...
TL;DR: A comprehensive computational evaluation including several state-of-the-art algorithms, together with statistical analyses, show that the proposed DIWO algorithm produces better results than all compared algorithms by significant margin.
TL;DR: This work shows that Industry 4.0 systems can autonomously manage the production management process, and presents a framework based on tolerance planning strategies (tolerance scheduling problem), to determine which changes can be carried out.
Abstract: Contemporary assembly line systems are characterized by an increasing capability to offer each client a different product, more tuned to her needs and preferences. These assembly systems will be heavily influenced by the advent of Industry 4.0 technologies, enabling the proposal of business models that allow the late customization of the products, i.e., the customer can modify attributes of its product once the production of it is started. This business model requires that the manufacturing tools are able to make decisions online and negotiate with the customer the changes that can be carried out, according to the workload flowing through the production system. In this work, we analyze the possibilities and limitations of this new paradigm. First, we show that Industry 4.0 systems can autonomously manage the production management process, and then, we present a framework based on tolerance planning strategies (tolerance scheduling problem), to determine which changes can be carried out. The ability of resequencing the production process is also implemented in the case that the operations associated with late customization allow it (i.e., when intermediate buffers are available). This establishes a parallelism with the problem of non-permutation flow shop. We finally discuss future developments necessary to implement these procedures.