Simultaneous versus sequential loading and scheduling of flexible assembly systems

A monolithic and a hierarchical approach is presented for loading and scheduling in a general flexible assembly system and a flexible assembly line. The system is made up of a set of assembly stations of various types each with limited working space and is capable of simultaneously producing a mix of product types. The objective is to determine an assignment of assembly tasks to stations and an assembly schedule for all products so as to complete the products in a minimum time. In the monolithic approach loading and scheduling decisions are made simultaneously. In the hierarchical approach, however, first the station workloads are balanced by solving the loading problem, and then detailed assembly schedule is determined for prefixed task assignments and assembly routes by solving a standard job-shop problem. Mixed integer programming formulations are presented for simultaneous and for sequential loading and scheduling. Loading and scheduling with alternative or with single task assignments are considered. Numerical examples are included to illustrate and compare the two approaches proposed.     

Optimal versus heuristic scheduling of surface mount technology lines

This paper presents and compares an exact and a heuristic approach for scheduling of printed wiring board assembly in surface mount technology (SMT) lines. A typical SMT line consists of several assembly stations in series and/or in parallel, separated by finite intermediate buffers. The objective of the scheduling problem is to determine the detailed sequencing and timing of all assembly tasks for each individual board, so as to maximize the line's productivity, which is defined in terms of makespan for a mix of board types. The limited intermediate buffers between stations result in a scheduling problem with machine blocking, where a completed board may remain on a machine and block it until a downstream machine becomes available. In addition, limited machine availability due to scheduled downtimes is considered. The exact approach is based on a mixed integer programming formulation that can be used for optimization of assembly schedules by using commercially available software for integer programming, whereas the heuristic approach is designed as a combination of tabu search and a set of dispatching rules. Numerical examples modelled after real-world SMT lines and some computational results are provided to illustrate and compare the two approaches.     

Multiple response optimization using mixture-designed experiments and desirability functions in semiconductor scheduling

Today's highly competitive semiconductor markets place a great emphasis on responsiveness to customers. In the past, competition has primarily focused on the product design arena. More recently, short lead times and good on-time delivery performance have become equally important to winning customer satisfaction. To meet these criteria, a recent thrust of manufacturing management has focused on the use of effective scheduling techniques to manage wafer movement. Dabbas and Fowler (1999) proposed an approach that combines multiple dispatching criteria into a single rule with the objective of maximizing multiple response measures simultaneously. This is accomplished using a linear combination with relative weights. The weights identify the contribution of the different criteria. This paper details the use of experimental design methodology as well as a desirability function approach in the optimization of the weights' assignment to the different criteria. The basic idea of the desirability function approach is to transform a multi-response problem into a single-response problem by means of a mathematical transformation. The responses of interest are on time delivery, variance of lateness, mean cycle time and variance of cycle time. Results demonstrate that the proposed approach is superior to the use of single-dispatching criteria with an average of 20% improvement for all responses. All data presented in this paper have been normalized to disguise actual performance results as the raw data are considered to be Motorola confidential data.     

Balancing and scheduling of surface mount technology lines

A mixed-integer programming approach to simultaneous or sequential balancing and scheduling of surface mount technology (SMT) lines for printed wiring board (PWB) assembly is presented. The SMT line consists of several processing stages in series separated by finite intermediate buffers, where each stage has one or more identical parallel machines. In the line, different types of PWBs are assembled using various types of electronic components. The components are assigned to feeder slots of a feeder carrier at each placement station. Different types of components occupy a different number of feeder slots. The total number of slots available at each station was limited. The problem objective was to determine an assignment of components to feeder slots at each placement station and to determine an assembly schedule for a mix of board types to complete the boards in minimum time. Numerical examples and some computational results are presented to illustrate applications of the proposed approach.     

New formulations for the setup assembly line balancing and scheduling problem

We present three new formulations for the setup assembly line balancing and scheduling problem (SUALBSP). Unlike the simple assembly line balancing problem, sequence-dependent setup times are considered between the tasks in the SUALBSP. These setup times may significantly influence the station times. Thus, there is a need for scheduling the list of tasks within each station so as to optimize the overall performance of the assembly line. In this study, we first scrutinize the previous formulation of the problem, which is a station-based model. Then, three new formulations are developed by the use of new sets of decision variables. In one of these formulations, the schedule-based formulation, SUALBSP is completely formulated as a scheduling problem. That is, no decision variable in the model directly denotes a station. All the proposed formulations will be improved by the use of several enhancement techniques such as preprocessing and valid inequalities. These improved formulations can be applied to establishing lower bounds on the problem. To assess the performance of new formulations, results of an extensive computational study on the benchmark data sets are also reported.     

生产调度干扰管理模型构建及智能算法研究

在现代企业生产经营过程中,生产调度的作用日益突出。它是生产管理领域内的关键生产环节。干扰管理是近些年来学者提出的一种新的处理生产过程中突发事件的思想和方法,已在供应链、物流以及某些特定领域的调度方面有所应用。流水车间调度问题(Flow-shopScheduling Problem,FSP)是一类复杂且极有代表性的流水线生产调度问题的简化模型,它无论是在离散制造工业还是在流程工业中都具有广泛的应用,具有一定的代表性。构建了流水车间调度问题以及干扰为工件到达的流水车间调度干扰管理模型,其经典目标函数为最大完工时间和干扰目标函数为干扰时间差相混合。     

Level scheduling of mixed-model assembly lines under storage constraints

In a mixed-model assembly line, different models of a common base product can be manufactured in intermixed production sequences. A famous solution approach for the resulting short-term sequencing problem is the so-called level scheduling problem, which aims at evenly smoothing the material requirements over time in order to facilitate a just-in-time supply. However, if materials are delivered in discrete quantities, the resulting spread of material usages implies that issued cargo carriers of a respective material remain at a station for a longer period of time. In practical applications with many materials required per station, this procedure might lead to bottlenecks with respect to the scarce storage space at stations. This paper investigates level scheduling under the constraint that the induced part usage patterns may not violate given storage constraints. The resulting sequencing problem is formalised and solved by suitable exact and heuristic solution approaches.     

A genetic algorithm based approach for scheduling of jobs containing multiple orders in a three-machine flowshop

This paper investigates a new scheduling problem of multiple orders per job (MOJ) in a three-machine flowshop consisting of an item-processing machine, a lot-processing machine and a batch-processing machine, for a semiconductor manufacturing operation that must form a layer on the wafers. The three-machine flowshop MOJ scheduling problem deals with sequencing customer orders, assigning orders to jobs, and then combining the formed jobs into batches. Genetic algorithms are presented for this scheduling problem to minimise the total weighted tardiness (TWT), in the presence of non-zero order ready times, different order due dates, different order weights and unequal order sizes. Extensive experiments were performed to compare the proposed genetic algorithm (GA)-based approach with the benchmark heuristics presented in previous studies. The experiments led to the conclusions that the GA-based approach is significantly superior over other heuristics in terms of TWT and can find near-optimal solutions in an acceptable amount of computation time.     

Stochastic two-sided U-type assembly line balancing: a genetic algorithm approach

In this paper, a novel stochastic two-sided U-type assembly line balancing (STUALB) procedure, an algorithm based on the genetic algorithm and a heuristic priority rule-based procedure to solve STUALB problem are proposed. With this new proposed assembly line design, all advantages of both two-sided assembly lines and U-type assembly lines are combined. Due to the variability of the real-life conditions, stochastic task times are also considered in the study. The proposed approach aims to minimise the number of positions (i.e. the U-type assembly line length) as the primary objective and to minimise the number of stations (i.e. the number of operators) as a secondary objective for a given cycle time. An example problem is solved to illustrate the proposed approach. In order to evaluate the efficiency of the proposed algorithm, test problems taken from the literature are used. The experimental results show that the proposed approach performs well.     

Scheduling in dynamic assembly job-shops with jobs having different holding and tardiness costs

Most studies on scheduling in dynamic job-shops assume that the holding cost of a job is given by the flowtime of the job and that the tardiness cost of a job is given by the tardiness of the job. In other words, unit holding and unit tardiness costs of a job are assumed. However, in reality, such an assumption need not hold, and it is quite possible that there are different costs for holding and tardiness for different jobs. In addition, most studies on job-shop scheduling assume that jobs are independent and that no assembly operations exist. The current study addresses the problem of scheduling in dynamic assembly job-shops (manufacturing multilevel jobs) with the consideration of different holding and tardiness costs for different jobs. An attempt is made to develop efficient dispatching rules by incorporating the relative costs of holding and tardiness of jobs in the form of scalar weights. The primary objective of scheduling considered here is the minimization of the total scheduling cost consisting of the sum of holding and tardiness costs. The performance of the scheduling rules in minimizing the individual components of total scheduling cost is also observed. The results of an extensive simulation study on the performance of different dispatching rules show that the proposed rules are effective in minimizing the means and maximums of the primary measure, and are quite robust with respect to different job structures and experimental settings.     

Integrated planning for product module selection and assembly line design/reconfiguration

To take full advantage of product modularity, modular product design and assembly system design/sreconfiguration have to be simultaneously addressed. The emerging reconfigurable production and flexible assembly techniques have made such an integrated approach possible. As such, this paper proposes an integrated approach to product module selection and assembly line design/reconfiguration problems. It further suggests that quality loss functions be used in a generic sense to quantify non-comparable and possibly conflicting performance criteria involved in the integrated problem. The complexity of the problem precludes the use of commercial software for solving meaningful sized problems in polynomial time. A genetic algorithm is therefore developed to provide quick solutions. An example problem is solved to illustrate the application of the proposed approach. Based on 72 randomly generated test problems, ANOVA analysis is further carried out to investigate the effects of genetic algorithm parameters. The convergence behaviour of the search processes is also examined by solving large problems with different numbers of operations and product modules.     

Synchronisation of production scheduling and shipment in an assembly flowshop

This paper studies a synchronised scheduling problem of production simultaneity and shipment punctuality in a two-stage assembly flowshop system. Production simultaneity seeks to ensure all products belonging to a same customer order are simultaneously completed (at least as close as possible). Shipment punctuality attempts to satisfy orders’ individual shipment due dates. We provide two criteria, i.e. mean longest waiting duration and mean earliness and tardiness, for measuring production simultaneity and shipment punctuality, respectively. A synchronised scheduling model is developed by balancing the two criteria using linear weighted sum method. A modified genetic algorithm (GA) is then proposed for solving this model. Numerical studies demonstrate the effectiveness of the proposed approach. The results indicate that considering production simultaneity can remarkably reduce finished products inventory. A prioritised weight combination interval for production simultaneity and shipment punctuality has been suggested. Production simultaneity is affected by the production system configuration, especially in peak seasons.     

A multi-decision genetic approach for workload balancing of mixed-model U-shaped assembly line systems

A mixed-model assembly line is a type of production line where a variety of product models similar in product characteristics are produced. As a consequence of introducing the just-in-time (JIT) production principle, it has been recognised that a U-shaped assembly line system offers several benefits over the traditional straight line system. This paper proposes a new evolutionary approach to deal with workload balancing problems in mixed-model U-shaped lines. The proposed method is based on the multi-decision of an amelioration structure to improve a variation of the workload. This paper considers both the traditional straight line system and the U-shaped assembly line, and is thus an unbiased examination of line efficiency. The performance criteria considered are the number of workstations (the line efficiency) and the variation of workload, simultaneously. The results of experiments enhanced the decision process during multi-model assembly line system production; thus, it is therefore suitable for the augmentation of line efficiency in workstation integration and simultaneously enhancement of the variation of the workload. A case study is examined as a validity check in collaboration with a manufacturing company.     

A two-stage AIS approach for grid scheduling problems

Grid workflow scheduling problem has been a research focus in grid computing in recent years. Various deterministic or meta-heuristic scheduling approaches have been proposed to solve this NP-complete problem. A perusal of published papers on the artificial immune system (AIS) reveals that most researchers use the clonal selection of B cells during the evolving processes and the affinity function of B cells to solve various optimisation problems. This research takes a different approach to the subject – firstly by applying a modified algorithm (Hu, T.C., 1961. Parallel sequencing and assembly line problem. Operations Research, 9 (6), 841–848) to sequence the job and this sequence is applied for further application. Secondly, the derived sequence is then used for machine allocations using the AIS approach. The proposed AIS apply B cells to reduce the antigens and then combining T helper cells and T suppressor cells to solve the grid scheduling problems. Our proposed methodology differs from other earlier approaches as follows: 1. A two-stage approach is applied using a fixed sequence derived from heuristic to allocate machine. 2. AIS apply B cells as bases and then T cells are employed next. T helper cells are used to help improve the solution and then T suppressor cells are generated to increase the diversity of the population. A new formula is proposed to calculate the affinity of the antibody with the antigen. The total difference of completion time of each job is applied instead of the difference of makespan of the schedule. This new AIS method can supplement the flaw of genetic algorithms (GA) using fitness as the basis and a new lifespan which will keep good diversified chromosomes within the population to extend the searching spaces. The experimental tests show that this novel AIS method is very effective when compared with other meta-heuristics such as GA, simulated annealing (SA), and ant colony optimisation (ACO).     

Solving the spatial scheduling problem: a two-stage approach

The spatial scheduling problem that arises in hull block assembly shops occurs when scheduling and spatial allocation of the blocks must be considered simultaneously. We present a two-stage approach to this type of problem. The first stage aims to reduce the number of blocks. The second stage optimises the scheduling and spatial allocation of blocks using nonlinear mixed integer programming (NMIP) methods. The procedure proposed in this paper uses an agglomeration algorithm (AA) for the blocks. This procedure is based on the space–time coupling mechanism. The AA is a three-dimensional classification used to cluster blocks linked closely in time and space into virtual blocks. Extensive computational results from real cases are presented to demonstrate the effectiveness of the proposed approach, demonstrating a significant improvement over results obtained from existing methods.     

Capacity-constrained scheduling for a logic IC final test facility

A capacity-constrained scheduling using the concept of the theory of constraints for a semiconductor Logic IC final test operation is presented. The scheduling of the IC final test considers unrelated parallel machines with multiple constraint problems. A broad product mix, variable lot sizes and yields, long and variable set-up times, as well as limited test equipment capacity characterize the operations in this test facility. Discrete event simulation models based on e-M-Plant? are developed to implement the capacity-constrained scheduling algorithm. A comparison is also made with other rules, which are combinations of the rules such as first come first serve and earliest due date for the order scheduling, and the rules such as minimum set-up time, shortest processing time and shortest set-up time plus processing time for the dispatching test equipment. The simulation results show that the proposed capacity-constrained scheduling outperforms other rules for the committed volume performance in many different operational conditions. Directions for future research are also presented.     

Single machine scheduling problem with stochastic sequence-dependent setup times

In this study, we consider stochastic single machine scheduling problem. We assume that setup times are both sequence dependent and uncertain while processing times and due dates are deterministic. In the literature, most of the studies consider the uncertainty on processing times or due dates. However, in the real-world applications (i.e. plastic moulding industry, appliance assembly, etc.), it is common to see varying setup times due to labour or setup tools availability. In order to cover this fact in machine scheduling, we set our objective as to minimise the total expected tardiness under uncertain sequence-dependent setup times. For the solution of this NP-hard problem, several heuristics and some dynamic programming algorithms have been developed. However, none of these approaches provide an exact solution for the problem. In this study, a two-stage stochastic-programming method is utilised for the optimal solution of the problem. In addition, a Genetic Algorithm approach is proposed to solve the large-size problems approximately. Finally, the results of the stochastic approach are compared with the deterministic one to demonstrate the value of the stochastic solution.     

Monolithic versus hierarchical approach to integrated scheduling in a supply chain

The two approaches, monolithic and hierarchical, with a set of mixed integer programming formulations are proposed and compared for multi-objective integrated scheduling in a customer driven supply chain. The supply chain consists of multiple manufacturers (suppliers) of parts, a single producer of finished products and a set of customers who generate final demand for the products. Each supplier has a number of identical production lines in parallel for the manufacture of parts, and the producer has a flexible assembly line for assembly of products. Given a set of orders, the problem objective is to determine which orders are to be provided with parts by each supplier, find a schedule for the manufacture of parts by each supplier and for the delivery parts from each supplier to the producer, and find a schedule for the assembly of products for each order by the producer, such that a certain performance measure of the supply chain is optimised. The selection of the parts supplier for each order is combined with due date setting for some orders, subject to the suppliers and the producer available capacity. Different objective functions are considered that take into account both customer service level and total manufacturing, delivery and production cost. Numerical examples are presented that are modelled by real-world integrated scheduling in a customer driven supply chain of high-tech products, and some computational results are reported to compare the two approaches.     

Meeting demand variation using flexible U-shaped assembly lines

Nowadays, companies must be able to provide a higher degree of product customisation to fulfil the needs of the increasingly sophisticated customer demand. This can only be achieved by having flexible production systems, able to cope with extended product ranges and with the uncertainty and variability of demand in the current market environment. The purpose of this paper is to present a contribution related to facilities design that accounts for this issue, by presenting flexible U-shaped line configurations for an assembly system. In this type of line, whenever the production volume or product mix changes, the only modification in the line will be the number of operators working in the line, as the physical workstations remain fixed. The relevance of the problem is stated and a heuristic procedure, based on ant colony algorithms, developed to address this problem is described. The results of the application of the proposed procedure to an assembly line of a major manufacturer of electronic security systems are reported.     

Order-oriented cooperative sequencing optimisation in multi-mix-model assembly lines

Order-oriented products assembly sequence among different assembly lines becomes a critical problem for mass customisation manufacturing systems. It significantly affects system productivity, delivery time, and manufacturing cost. In this paper, we propose a new approach to extend the traditional products sequencing from mixed model assembly line (MMAL) to multi-mixed model assembly lines (MMMALs) to obtain the optimal assembly sequence with the objectives of minimising consumption waviness of each material in the lines, assembly line setup cost, and lead-time. A multi-objective optimisation algorithm based on variable neighbourhood search methods (VNS) is developed. We perform an industrial case study in order to demonstrate the practicality and effectiveness of the proposed approach.