Controlling work in process during semiconductor assembly and test operations

This paper introduces a mid-term planning model for scheduling assembly and test operations aimed at minimising the difference between customer demand and product completions each day. A secondary objective is to maximise daily surplus which is a surrogate for throughput. Typically, semiconductor companies have 1000s of products or devices in their catalogue that can be organised into unique groups of up to a 100 devices each. This simplifies the planning process because it is only necessary to consider the groups as a whole rather than the individual devices when constructing schedules. In all, we developed and tested three related models. Each provides daily production rates at each process step for each device group for up to one month at a time. The models are distinguished by how cycle time is treated. The first takes a steady-state approach and uses Little’s Law to formulate a WIP target constraint based on the average cycle time at each processing step. The second and third include integer and fractional cycle times in the variable definitions. To find solutions, raw production data are analysed in a preprocessing step and then converted to input files in a standard format. FlopC++ from the COIN-OR open source software project is used to write and solve the model. Testing was done using three data-sets from the Taiwan AT facility of a global semiconductor firm. By comparing model output with historical data for 6 device groups and 33 process steps, we were able to realise decreases in shortages of up to 40% per month.     

Constructing the closed-form solution of control-related states real-time information for insufficient k-th order systems with one non-sharing resource to realize dynamic modeling large TNCS systems of petri nets

Since the contribution from the closed-form solution (CFS) of the number of control-related states (CRSs) of the variant k-th order system can enumerate the number of each type of CRS in real time, we can apply this real-time information to enhance the capability for dynamic modeling of such systems. For example, allocating a non-sharing waiting dummy resource (known as a deadlock thread-holder [DTH]) in each forbidden substate at that location will increase the maximum number of reachable states that can be derived using a CFS in real time. We can thus avoid the occurrence of deadlock without implementing an additional controller. To extend this capability to model a k-th order system with one non-sharing circle subnet allocated at the top position of the left-hand process (denoted as a top non-sharing circle subnet [TNCS] k-th order system) by Petri net (PN), which is the fundamental manufacturing model for different products sharing common parts, this paper extends the existing research on CFS for PNs to an insufficient k-th order system, which is the essential element for a TNCS system with one non-sharing resource. The proposed deadlock avoidance algorithm can be employed to realize the allocation of dynamic non-sharing processes.     

Optimal batching in a wafer fabrication facility using a multiproduct G/G/c model with batch processing

Wafer fabrication, the first portion of semiconductor manufacturing, typically involves numerous batch-processing operations. These operations play an important role in determining how the system performs in terms of throughput, WIP and cycle time. In this paper, batch sizes that minimize the expected cycle time of batch-processing operations for a real-world semiconductor manufacturer are determined by a new approximated analytical model. This model, denoted by G / G ( bp ) , represents multiple products, multiple servers, batch-processing, incompatible products and unequal batch service size queues. Incompatible products mean that different products are not allowed to be in the same batch. Unequal batch service size means that batch service sizes depend upon products. Steady-state approximation formulas for cycle time and WIP of this queuing system are derived. These approximate performance measures are compared with those of discrete-event simulation. The results are reasonable and the approximation formulas much more computationally efficient than conducting the corresponding simulation studies. Finally, a batch-processing system with the goal of minimizing the total expected cycle times of items by determining the 'optimal' batch sizes is presented. Solutions are obtained using genetic algorithms.     

工序分析法在投影仪装配线改善过程中的应用

将投影仪组装作业按照其先后逻辑顺序和作业目的,使用工序图符号对产品组装流程进行工序分析,识别出生产流程改善点.通过改变生产工艺来减少机体反光镜组件的库存,减少在制品库存来缩短停滞时间,改善生产线布局来消除多余搬运活动.通过实施改善方案,工序总数减少,在制品库存降低70%左右,投影仪加工周期大幅降低.     

Scheduling manufacturing systems with work-in-process inventory control: Reentrant systems

In this paper, we propose a procedure for production flow control in reentrant manufacturing systems. The system under study consists ofN machines and producesM product types simultaneously. Each part goes through the system following a predefined process and may visit a machine many times. All machines are subject to random failures and need random repair times. The scheduling objectives are to keep the production close to demand and to keep the WIP inventory level and cycle times at low values. The model is motivated by semiconductor fabrication production. A three-level hierarchical controller is constructed to regulate the production. At the top level of this hierarchy, we perform capacity planning by selecting the desirable buffer sizes and the target production level for each operation. A production flow rate controller is at the middle level which recalculates the production rates whenever a machine fails or is starved or blocked. The loading times for individual parts are determined at the bottom level of the hierarchy. Comparison with alternative control is made through simulation and it shows that the control policy performs well.     

基于eM-Plant对注塑企业的生产线建模仿真

分析了注塑企业生产流程,并建立其生产工序的数学模型和仿真程序。根据企业的订单数量、车间生产线的规模等因素,通过对生产过程中批量的控制,研究批量和在制品库存水平的关系,提出了通过控制批量实现控制在制品的数学关系。     

Setting WIP levels with statistical throughput control (STC) in CONWIP production lines

We develop a simple adaptive production control method for setting WIP levels to meet target production rates in a pull production operating under the CONWIP (Constant work in process) protocol. This method, termed Statistical Throughput Control (STC), uses real-time data to automatically adjust WIP levels (via kanban cards) in the face of noisy estimates of throughput. Because STC does not rely on a steady-state model, it is well-suited to systems subject to environmental changes such as those induced by continuous improvement efforts. Using simulation, we demonstrate the effectivness of STC under a variety of conditions, including single and multiple products, simple flow lines, routeings with shared resources and assembly systems.     

Optimal composition of number and size of machines in a multi-stage make-to-order system with due dates

We develop an optimisation model to minimise costs for work-in-process (WIP), finished goods inventory (FGI), backorders, and capacity for a multi-stage production system applying a work-ahead window work release policy. Customers arrive to a make-to-order production system and have stochastic due dates. The parameters to optimise are the capacity invested at each stage, consisting of the number of machines and the processing rate (defined by a set of possible processing rates), as well as the work-ahead window. An optimality condition is provided showing when it is optimal to invest into a single machine at each stage if processing rates are continuous decision variables. The optimality of increasing capacity towards the customer end of the production line is proven under certain conditions. For a special case consisting of two stages with M/M/s queues with exponentially distributed customer required lead time, explicit expressions for WIP, FGI and backorders are developed. A set of numerical examples illustrates the influence of predefined processing rates on the optimal number and selection of machines. A simple solution heuristic for the problem with a predefined set of processing rates is proposed and its performance is shown in a numerical example. Additionally, the influence of uncertain input rates into the production system is discussed.     

多产品串并联生产系统动态看板的设计和计算

针对机电产品企业普遍采用的多品种、串并联生产系统,提出了批量轮番生产方式下采用动态看板作为控制手段时看板内容的设置和看板数量的计算方法,使得看板的内容和数量能随“需求”而动态变化,实现了“多品种均衡”生产和现场在制品数量的有效控制。     

Event-driven multi-agent ubiquitous manufacturing execution platform for shop floor work-in-progress management

It has been reported that radio frequency identification (RFID) technology is applied to manufacturing shop floors for capturing and collecting real-time field data. Real-time information visibility and traceability allows decision makers to make better-informed shop floor decisions. It has been a great challenge to process a huge amount of RFID data into useful information for managerial uses. This paper presents an event-driven shop floor work-in-progress (WIP) management platform for creating a ubiquitous manufacturing (UM) environment. The platform aims to monitor and control dynamic production and material handling through RFID-enabled traceability and visibility of shop floor manufacturing processes. The platform provides facilities to process shop floor real-time RFID events and to aggregate actionable and meaningful operational information to support decision-making activities. An information processing mechanism based on a critical event model is proposed to organise real-time field data in various abstract levels for enterprise decisions. A case study at an air conditioner manufacturing company is used to demonstrate how the proposed platform can benefit its shop floor WIP management by showing how production and logistic operators and their supervisors accomplish their tasks.     

光通讯产品在制品数量目标研究

以实际的光通讯生产线在制品数量为研究对象,研究生产线在制品数量的设定方法。分别运用分段计算方法和排队论的［M/M/s］∶［∞/∞/FCFS］ 模型以及［M/M/s］∶［N/∞/FCFS］模型研究其目标值,分析结果表明： ［M/M/s］∶［N/∞/FCFS］模型建立的目标值切合实际,故以此为目标,提出生产管理改善措施,实现在制品数量目标控制,使在制品数量降低50%,生产周期减少50%,流动资金占用减少1875万元,很好地验证了该方法的合理性和科学性。     

Base stock versus WIP cap in single-stage make-to-stock production–inventory systems

A single-stage production-inventory system produces parts in a make-to-stock mode, and unsatisfied demand is backordered. The system operates under a so-called base stock with WIP cap replenishment policy, which works as follows. Whenever the Work-In-Process (WIP) plus finished goods inventory falls below a specified level, called base stock, a replenishment order for the production of a new part is issued. If the WIP inventory is below a different specified level, called WIP cap, the order goes through and a new part is released for production; otherwise, the order is put on hold until the WIP inventory drops below the WIP cap. First, it is shown that the optimal base stock that minimizes the long-run, average, inventory holding cost for a given minimum customer service level, is a non-increasing function of the WIP cap that reaches a minimum value, called minimum optimal base stock, at a finite WIP cap value, called critical WIP cap. Then, it is shown that the optimal WIP cap is less than or equal to the critical WIP cap and therefore the optima! base stock is greater than or equal to the minimum optimal base stock. More interestingly, however, it is conjectured that the optimal WIP cap is in fact exactly equal to the critical WIP cap and therefore the optimal base stock is exactly equal to the minimum optimal base stock. The minimum optimal base stock is none other than the optimal base slock of the same system operating under a classical base stock policy (with no WIP cap). Finally, the optimal parameters of a system operating under a base stock with WIP cap policy are related to the optimal parameter of the same system operating under a make-to-stock CONWIP policy.     

An exploratory study of disaggregated clearing functions for production systems with multiple products

Clearing functions (CFs) have shown considerable promise for representing production capacity in production planning models due to their ability to capture the non-linear relationships between throughput, order releases and lead times. Most CFs developed to date use the total work in progress of all products, in units of processing time, as the state variable. In this paper, we investigate CFs for multi-product systems where the overall throughput of the system is affected by the product mix. We show that the aggregate work in process (WIP) variable used in the previous CF literature may lead to inaccurate estimates of expected throughput for individual products. To address this issue, we explore the use of multi-dimensional CFs (MDCFs) that use an extended definition of resource state based on the disaggregated WIP levels for individual products. Several new functional forms for MDCFs are postulated for single machine multi-product systems and their ability to represent system behaviour is assessed using simulation experiments. Results reveal that MDCFs are better able to predict system performance in the presence of mix-dependent capacity losses. We also discuss the extension of the MDCF approach to multi-stage production systems.     

Solving coupled task assignment and capacity planning problems for a job shop by using a concurrent genetic algorithm

The problems of task assignment and capacity planning of manufacturing systems have been researched for many years. However, in the existing literature, these two types of problems are researched independently. Namely, when solving the task assignment problem, it is usually assumed that the production capacity of the manufacturing systems has been determined. On the other hand, when solving the capacity planning problem, the production tasks assigned to the workstations in the manufacturing system have also been determined. Actually, the task assignment problem and the capacity planning problem are coupled with each other. When we assign production tasks to workstations, production capacities of these workstations should be regulated so that they are enough for completing the tasks. At the same time, when planning the production capacity, we must know what production tasks are assigned to what workstations. This research focuses on the coupling relations between the two problems for a closed job shop, in which the total work-in-process (WIP) is assumed to be constant. The objective of the task assignment problem is to balance the workloads of the workstations and the objectives of the capacity planning problem are maximising the throughput and minimising total costs of machine purchasing and WIP inventory. We construct the fundamental system architecture for controlling the two coupled optimisation processes, and propose a concurrent genetic algorithm (CGA) to solve the two coupled optimisation problems. The influences of the decision variables of one problem on the objective function of the other problem are taken into consideration when the fitness functions of the CGA are constructed. Numerical experiments are done to verify the effectiveness of the algorithm.     

Design and storage cycle time analysis for the automated storage system with a conveyor and a rotary rack

In this paper, we analyse the performance of an automated Work-In-Process (WIP) storage system consisting of a conveyor and a rotary rack. The stability condition and the expected storage cycle time are derived to analyse the performance of the WIP storage system. As part of the storage cycle time analysis, the derived expected waiting times at the conveyor and the rotary rack are important performance measures that can be used for buffer-sizing purpose in such systems. Given the fixed storage space of the rotary rack, we also develop a heuristic approach to determine the near optimum ‘shape’ of the rotary rack so that the expected storage cycle time is minimized. Numerical results are presented to examine the storage cycle time model and the proposed shape design. The analytical model introduces a simple approach over simulation with acceptable accuracy; it is useful when designing such WIP storage systems. Moreover, it can be expanded to model more complex systems. The derived model also provides insightful information on the design parameters that a typical simulation tool can hardly provide.     

Capacitated lot sizing with alternative routings and overtime decisions

Material requirements planning (MRP) is a basic tool for performing detailed material planning function in the manufacture of component parts and their assembly into finished items. MRP's managerial objective is to provide ‘the right part at the right time’ to meet the schedules for completed products. However satisfying end customer demands faster with lower inventories implies smarter scheduling which must simultaneously reflect actual capacity conditions. Therefore, the need is to schedule both capacity and materials simultaneously. Since MRP does not consider the availability of capacity resources to schedule production, consequently the schedules so developed are usually capacity infeasible. This paper proposes a three-step procedure to develop capacity feasible material and production schedules in a finite capacity environment. In the first step, an LP model produces capacity feasible but lot size relaxed planned order releases for all end products and assembly components which are then fed into a MRP processor, where a bill of material (BOM) explosion process generates material plans. Finally, these material plans are introduced to another LP model which assures that capacity feasibility is again restored. The mathematical models developed consider restrictions on lot sizes as well as alternative production routings and overtime decisions. A numerical example also is provided and some future research directions are outlined.     

Optimal process targeting for multi-inputs,multi-stages and multi-characteristics production systems

In this paper, a process targeting model is developed for multi-stages, multi-inputs and multi-characteristics production systems. The model extends a previous single stage, multi-inputs and multi-characteristics production system to an n-stage flow line. Recursion and augmented matrix approaches were used to formulate the n-stage model. The optimal process targeting solution is based on minimising a Taguchi-type quadratic loss function across all production stages. A constrained version of the problem is considered in order to cover a wider class of real life industrial applications. The model is very useful especially for mixing-based processes, batch processes, and other multi-stage and multi-characteristic production processes. Finally, an illustrative example is provided.     

Determining the number of kanbans: a step toward non-stock-production

Just-in-time (JIT) production is a philosophy that calls for reducing work-in-process (WIP) inventory to aid process improvement and reduce process variability. In some cases, JIT production has been misinterpreted as a method that would lead to zero or minimal WIP with a lot size of one. There are no models or theories to achieve the JIT goal, i.e. non-stock-production (NSP), and, in particular, to help determine when and where to maintain this minimal inventory. A kanban system acts as the nerve of a JIT production system whose functions are to direct materials just-in-time to workstations in stages of manufacturing, and to pass information as to what and how much to produce. Indeed, the number of kanbans between two adjacent workstations decides the inventory level of that pair of workstations. With the objective of minimizing WIP inventory level, one model dealing with three cases of production configuration is developed for deciding the optimum number of kanbans. The model is then solved using a Markov process approach which considers the demand of finished products as the departure rate and the production rates of stations as arrival rate. In this paper, the model and solution procedure are illustrated with a numerical example.     

Distribution function of the shortest path in networks of queues

In this paper, we consider acyclic networks of queues as a model to support the design of a dynamic production system. Each service station in the network represents a manufacturing or assembly operation. Only one type of product is produced by the system, but there exist several distinct production processes for manufacturing this product, each one corresponding with a directed path in the network of queues. In each network node, the number of servers in the corresponding service station is either one or infinity. The service time in each station is either exponentially distributed or belongs to a special class of Coxian distribution. Only in the source node, the service system may be modeled by an queue. The transport times between every pair of service stations are independent random variables with exponential distributions. In method proposed in this paper, the network of queues is transformed into an equivalent stochastic network. Next, we develop a method for approximating the distribution function of the length of the shortest path of the transformed stochastic network, from the source to the sink node. Hence, the method leads to determining the distribution function of the time required to complete a product in this system (called the manufacturing lead time). This is done through solving a system of linear differential equations with non-constant coefficients, which is obtained from a related continuous-time Markov process. The results are verified by simulation.This complete issue was revised and published online in November 2004. The previous version contained a false date. Correspondence to: Mohammad Modarres     

AMHS capacity determination model for wafer fabrication based on production performance optimization

Automatic material handling system (AMHS) is becoming more important in 300?mm wafer fabrication factories (fab). Effective and efficient design and control of AMHS has become more critical particularly in capacity planning. The major concept of the AMHS capacity determination model is to maintain the originally designed optimal production throughput or cycle time of products. In order to maintain fab’s throughput or cycle time of products, WIP (work in process) portfolio of the constraint or the fastest workstation should be kept. Based on this concept, a GI/G/m queuing model based on FCFS (First-come-first-serve) dispatching rule of AMHS is applied to determine the required number of vehicles. Basically, products should be transported to the specific workstation (constraint or fastest workstation) before the workstation finishes the existing process; therefore, sufficient WIP in front of this specific workstation should be kept. Under this condition, the probability that transportation time exceeds product processing time under a certain transportation capacity level can be calculated by the proposed model. Hence, we can get the required capacity of AMHS to achieve the probability target set in advance. Due to the capacity of AMHS can be set according to the acceptable probability of non-exceeding the processing time of the constraint or fastest workstation, the level of WIP in front of this workstation can be kept. It also can be ensured that AMHS will not affect the production performance as well as keep the reasonable investment level.