Flow shop scheduling problems with assembly operations: a review and new trends

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 consists of two types of stages: fabrication or machining stage and assembly stage. Machining and assembly stages are composed of either one or a set of machines that are working in parallel. Final products have hierarchical assembly structure with several components and assembly operation(s). The components need to be processed in the machining stage(s) and then assembled based on hierarchical assembly structure. The goal is to find the sequence of jobs that optimises certain objectives. Assembly flow shop scheduling problem has several interesting derivatives and applications in various manufacturing and service industries. This paper provides a consolidated survey of assembly flow shop models with their solution methodology. Finally, the paper concludes by presenting some problems receiving less attention and proposes several salient research opportunities.     

A simulation comparison of group technology with traditional job shop manufacturing

A simulation model of an actual job shop was used to compare group technology with traditional job shop manufacturing. The experiment compared shops which had four different layouts, designed to emphasize different features of traditional job shops and group technology shops, and four distributions of demand for end items. The group technology shops exhibited superior performance in terms of average move time and average set-up time. The traditional job shops had superior performance in queue related variables (average queue length, average waiting time, work-in-process inventory, etc.). This was caused by group technology's dedication of machines. The effects of the queue related variables outweighed the effects of average move time and average set-up time: the average flow time was shorter in the traditional job shop than in the group technology shops.     

Lotsizing in Multi-Item Multi- Machine Job Shops

A great many manufacturing facilities can be described as closed job shops which process multiple items through multiple work centers for stock or for assembly. The performance of these shops is strongly dependent on the batching policies employed for work in the shop. In particular, waiting time in queue and total manufacturing lead time for batches are functions of lotsizes. In turn these affect work-in-process costs, safety stock requirements, schedule performance and part coordination for assembly. The relationship between lot-sizing and shop performance is represented using a queueing network model which is then embedded in an optimization routine that searches for optimal lot sizes.     

Critical Ratio Scheduling: Dynamic Due-Date Procedures under Demand Uncertainty

This paper is concerned with the problem of maintaining order due dates in job shops that manufacture products to replenish a finished goods inventory controlled by an order point system. Two different strategies for maintaining order due dates—static and dynamic due date procedures—are analyzed using both shop and inventory system performance measures. This study examines the influence of the degree of predictability of the final product demand pattern on the performance of the static and dynamic procedures. The demand pattern for individual products is characterized by a long-run demand rate, a period-to-period serial correlation coefficient of demand, and a coefficient of demand variation. The results indicate that the dynamic due-date procedure does not provide a significant improvement in the performance of the production system in comparison with the static procedure - even when the predictability of the demand during the replenishment lead time is improved.     

A graph-based model for manufacturing complexity

This paper presents a graph-based model to measure the relative manufacturing complexity of and the manufacturing similarity of products in job shop manufacturing systems. This model depicts the impact of the complexity factors on the profit realisable from products based on their manufacturing process and required resources/skills. These resources deal with the process required for a component to reach assembly, the process of assembling the components to a whole product. This relative manufacturing complexity measure not only can support assembly and production cost estimation, but also can provide a guideline for creating a product with the most effective balance of manufacturing and assembly. Also, the results of this study can help improve budgeting and resource allocation, and the product life cycle cost estimation for future products. A numerical example is also presented to demonstrate the application of the proposed approach.     

Minimizing production flow time in a process and assembly job shop

Scheduling is one of the most important issues in the planning and operation of production systems, but in medium to large shops, the generation of consistently good schedules has proven to be extremely difficult. The problem is that optimal scheduling solutions involve costly and impractical enumeration procedures. In the literature, most scheduling problems only address jobs with serial or sequential operations. Rarely do they consider jobs in which machining and assembly operations are simultaneously involved. This lack of attention to scheduling problems that involve both machining and assembly goes against what one would normally find in most job shops. In this paper, the problem of scheduling a set of N final products on M machines in a job shop environment that involve both machining and assembly operations is addressed. The objective pursued is the minimization of production flow time (makespan). A mathematical model is developed in an effort to obtain optimal solutions. Because this type of model grows exponentially as the size of the problems increases, an heuristic solution approach is developed to solve the problems more efficiently. The models are tested and compared on several test problems.     

Integrated scheduling and self-reconfiguration for assembly job shop in knowledgeable manufacturing

The problems of integrated assembly job shop (AJS) scheduling and self-reconfiguration in knowledgeable manufacturing are studied with the objective of minimising the weighted sum of completion cost of products, the earliness penalty of operations and the training cost of workers. In AJS, each workstation consists of a certain number of teams of workers. A product is assumed to have a tree structure consisting of components and subassemblies. The assembly of components, subassemblies and final products are optimised with the capacity of workstations simultaneously. A heuristic algorithm is developed to solve the problem. Dominance relations of operations are derived and applied in the development of the heuristic. A backward insertion search strategy is designed to locally optimise the operation sequence. Once the optimal schedule is acquired, the teams are reconfigured by transferring them from workstations of lower utilisation to those of higher utilisation. Effectiveness of the proposed algorithm is tested by a number of numerical experiments. The results show that the proposed algorithm promises lower total cost and desirable simultaneous self-reconfiguration in accordance with scheduling.     

The application of workload control in assembly job shops: an assessment by simulation

Workload control (WLC) is a production planning and control concept developed to meet the needs of small- and medium-sized make-to-order companies, where a job shop configuration is common. Although simulation has shown WLC can improve job shop performance, field researchers have encountered significant implementation challenges. One of the most notable challenges is the presence of ‘assembly job shops’ where product structures are more complex than typically modelled in simulation and where the final product consists of several sub-assemblies (or work orders) which have to be co-ordinated. WLC theory has not been developed sufficiently to handle such contexts, and the available literature on assembly job shops is limited. In response, this paper extends the applicability of WLC to assembly job shops by determining the best combination of: (i) WLC due date (DD) setting policy, (ii) release method and (iii) policy for coordinating the progress of work orders. When DDs are predominantly set by the company, the DD setting policy should play the leading role while the role of order release should be limited and the progress of work orders should not be co-ordinated in accordance with the DD of the final product. But when DDs are predominantly specified by customers, the importance of order release as a second workload balancing mechanism increases and work orders should be coordinated by backward scheduling from the DD of the final product. Results indicate that WLC can improve performance in assembly job shops and outperform alternative control policies. Future research should implement these findings in practice.     

Priority scheduling policies for repair shops

The use of repair as an alternative to the replacement of products is a growing trend in many industries, especially those employing expensive assets. Repair shop environments are characterized by a greater degree of uncertainty than traditional job or assembly shop environments, and this introduces unique managerial complications. In this study, scheduling policies are examined in the repair shop environment where no end-item spares are available or where the spares stocking decision is deferred until the minimum obtainable flowtimes for enditems are established. Previous studies of scheduling policies have focused on the case where spares are allowed and have not considered all of the sources of variation in the repair environment. The model developed in this study incorporates these sources of uncertainty, as well as other factors likely to influence repair shop performance. The results show that the variability in repair shops is sufficiently higher than in traditional job or assembly shops to warrant different scheduling policies than those previously reported. The choice of scheduling policy to provide minimum flowtimes and RMS tardiness is operating-environment specific, and clear guidelines are presented for the manager in a repair shop environment.     

The economic lot and delivery scheduling problem: the common cycle case

We analyze the interface between a supplier and an assembly facility, where direct shipments are made from one to the other. The final manufacturing step at the supplier involves multiple components produced on a single machine or production line. The assembly facility uses these components at a constant rate. The supplier incurs a sequence-independent setup cost and/or setup time each time the production line is changed over from one component to another. On the other hand, setup costs and times for the assembly facility are negligible. We consider two types of delivery cost: a fixed charge for each delivery, and a fixed-charge-per-truck cost.

We develop a heuristic procedure to find a 'just-in-time' schedule in which one production run of each product and a subsequent delivery of these products to the assembly facility occur in each cycle. The objective is to find the cycle duration that minimizes the average cost per unit time of transportation, inventory at both the supplier and the assembly facility, and setup costs at the supplier. We also develop an error bound for this procedure, and use some of the insights gained from the analysis to explain how delivery schedules can influence the attractiveness of reductions in production setup costs.     

Impact of worker and shop flexibility on assembly cells

Flexibility can counter the negative effects of the loss of pooling synergy in cellular systems. In this study we define flexibility as the ability of assembly cells to reallocate resources to accommodate changes in family assignments (i.e. shop flexibility) and the ability of workers to move between cells (i.e. worker flexibility). We investigate the impact of shop and worker flexibility on different assembly cells faced with product mix variability over a wide range of experimental conditions. Three types of cellular shops are considered: strict cell shops (where each cell is dedicated to producing only one product family), flexible cell shops (where each cell can produce multiple product families), and hybrid cell shops (where some of the cells are strict and the rest are flexible). Results indicate that there is no cell shop that outperforms others, under all experimental environments. However, flexible cell shops showed significant advantages when the setup times were low, while hybrid cell shops provided an excellent alternative when setup times and the product mix unbalance were at ‘moderate to high’ levels. The strict cell shops demonstrated excellent performance when setup times were high, and the product mix unbalance was ‘minor’. Finally, the results suggest that in most cases, the implementation of only worker flexibility resulted in the majority of improvements with respect to the average percentage of jobs tardy.     

Component replacement policies for re workable assemblies

In an assembly process, test operations are often introduced to ensure product quality. After having been rejected by a test operation due to a bad component, a product may be sent to a rework station for component replacement. Some products, however, may have two or more identical components for better reliability or higher capacity. For example, a rack holds a number of identical magnetic storage devices or a computer has multiple processors. Under this situation, different replacement policies may be considered. Bad components can be replaced by either untested ones or known good ones. In the latter case, the assembly line must keep an inventory of good components. Contingent on the condition of replacement components and the method of inventory replenishment, three different policies are identified. Under the first policy, all bad components will be replaced by untested ones, and therefore, the product must be retested. The second policy will replace all bad components with good ones if available. In this case, no additional test is required. However, if the number of bad components is greater than the inventory level, all components ( both good and bad) will be replaced by untested ones. Then the product is sent for retest and good components are placed in inventory. Policy III always replaces the bad ones with good ones. It is assumed that all (good) replacement components come from an independent source. If there are not enough good components for replacement, the product must wait. This paper investigates all three policies, using stochastic models. The performance of a policy is dependent on yield, test time, product configuration, and production demand. A good choice should consider the tradeoff between production lead time and inventory cycle. Numerical results, derived from a real-life case, are presented.     

Mechanism to minimise the assembly time with feeder assignment for a multi-headed gantry and high-speed SMT machine

This paper proposes the development of a mechanism to minimise the assembly time for a multi-headed gantry and high-speed surface mounting technology machine by determining the component assignment to feeder slots. Since a gantry moves long distances in order to pick components, place them on the board and then return them to the feeder slots, we classified the overall assembly time according to the different movements of a gantry. The overall assembly time is then minimised by presenting a new heuristic for the feeder assignment, consisting of Nearest Component Allocation (NCA) and Globally Updated Assignment (GUA). NCA contains information about how each component type locates closely to others on the board. Using the solution from NCA, the component distance function calculates the most representative distance between component types. Then, GUA is applied to improve the NCA solution. The experiments consist of several printed circuit boards with numbers of component types and points to be placed. Highlights of this paper are that: a classification of the gantry movements is proposed based on the average speed; a heuristic NCA-GUA for feeder assignment is developed by considering the placements on the board; the computational time is greatly reduced by NCA-GUA without degrading the solution quality; and a decision process for nozzle assignment is proposed to minimise the overall assembly time. The results show how NCA and GUA affect the final results, and how this mechanism leads to better performance than a genetic algorithms or 2-opt swap search. This comparison proves that our method provides competitive and effective solutions in terms of minimising the overall assembly time.     

Scheduling manufacturing systems for delayed product differentiation in agile manufacturing

Production of customized products to respond to changing markets in a short time and at a low cost for agile manufacturing can be implemented with delayed product differentiation in a manufacturing system. The successful implementation of delayed product differentiation lies in efficient scheduling of the manufacturing system. Scheduling problems in implementing delayed product differentiation in a general flexible manufacturing system are defined, formulated and solved here. The manufacturing system consists of two stages: machining and assembly. At the machining stage, a single machine is used to produce standard component parts for assembly products. These parts are then assembled at the assembly stage by multiple identical assembly stations to form customized products. The products to be produced in the system are characterized by their assembly sequences represented by digraphs. The scheduling problem is to determine the sequence of products to be produced in the system so that the maximum completion time (makespan) is minimized for any given number of assembly stations at the assembly stage. Based on the representation of assembly sequence of the products, three production modes are defined: production of a single product with a simple assembly sequence ; production of a single product with a complex assembly sequence ; and production of N products . According to the three defined production modes, the associated scheduling problems are defined as G s scheduling problems, G c scheduling problems and N-product scheduling problems, respectively. Optimal and heuristic methods for solving the scheduling problems are developed. The computational experiment shows that the heuristics provide good solutions to the scheduling problems.     

Balancing printed circuit board assembly line systems

This paper considers the placement of components onto printed circuit boards (PCBs) using surface mount technology. Multiple automatic placement machines, a variety of PCB types and a large volume for each PCB type characterize the environment studied. The problem addressed is that of allocating and arranging the components on several placement machines, organized into one or several assembly lines, while considering a different assembly time if components are located at different feeder locations. The one assembly line problem is equivalent to balancing a multi-model assembly line where models are assembled in small batches without component rearrangement between model changes. The objective is tominimize the weighted sum of each assembly PCBcycle time, which is defined as the maximum time a PCB has to spend on each machine. We solve this problem with Lagrangian relaxation techniques. Industrial case study results are presented. We also compare the global performance of five placement machines if they are organized as a single assembly line or broken down into two or more assembly lines.     

Integrated optimisation of scheduling and ordering based on semi-finished goods delayed differentiation

The implementation of dynamic ordering policies is becoming increasingly important for the competitiveness of modern manufacturing systems. However, existing models on dynamic ordering pay little attention to production scheduling, which greatly affects the fulfilment of dynamic ordering, especially in complex manufacturing systems. Therefore, it is imperative to establish a new model which integrates both dynamic ordering and production scheduling. Accordingly, a quantitative measurement method for integration is needed. To this end, this paper proposes a semi-finished goods delayed differentiation (SFGDD) model by taking into account integration of the scheduling inventory control and dynamic ordering simultaneously. The objective of this model is to study the relationship between the shop floor inventory and the ordering control based on the semi-finished goods dynamic dispatching mechanism. In addition, the days of inventory (DOI) and a backorder penalty exponential function are developed to quantitatively measure such a relationship. To obtain the optimal results, this paper employs a heuristic genetic algorithm (HGA) with a heuristic encoding scheme to synchronise the generation and selection of inventory variables coherently. A case study on a semiconductor assembly and test manufacturing (ATM) is presented, and a significant revenue enhancement and inventory reduction are achieved accordingly.     

Component Inventory Costs in an Assembly Problem with Uncertain Supplier Lead-Times

We present a generic study of inventory costs in a factory stockroom that supplies component parts to an assembly line. Specifically, we are concerned with the increase in component inventories due to uncertainty in supplier lead-times, and the fact that several different components must be present before assembly can begin. It is assumed that the suppliers of the various components are independent, that the suppliers' operations are in statistical equilibrium, and that the same amount of each type of component is demanded by the assembly line each time a new assembly cycle is scheduled to begin. We use, as a measure of inventory cost, the expected time for which an order of components must be held in the stockroom from the time it is delivered until the time it is consumed by the assembly line. Our work reveals the effects of supplier lead-time variability, the number of different types of components, and their desired service levels, on the inventory cost. In addition, under the assumptions that inventory holding costs and the cost of delaying assembly are linear in time, we study optimal ordering policies and present an interesting characterization that is independent of the supplier lead-time distributions.     

Mixed model assembly system with multiple secondary feeder lines: layout design and balancing procedure for ATO environment

The constant research for efficiency and flexibility has forced assembly systems to change from simple/single assembly lines to mixed model assembly lines, while the necessity to reduce inventory has led the transition from single to multi-line systems, where some components are assembled in secondary lines, called feeder lines, connected to the main one by a ‘pull philosophy’. A possible approach to configure such an assembly system is to balance the main line first and use the retrieved cycle time to balance each feeder line separately, which is a questionable solution, especially if operators can perform tasks on both the feeder and the main line. Moreover for its complexity the mixed model balancing problem is usually solved transforming it into a single model by creating a single ‘virtual average model’, representative of the whole production mix. The use of a virtual average model assumes that the processing times of some models are higher or lower than the cycle time, which creates overload/idle time at the stations. This approach, especially in complex multi line production systems, largely reduces the assembly line productivity and increases the buffers dimensions. This paper faces the mixed model assembly line balancing problem in the presence of multiple feeder lines, introducing an innovative integrated main-feeder lines balancing procedure in case of unpaced assembly systems. The proposed approach is compared with the classical one and validated through simulation and industrial applications.     

Investigations into the impact of flexibility on manufacturing performance

This paper provides investigative insights into the impact of routeing flexibility, machine flexibility, and product-mix flexibility on the performance of a manufacturing plant. The study employs simulation modelling as the primary tool. The facility modelled is an automobile engine assembly plant consisting of a FMS (flexible manufacturing systems), job shop, and assembly line. A variety of experiments, with the FMS exhibiting one or more of the above three flexibilities at different levels, were simulated on the model. In each experiment the manufacturing performance as given by flow time and work-in-process inventory was tracked. The experiments focused first on the FMS itself, and then on the entire plant. Measures for the three flexibilities are introduced. The simulation results are analysed in detail. The results indicate significant performance benefits in context of the FMS, but little in context of the overall plant     

LOT SIZING IN ASSEMBLY SYSTEMS WITH RANDOM COMPONENT YIELDS

We investigate the problem of choosing optimal lot sizes in assembly systems when component manufacturing or procurement yields, and possibly assembly yields, are random. For a single-period setting, we analyze two models. The first has components with identical yield distributions and costs, random demand and an imperfect assembly stage. We analyze this two-stage problem, and highlight the implications of the results for the single-stage case where the final product is just a set of good components. The second model is a single-stage system where components have non-identical yield distributions and costs. We analyze a two-component system with known demand, identify conditions for concavity, and derive the optimality conditions.