Multiproduct production/inventory control under random demands

Studies the optimal production/inventory control policy for a single machine multiproduct production system. The machine produces to fill the end-product inventory stock and the demand is satisfied from the inventory when available; unsatisfied demand is backlogged until the product becomes available as the result of production. For each product, the demand follows a Poisson process and the unit processing time is known. When the machine switches production from one product to another, it incurs a set-up time and a set-up cost. The relevant costs include the set-up cost, a cost per unit time while the machine is running, and linear costs for inventory and backlogging. This problem is modeled as a semi-Markov decision process using the criterion of minimizing expected total cost with discounting over an infinite horizon. Procedures for computing near-optimal policies and their error bounds are developed. The error bound given by the authors' procedure is shown to be much tighter than the one given by the “norm-based” approach. Computational test results are presented to show the structure of the near-optimal policy and how its accuracy is affected by the system characteristics such as capacity utilization and set-up time     

Manufacturing cost modelling for concurrent product development

This research work aims to develop an intelligent knowledge-based system that accomplishes an environment to assist inexperienced users to estimate the manufacturing cost modelling of a product at the conceptual design stage of the product life cycle. Therefore, a quicker response to customers’ expectations is generated. This paper discusses the development process of the proposed system for cost modelling of machining processes. It embodies a CAD solid modelling system, user interface, material selection, process/machine selection, and cost estimation techniques. The main function of the system, besides estimating the product cost, is to generate initial process planning includes generation and selection of machining processes, their sequence and their machining parameters. Therefore, the developed system differs from conventional product cost estimating systems, in that it is structured to support concurrent engineering. Manufacturing knowledge is represented by hybrid knowledge representation techniques, such as production rules, frames and object oriented. To handle the uncertainty in cost estimation model that cannot be addressed by traditional analytical methods, a fuzzy logic-based knowledge representation is implemented in the developed system. Based on the analysis of product life cycle, the estimated cost included material, processing, machine set-up and non-productive costs. A case study is discussed and demonstrated to validate the proposed system.     

Scheduling concurrent production over a finite planning horizon: polynomially solvable cases

The paper analyzes a manufacturing system made up of one workstation which is able to produce concurrently a number of product types with controllable production rates in response to time-dependent product demands. Given a finite planning horizon, the objective is to minimize production cost, which is incurred when the workstation is not idle and inventory and backlog costs, which are incurred when the meeting of demand results in inventory surpluses and shortages. With the aid of the maximum principle, optimal production regimes are derived and continuous-time scheduling is reduced to a combinatorial problem of sequencing and timing the regimes. The problem is proved to be polynomially solvable if demand does not exceed the capacity of the workstation or it is steadily pressing and the costs are “agreeable”.

Scope and purpose

Efficient utilization of modern flexible manufacturing systems is heavily dependent on proper scheduling of products throughout the available facilities. Scheduling of a workstation which produces concurrently a number of product types with controllable production rates in response to continuous, time-dependent demand is under consideration. Similar to the systems considered by many authors in recent years, a buffer with unlimited capacity is placed after the workstation for each product type. The objective is to minimize inventory storage, backlog and production costs over a finite planning horizon. Numerical approaches are commonly used to approximate the optimal solution for similar problems. The key contribution of this work is that the continuous-time scheduling problem is reduced to a combinatorial problem, exactly solvable in polynomial time if demand does not exceed the capacity of the workstation or the manufacturing system is organized such that the early production and storage of a product to reduce later backlogs are justified.     

Modelling the effect of demand variations on the performance of a production system

Modelling the effect of demand variations on a production system manufacturing multiple products is discussed. The various system costs involved in the production system, namely set-up cost and inventory cost incurred due to change in demands for the products with respect to products and planning periods are estimated. A statistical modelling is presented for determining the production capacity and inventory level requirement to satisfy the customer to a certain level decided by the management. Two important factors, (i) number of types of products and (ii) multiple planning horizons are considered to identify the costs as well as the production capacity and inventory level requirements. A statistical method, analysis of variance (ANOVA) is used to study the variations in the demands and costs involved. Finally, an example is presented to explain the application and the behaviour of the statistical model.     

Intra-supply chain system with multiple sales locations and quality assurance

The emergence of the global economy has transformed the interdepartmental nature of a transnational enterprise into a highly collaborative oriented team. This transformation enables the enterprise to lower its transaction and coordination costs and increase its competitive advantage in the global market. This study investigates such a so-called intra-supply chain system that exists in present-day transnational firms, wherein a single production unit manufactures products to meet the demands of multiple regional sales offices and incorporates quality assurance in its production. The objective of the present study is to determine an optimal production quantity and shipment policy that minimizes the integrated production–inventory–delivery costs for the intra-supply chain system. In this study, considerations related to a product’s quality assurance include inspection for quality, rework of defective items and failure in rework. Delivery of the finished products starts when quality of the entire production lot is assured. Multi-shipment policy is used to synchronously transport finished items to multiple locations for satisfying customer demands in each cycle. Mathematical modeling along with Hessian matrix equations is employed to solve the proposed intra-supply chain system. A numerical example with a discussion and cost-benefit analysis of outsourcing work to an external distributor is presented to demonstrate the practical applicability of the obtained results.     

Finite horizon planning for a production system with permitted shortage and fixed-interval deliveries

Raw material ordering policy and the manufacturing batch size for frequent deliveries of finished goods for a finite horizon plays a significant role in managing the supply chain logistics economically. This research develops an ordering policy for raw materials and determines an economic batch size for a product in a manufacturing system that supplies finished products to customers for a finite planning horizon. Fixed quantities of finished products are delivered to customers frequently at a fixed interval of time. In this model, an optimal multi-ordering policy for procurement of raw materials and production cycle time for a two-stage production and supply system is developed to minimize the total cost incurred due to raw materials and finished goods inventories. The problem is then extended to compensate for the lost sales of finished products. A closed-form solution to the problem is obtained for the minimal total cost. A lower bound on the optimal solution is also developed for problem with lost sale. It is shown that the solution and the lower bound are consistently tight.     

Hierarchical production and setup scheduling in stochasticmanufacturing systems

This paper is concerned with an asymptotic analysis of hierarchical production and setup scheduling in a stochastic manufacturing system consisting of a single failure-prone machine and facing constant demands for a number of products. At any given time the system can only produce one type of product, and the system requires a setup if production is to be switched from one type of product to another. A setup may involve setup time or setup cost or both. The objective of the problem is to minimize the total costs of setup, production, and surplus. The control variables are a sequence of setups and a production plan. An asymptotic analysis with respect to increasing rates of change in machine states gives rise to a deterministic limiting optimal control problem in which there is a control variable associated with each of the machine states and the production rate is obtained by weighting these controls with the stationary probabilities of the corresponding states. Asymptotic optimal controls for the original problem from optimal or near-optimal controls for the limiting problem are constructed     

基于二阶段时间延迟的多产品生产系统生产与维修联合优化研究

针对多产品生产部件串联系统的生产和维修问题进行了研究,提出了基于二阶段时间延迟的联合优化模型。首先,基于生产周期分段理论,将整个周期等分成若干单位时间段,生产与维修共用每段时间,且若干时间段后采取一次预防维修。其次,考虑生产系统的实际生产时间、可用生产时间和维修耗费时间,建立了生产计划与维修计划总成本模型。其中,维修计划考虑缺陷和故障维修费用、维修检查费用,以及非正常状态下设备运行可能产生的不合格产品损失费用;生产计划考虑生产成本、库存成本、延期未交货成本和维修停机后恢复生产的设备启动成本。最后,通过算例分析,计算最优预防维修周期和各单位时间段各产品产量,验证了模型的有效性。     

Determining the capacity and its level of utilization in make-to-order manufacturing: A simple deterministic model for single-machine multiple-product case

A simple deterministic model is developed to determine the capacity and its level of utilization for a single specific machine producing multiple products in make-to-order manufacturing plants. It integrates the variables of processing time, set-up time, product defective rate, and maintenance downtime. The number of product types and the number of lots per product are critical determinants. The model first computes the net production quantities per unit of time for each product type and for the product mixtures, and then, capacity utilization figures are derived based on the net capacity inverse coefficients and net product quantities per planned time unit for each product type and product mixture.     

Supply management for cost minimization in assembly systems with random component yield times

This paper is concerned with inventory control in assembly systems for minimizing production costs. The system manufactures multiple products assembled from various components, and it operates according to a cyclic schedule. At the start of each cycle time, two decisions are made: the product volumes to be assembled during the current cycle, and the component-stock levels to be ordered. For a given decision, there is an associated cost incurred by backlogging of the finished products on one hand, and the component inventory holding cost, on the other hand. The objective here is to balance the two costs so as to minimize their sum. One complicating factor stems from uncertainties in both product demand levels and components yield times. These uncertainties can be modelled by probabilistic means, and hence the cost minimization problem becomes a stochastic problem. This problem can be quite difficult due to the nonlinearity of the equations involved, the mix of integer and continuous parameters, and their large number in moderate-size problems. Our approach in this paper is to first define certain control parameters and thus reduce the number of the variables involved in the optimization problem, and then solve the latter problem by using sophisticated optimization techniques in conjunction with heuristic modelling. We will demonstrate, by numerical means, the resolution of fairly difficult problems and thus establish the viability of the proposed numerical techniques.     

Simulation and design of a dual-kanban production system

A procedure to evaluate system design parameters for “pull” production strategies is presented in this paper. The evaluation procedure is based on a cost function which includes the inventory carrying, storage, setup, stockout, and idle costs. A combined SLAM II/FORTRAN simulation model and electronic spreadsheets support the evaluation procedure. A “pull” production strategy using the dual-kanban production control method is modeled. The best design in terms of unit load size/number of kanbans is found to (a) satisfy daily production requirements and (b) minimize the cost function.     

Electronic spreadsheet implementation of a lot sizing procedure for a single-card kanban system

A cost based procedure to evaluate lot sizing alternatives for a single-card kanban system (also known as “push-pull” system) using a specific production strategy is implemented in an electronic spreadsheet. The spreadsheet and a case study are used to illustrate the cost procedure and sensitivity analysis.

Inventory carrying, storage, and handling costs are considered in the procedure. The lot sizing alternatives generated for the case study were based on the utilization of pallet and tray capacity, and a bottleneck process which complicated the implementation of the “push-pull” strategy.     

制造系统的递阶滚动优化调度模型

研究的对象是只有一台不可靠（failure-prone)机器的非完全柔性制造系统，该系统能生产多种产品，但在同一时刻只能生产一种产品，并且当机器由生产一种产品向生产另一种产品切换时，需要考虑setup时间及其成本，待决策变量是setup序列及产品生产率，本文基于非完全柔性制造系统的特点，引入递阶层控的思想，采用新的递阶结构框架和阈值控制策略，对问题进行分解，建立了考虑setup时间及成本的递阶流率控制最优化调度模型，并给出了递阶的滚动优化算法，仿真结果表明，这种调度策略更易于工程实现。     

Data-Enabled Modeling and Analysis of Multistage Manufacturing Systems with Quality Rework Loops

In a multistage serial production line, multiple inspection stations and repair processes are typically involved to ensure high product quality. Quality rework is the activity to repair or repeat the work on the defect parts during manufacturing processes. The rework process after each inspection can add cost and cycle time to the normal process and impose negative impact on the throughput. This paper studies real-time performance of multistage serial manufacturing systems with quality rework loops and machine random failures. A production line with multiple quality rework loops is first unify by segmenting it into a set of serially connected quality rework loops. An event-based data-enabled mathematical model is developed to evaluate real-time production rate of each machine for such a system. In addition, the system properties are analyzed and permanent production loss due to quality rework loops and random machine failures are identified respectively. The permanent production loss attribution to each disruption event and machine can be used as real-time performance indicators to diagnose production system inefficiency. The mathematical model and system performance identification methodology are studied analytically and validated through numerical case studies.     

Buffer sizing in complex cellular manufacturing systems

This paper addresses the buffer-sizing problem in cellular manufacturing systems. In view of the complex problem structure, an efficient cost-based approach is developed to determine the total buffer capacity and to allocate the buffer spaces to each machine cell. The cost function to be minimized includes the set-up cost to install the buffer storage and the cost of production loss due to limited buffer storage. The first phase of the approach utilizes steady-state queuing statistics to determine the rough-cut buffer size, which is then allocated to each machine cell. In the second phase, a one-dimensional, line-search based procedure is used to determine the minimal cost buffer design. Finally, a local improvement routine is used for the cost minimization. The computational procedure is illustrated by a large, industry-size example. Limited computational results demonstrate the viability of the proposed approach.     

建立在密度聚类与模糊支持向量机基础上的半导体成品率预测

在半导体生产过程中,半导体的成品率即合格品占整个生产线上产品的比例是衡量一个企业生产水平的重要指标之一,成品率的高低直接决定了企业的生产成本,因而研究了一种在密度聚类与模糊支持向量机基础上的半导体成品率预测方法来提高成品率预测的精准度。先介绍了成品率预测中的经验模型和非经验模型两类模型,总结了各自的特点,然后利用密度聚类的方法对晶圆的缺陷进行分析,得到了晶圆缺陷的分布模式和密度参数两个描述缺陷的重要指标,结合两个指标提出了用模糊支持向量机模型预测成品率。通过仿真实验分析,发现提出的采用模糊支持向量机模型比泊松模糊和二项式分布模型有更高的准确率。     

On the search of workstations arrangement in pull production systems

This research presents a model to determine the workstation arrangement and kanban number for pull production systems. Several practical production line characters are considered, and evolutionary algorithms are utilized to obtain the optimal/near-optimal result. The proposed system is a flow-shop, pull production line with N unreliable workstations and N ? 1 inter-stage buffers. Workstations may be allocated to any stage in the production line and have a different processing rate at each stage. Workstations will breakdown/recover at fixed rates, and the operating-breakdown-recovery process is formulated as a Markov process in this model. The size of the inter-stage buffers varies according to the arrangements of workstations. A model is established on the objective of minimizing the total production cost per item of the finished product. The costs considered in the system contain the allocation of workstations, operations, inventory, and production shortage costs. An evolutionary algorithm, genetic algorithm, is used to obtain the allocation of workstations in the production line.     

Job-Shop Scheduling with Cost Indexes: A Probabilistic Model

A production complex for concurrently manufacturing several products is studied. Every product has its own technological route, which is a sequence of jobs implemented on particular machines. The duration of every job is a random variable distributed by a given law. A discrete production time is defined for every product. A schedule for starting the production of all products that minimizes the expectation of total expenses on penalties and storage, i.e., overhead charges, is determined. Such a schedule is random and is formed by choosing a product from a queue for a given period. A decision making model is designed for determining cost indexes.     

A study for optional inspection policies in a flexible manufacturing cell

The objective of the paper is to determine the location of inspection stages in order to minimize the expected total manufacturing cost while satisfying the high-quality product demand of customers in a flexible manufacturing cell (FMC). This allows a designer to examine alternative designs in order to select those which are optimal, or near optimal, in manufacturing cost terms. To accomplish this objective, we have formulated a total manufacturing decision model consisting of machine set-up and processing costs. Inspection set-up and inspection costs, and cost due to defective. A case study and sensitivity analysis are presented to demonstrate the application of the decision model developed.     

Developing a quantitative intelligent system for implementing concurrent engineering design

This research focuses on the development of a quantitative intelligent system for implementing concurrent engineering design. The paper first discusses the task of concurrent engineering design and the basic requirements for conducting integrated concurrent engineering design. The proposed quantitative intelligent system approach combines qualitative reasoning, based upon design and manufacturing knowledge, and quantitative evaluation and optimization, conducted using design information and manufacturing data generated in the knowledge-based reasoning. The method allows considerations on non-operating principle aspects of a product to be incorporated into the design phase, such as manufacturing, maintenance, service, recycle, etc., with an emphasis on production costs. The proposed method serves as a convenient software tool for gathering information required in the concurrent engineering design process and integrates tasks from different parts of the product development life cycle, particularly function design, manufacturability analysis and production cost estimation. A prototype software system is developed based upon this method using Smalltalk-80. In the prototype system, concurrent engineering design is carried out by: (1) describing and representing design requirements; (2) generating feasible design candidates and evaluating their design functions; (3) representing design geometry; (4) finding the associated production processes and predicting the production costs of each feasible design; and (5) identifying the costeffective design that satisfies given design requirements and requires minimum production costs.