Impact of random defective rate on lot size focusing work-in-process inventory in manufacturing system

Literature has focused inventory models with intensive emphasis on imperfect production processes in recent past. However, the work-in-process-based inventory models have been ignored, relatively, in general and the impact of random defects in the form of reworkable and non-reworkable defect rate on lot size and total cost function in particular. This paper develops mathematical models for work-in-process-based inventory by incorporating the effect of random defects rate on lot size and expected total cost function. Our proposed models assume that defective products produced during the production process follow random distributions. Defective products, either in the form of reworkable or rejected production units, follow four types of distribution density functions: uniform, triangular, double triangular and beta distribution. Mathematical models are derived for optimum lot size based on minimization of expected total cost function through the analytical optimization approach. Numerical examples and detailed sensitivity analysis are carried to illustrate and compare the proposed models at different levels of distribution functions’ parameters.     

Capability-based distributed layout approach for virtual manufacturing cells

It is shown in the literature that in highly volatile manufacturing environments functional job shops and classical cellular manufacturing systems do not perform well. Classical cellular manufacturing systems are very sensitive to changing production requirements due to their limited flexibility. In order to adapt cellular manufacturing systems to volatile manufacturing environments, the virtual cellular manufacturing concept was proposed in the 1980s by the National Bureau of Standards in USA. This concept is similar to group technology where job families are processed in manufacturing cells. The main difference between a virtual cell and the classic cell is in the dynamic nature of the virtual manufacturing cell; whereas the physical location and identity of classic cell is fixed, the virtual cell is not fixed and will vary with changing production requirements. The virtual manufacturing cell concept allows the flexible reconfiguration of shop floors in response to changing requirements. In the literature, the formation and scheduling process of virtual cells are clearly explained and researched in detail. However, the layout issue is not addressed entirely. Virtual cells are generally formed over functionally divided job shops. Forming virtual cells over a functional layout may adversely affect the performance of a virtual cellular manufacturing system. There is a need to search for different layout strategies in order to enhance the performance. The distributed layout approach may be a better alternative for virtual cellular manufacturing applications. In this research paper, a novel capability-based approach is proposed for the design of distributed layouts. A simulated annealing based heuristic algorithm is developed from the distributed layout. The proposed approach is tested with a problem with real data. An example is also shown in order to give an idea about the superiority of a capability-based distributed layout over the functional layouts in forming virtual manufacturing cells.     

Maximising profit for multiple-product,single-period,single-machine manufacturing under sequential set-up constraints that depend on lot size

The classical problem of order acceptance/rejection in make-to-order environments, when aiming to maximise profit with machine set-ups is extended in this paper to multiple set-ups depending on manufacturing batch size. In this case, if the manufacturing batch is larger than certain product-dependent bounds, not only is the initial set-up required but also periodic reset-ups are in order, generating sub-batches of the same order, such as tool resharpening and machine recalibration. A network formulation provides the basis for identifying effective algorithms to obtain a solution to the problem. A binary programming model (BPM) and a dynamic programming formulation (DPF) are proposed to solve the problem to optimality. In addition, two heuristics are developed to obtain lower bounds on maximum profit: each attempt to maximise customer satisfaction under production time restrictions, and to provide an extension to the classical knapsack problem. Numerical experimentation shows that computational time is not an issue when BPM and heuristics are applied, but the cost of commercial solvers for BPM algorithms might be problematic. However, if the aim is to code the DPF in-house, the curse of dimensionality in dynamic programming must be addressed, although dynamic programming does yield a full sensitivity analysis, which is useful for decision-making.     

Stochastic lot sizing for maximisation of shareholder wealth in make-to-order manufacturing

Current research in production planning focuses mainly on optimising operational objectives, taking little consideration of the primary principle of corporate governance and investor interests. Such approaches often overlook the critical roles of the cost structure and financial position of a firm, rendering the optimisation results unreliable. This paper studies stochastic lot sizing optimisation in make-to-order manufacturing, with an aim to maximise the full investor interests, well known as shareholder wealth. It presents a relatively simple yet reliable lead time model based on probability theory and stochastic processes. Moreover, the impacts of macroeconomic factors are examined to seek potential drivers for shareholder wealth. Theoretical optimality properties are proved to validate the effectiveness of the proposed model in dealing with batch production planning. Numerical examples and analytical results are presented to illustrate the significance of considering such economic and financial constraints and shareholder wealth. These results highlight that the proposed model can help improve shareholder wealth, and that it is a useful tool for examining the potential challenges and opportunities of shareholder wealth creation in production planning.     

Subwavelength size determination by spatially modulated illumination virtual microscopy

A new approach for determining the sizes of individual, small fluorescent objects with diameters considerably below the optical resolution limit is described in which spatially modulated illumination (SMI) microscopy and 360-647-nm excitation wavelengths are used. The results of SMI virtual microscopy computer simulations indicate that, in this wavelength range, reliable measurements of sizes as small as approximately 20 nm are feasible if the low numbers of fluorescence photons that are usually detected from such small objects are taken into account. This method is based on the well-known fact that the modulation of the diffraction image in a SMI microscope is disturbed by the size of the object. Using appropriately calculated calibration functions, one can use this disturbance of the modulation to determine the size of the original object.     

Effect of learning and forgetting on economic lot size scheduling problem

The paper determines the sequence of set-ups and quantity to produce in each setup if two products are to be produced on a single facility, considering the effects of learning and forgetting. The cost expression which is to be minimized, consists of three factors: set-up cost, carrying cost and the cost of idle facility. A solution procedure is developed and the analysis is extended for the n-product system.     

Improvement of manufacturing processes with virtual reality-based CIP workshops

The Continuous Improvement Process (CIP) is a well-established method to improve manufacturing processes. A typical CIP workshop, carried out by a group of workers and engineers directly in production, often causes unwanted downtimes. Furthermore, improvements have to be realised without reliability testing. Virtual Reality (VR) provides a powerful means to support CIP workshops. This paper introduces the concept of a VR-based CIP workshop. User interfaces are proposed to integrate additional elements, e.g. findings of augmented reality, into VR. This allows meeting specific demands of different participants involved in a CIP workshop. The proposed concept is validated based on an industrial use case.     

Sequential stability of the constant cost dynamic lot size model-searching for monotonicity

The set of cost inputs for which an optimal solution of the dynamic lot size model remains valid is called stability region. The size of this region may be viewed as a measure of robustness of a solution. It is an expectation that the stability regions shrink with growing time horizons and that they are monotonous in this sense. In the present paper several sufficient conditions implying monotonicity will be studied. The conditions cover the existence of planning and forecast horizons and generalize the results of a previous paper in wich monotonicity results were presented for the case of ordinary planning horizons.     

A study of improving overlay accuracy by applying a new outlier handling method in FPD manufacturing

As the pixel size of display devices has been reduced, overlay accuracy between layers needs to be more improved in flat panel display (FPD) manufacturing. However, because of large substrate size and non-uniform processes in FPD manufacturing, an improvement of overlay accuracy has been a challenging work. As an effort to improve overlay accuracy, overlay error correction, which is a kind of feedback control similar to one in semiconductor manufacturing, has also been applied in the photo lithography processes for FPD. However, its characteristics and problems were not technically well investigated as much as in semiconductor manufacturing. This paper investigates one of the problems encountered in the practice of the overlay error correction: outliers in the measurement of overlay errors. Such outliers can cause undesirable effects on overlay accuracy, if used for the overlay error correction. In order to systematically cope with such outliers, a new framework is proposed for detecting and handling outliers as well as for verifying the result. In the consideration of the proposed framework, a new outlier detecting and handling method is also proposed. This method is based on a robust regression technique and is compared with others through simulation to confirm its better performance.     

Effect of rework,rejects and inspection on lot size with work-in-process inventory

The economic order quantity and economic production quantity models are the most commonly used inventory models in production environments for the calculation of optimum lot size. However, these models are based on the unrealistic assumption that every process produces good quality products every time. Moreover, the impact of inspection is neglected in all extended inventory control models involving work in process inventory. By taking both imperfect production and lot size inspection into consideration, this paper presents a more realistic approach for the modelling of optimum lot size and total cost with a focus on the work in process inventory. A mathematical model is derived for optimum lot size based on the minimisation of the average cost. Our approach incorporates the effect of rework, rejects and inspection on work in process inventory. The significant effect of imperfect production and inspection on optimum lot size is evaluated via numerical examples. In comparison to existing models, the proposed model is a more generalised and flexible form of inventory model for independent demands.     

The impact of lot sizing and sequencing on manufacturing performance in a two-stage hybrid flow shop

This paper deals with the problem of production scheduling in a two-stage hybrid flow shop, which consists of one machine in the first stage, and multiple process lines in the second stage. In the first stage, materials are batch-processed, which are then fed into one of several process lines in the second stage, depending on the final product specifications. First, we formulated the total flow time or makespan, the capacity utilization and the maximum work-in-process level as measures of manufacturing performance. We analysed, through a series of numerical experiments, how these performance measures are affected by lot sizing, sequencing rules and the scheduling scenario. The following points were clarified. (1) The ratio rule yields the best performance with regard to the makespan, but the LPT rule yields the best performance with regard to the maximum work-in-process level, (2) The optimum lot size is also affected by such operation conditions as the unit processing time, the setup time, and the ratio of unit processing times in the two stages. (3) The starting point for making a schedule should be set in the bottleneck stage with regard to the makespan.     

Design and implementation of a virtual information system for agile manufacturing

In the new and emerging agile manufacturing paradigm, where multiple firms cooperate under flexible virtual enterprise structures, there exists a great need for a mechanism to manage and control information flow among collaborating partners. In response to this pressing need, this paper addresses the design and implementation of an agile manufacturing information system integrating manufacturing databases dispersed at various partner sites. We propose a framework in which: (1) information is modeled in a hierarchical fashion using object-oriented methodology (OOM); (2) information transactions are specified by the workflow hierarchy consisting of partner workflows; (3) information flow between partners is controlled by a set of distributed workflow managers (WM) interacting with partner knowledge bases, which reflect partner specific information control rules on internal data exchange, as well as inter-partner mutual protocols for joint partner communications; (4) the prototype system is accomplished using the World Wide Web based on a client-server architecture. The overall approach and system provides within a dynamic environment, where virtual partnerships are synthesized in response to specific business initiatives, a dynamic and flexible mechanism to support partner information exchange and to keep the dispersed information consistent.     

The ergonomic design of workstations using virtual manufacturing and response surface methodology

The increasing use of computerized tools for virtual manufacturing in workstatin design has two main advantages over traditional methods first it enables the designer to examine a large number of design solutions; and second, simulation of the work task may be performedin order to obtain the values of various performance measures. In this paper a ne~ structural. methodology for the workstation design is presented. Factorial experiments and the response surface methodology are integrated 111 order to reduce the number of examined design solutions and obtain an estimate for the best design configuration With respect to multi-objective requirements.     

Development and application of a worker assignment model to evaluate a lean manufacturing cell

In lean manufacturing environments, cross-training is often used to achieve multi-skilling in order to increase flexibility in meeting fluctuating demand, to create a shared sense of responsibility, and to balance workload between cross-trained workers. This paper presents a model that assigns workers to tasks within a lean manufacturing cell while minimizing net present cost. In determining how to assign workers to tasks, the model addresses production requirements to meet customer demand, skill depth requirements for tasks, varying quality levels based on skill depth, and job rotation to retain skills for a cross-trained workforce. The model generates an assignment of workers to tasks and determines the training necessary for workers to meet skill requirements for tasks and customer demand. While the model can be used in a number of ways, in this paper it is used to generate a worker assignment schedule for cross-trained workers in a dedicated lean manufacturing cell in an electronics assembly plant and to evaluate the effect of increased cross-training on the cell. The resulting worker assignment schedules for the current state and several alternative scenarios for the cell are evaluated using cost results from the optimization model and from a simulation model to assess additional performance metrics. These results demonstrate the usefulness of the worker assignment model and indicate that moderate increases from current cross-training levels are not beneficial for this cell.     

Robust assignment of customer orders with uncertain configurations in a production network for aircraft manufacturing

Production of multi-variant products in a network requires the assignment of customer orders to locations and periods. This is a highly complex planning task, as requirements of procurement, production, distribution, and sales have to be considered. Providing customers with the flexibility of configuring their ordered products after order assignment further increases the complexity of the planning task by taking uncertainty into account. Therefore, a robust optimisation model, using scenarios representing potential customer-specific order configurations, is introduced. By providing enough flexibility to handle maximum work overload caused by the potential order configurations at locations, a robust assignment of orders can be guaranteed in order to avoid undesirable situations causing delays and additional costs. Therefore, the mid-term adjustments of the flexibility limits are enabled by the changeability of workforce supply by making use of external workers. An industrial application of the model in manufacturing of the Airbus A320 Family of aircrafts is presented. The costs for offering configuration flexibility to customers are quantified by the expected value of perfect information. The explicit consideration of configuration uncertainty through the use of scenarios is discussed based on the value of the stochastic solution in comparison to the results attained by simplistically using the expected value.     

Determination of batch size at a bottleneck machine in manufacturing systems

In manufacturing systems, there often exists a bottleneck machine whose capacity is equal to or less than the market demand. Any idle or waste time at the bottleneck machine directly impacts the output of the entire plant because it results in a loss of throughput. In order to maximize the capacity utilization by less setup losses at the bottleneck machine, the parts are often produced in batches. Traditionally, most batch sizing decisions are made based on the economic order quantity model where setup and inventory holding costs are considered. This paper presents an alternative method to determine batch size at a bottleneck machine. We present a new objective function and cost factors for batch sizing and investigate queuing and throughput models. A linear search algorithm is introduced to find the optimal throughput rate and batch size at the same time. Numerical examples are examined to see how the batching algorithm works.     

Development of electric virtual impactor with variable sampling particle size range

An electric virtual impactor with a capability of sampling fine and ultrafine particles was developed and its performance was evaluated both numerically and experimentally. The electric virtual impactor was provided with metallic electrodes, to which electric voltage in the range of 75–9000 V was applied for creating an electric field within the virtual impactor. Particle electric mobility was utilized to sample ultrafine particles at the major outflow section, while particle inertia was employed to collect fine particles at the minor outflow section. Silver nanoparticles with known charge level and Arizona test dust were used to experimentally validate the performance of the electric virtual impactor. Numerical and experimental outcomes agreed well with each other. The upper cutoff size of the electric virtual impactor was fixed at about 2.6 μm, while the lower cutoff size varied from 7 nm to 110 nm depending on the applied electric voltage. As a result, the proposed electric virtual impactor was able to sample both fine and ultrafine particles of a desired particle size range.     

Minimization of tool switches for a flexible manufacturing machine with slot assignment of different tool sizes

The problem addressed in this paper is the tool switching problem for an automated manufacturing environment, when each tool may occupy more than one slot of the tool magazine. A machine processes parts automatically by using a limited capacity tool magazine. Providing a tool that is needed for a certain processing operation is not in the magazine, a tool switch must occur before the job can be processed, a time/cost consuming operation. To solve this problem, one has to decide three types of decisions, namely, how to select the jobs' sequence (machine loading), which tools to switch before each processing operation (tool loading) and where to locate each tool in the magazine (slot loading). We present an integer programming formulation for the problem and suggest a heuristic procedure to obtain a solution. Our heuristic is partly a generalization of previously suggested approaches to the first two decision types, but it is mainly oriented towards answering the third decision type. The unified problem has not been addressed previously in the literature. We present a numerical study that demonstrates the efficiency of our procedure.     

Analysis of operating policies for manufacturing cells

We present an analytical model for error-recovery problems of unitary production cells and develop a framework for economic justification. Each production cell has its own machine and functional characteristics (e.g. precision, speed, operating cost). Each alternative operating policy of error-recovery for a production cell leads to a different system throughput, scrap rate, and required quantities of parts. However, error recovery cannot be accomplished without in-process inspections. Thus, the central problem discussed in this paper is to maximize profits or throughput rate by selecting an appropriate production cell along with an optimal set of inspection and error recovery policies.     

Performance comparison of virtual cellular manufacturing with functional and cellular layouts in DRC settings

This study investigates the performance of virtual cellular manufacturing (VCM) systems, comparing them with functional layouts (FL) and traditional, physical cellular layout (CL), in a dual-resource-constrained (DRC) system context. VCM systems employ logical cells, retaining the process layouts of job shops. Part family-based scheduling rules are applied to exploit the benefits of group technology while retaining the flexibility and functional synergies of the job shop. Past studies of VCM have been based entirely on single-resource-constrained (SRC) systems, i.e. as purely machine-limited systems, assuming that resources such as labour and tooling do not restrict the output. However, given the fact that labour forms a second major constraining resource, and many of the advantages associated with cellular manufacturing are derived from labour flexibility, it becomes necessary to extend the research to DRC systems. In this study, we assume several levels of labour flexibility in all three systems, in addition to other relevant factors such as lot size, set-up reduction, and labour assignment rules. It is shown that VCM can outperform efficiently operated FL and CL in certain parameter ranges, as preliminary research has shown so far. However, it is shown that CL tends to outperform both VCM and FL in the parameter ranges customarily advocated for CL, namely, low lot sizes, adequate levels of set-up reduction, cross training of workers, and worker mobility within cells.