A vector space model approach to production planning for a multi-product,multi-cell and multi-stage manufacturing system

This paper develops a formal mathematical approach to aggregate production planning for a multi-product, multi-cell and multi-stage manufacturing system. The model, based upon a vector space approach, includes all the important variables relating to the demand for individual items, inventory levels, the availability of machines taking into account any breakdowns, subcontracting of orders and overtime working. The computational procedure for determining the production planning strategies, in terms of overtime/undertime working and increase/decrease in the number of orders subcontracted, are presented. Three numerical examples are presented showing the use of the model developed. This approach makes it possible to develop realistic models of practical manufacturing systems. It is particularly applicable to flexible manufacturing systems.     

Singular perturbation methods in the synthesis of control policies for multi-stage production-inventory systems

In this paper, singular perturbation methods are used to synthesize control policies for a class of multi-stage production-inventory systems. It is shown that when the production-inventory sub-systems are connected in cascade, the control of each sub-system in isolation leads to undesirable transient behaviour. However, the control of the composite system is shown to yield improved transient behaviour. Furthermore, it is also shown that trade-off between rapid adjustments in production rate and large inventory-level deviation can be achieved by selecting an appropriate value for the feedback gain parameter.     

A multi-stage production-inventory model with learning and forgetting effects,rework and scrap

This paper studies a serial production line where a proportion of defective items is produced at each stage. Defective units enter a rework process, which is imperfect as well. Twice defective items are scrapped. This paper also considers learning and forgetting in production and rework processes and studies how the number of shipments of a lot from a production stage to the next influences the overall performance of the system. A model for a multi-stage production-inventory system is developed and optimized against an aggregate performance measure of four partial measures that are based on production time, process yield, in-process inventory and shipment frequency. Each of these partial performance measures is weighed by the system’s decision maker in accordance to importance. The numerical results show how the values of learning rates, weights assigned to the partial performance measures and the number of production stages influence the overall performance of the system.     

A disruption recovery plan in a three-stage production-inventory system

This paper proposes a recovery plan for managing disruptions in a three-stage production-inventory system under a mixed production environment. First, a mathematical model is developed to deal with a disruption at any stage while maximizing total profit during the recovery-time window. The model is solved after the occurrence of a disruption event, with changed data used to generate a revised plan. We also propose a new and efficient heuristic for solving the developed mathematical model. Second, multiple disruptions are considered, where a new disruption may or may not affect the recovery plans of earlier disruptions. The heuristic, developed for a single disruption, is extended to deal with a series of disruptions so that it can be implemented for disruption recovery on a real-time basis. We compare the heuristic solutions with those obtained by a standard search algorithm for a set of randomly generated disruption test problems, and that show the consistent performance of our developed heuristic with lower computational times. Finally, some numerical examples and a real-world case study are presented to demonstrate the benefits and usefulness of our proposed approach.     

Analysis of a production-inventory control system for a diffusion department

The dynamic behaviour of an actual production-inventory control system, designed for a diffusion department, is analysed by means of classical control theory. The actual control rule acts on the basis of norms for the production progress derived from the application of the line-of-balance technique to the production-inventory system. Attention is paid to the steady-state behaviour, the impulse response and the variance amplification of the controlled system. The cause of the poor dynamic performance observed after implementation of the system in practice is releaved. Especially the variance amplification can be decreased without a general loss of performance with respect to other criteria. An alternative control rule is derived from the application of design notions from classical control theory to the production-inventory problem. The new control rule shows an improved performance in some respects over the actual control rule. The case presented shows that some serious errors in production-inventory control design can be avoided through analysis by means of classical control theory.     

Disruption management in a constrained multi-product imperfect production system

Over several decades, production and inventory systems have been widely studied in different aspects, but only a few studies have considered the production disruption problem. In production systems, the production may be disrupted by priorly unknown disturbance and the entire manufacturing plan can be distorted. This research introduces a production-disruption model for a multi-product single-stage production-inventory system. First, a mathematical model for the multi-item production-inventory system is developed to maximize the total profit for a single-disruption recovery-time window. The main objective of the proposed model is to obtain the optimal manufacturing batch size for multi-item in the recovery time window so that the total profit is maximized. To maintain the matter of multi-product, budget and space constraints are used. A genetic algorithm and pattern search techniques are employed to solve this model and all randomly generated test results are compared. Some numerical examples and sensitivity analysis are given to explain the effectiveness and advantages of the proposed model. This proposed model offers a recovery plan for managers and decision-makers to make accurate and effective decisions in real time during the production disruption problems.     

A periodic tabular policy for scheduling of a single stage production-inventory system

In this paper, we consider scheduling of a multi-item single stage production-inventory system in the presence of uncertainty regarding demand patterns, production times and switchover times. For a given specification of base-stock levels of individual items and under (S − 1, S) requests for replenishment policy, a mathematical program to minimize long-run average system wide costs is formulated. We derive approximations for the first two moments of demand over lead time using residual service analysis of vacation queue models. Subsequently, we develop an approximate convex program for the original cost model and determine optimal production frequencies for individual types. Based on these relative frequencies, we determine a table size and devise an efficient heuristic to construct a tabular sequence in which individual items appear according to their respective absolute frequencies and items are positioned such that variance of their inter-visit times is minimized. A numerical study that demonstrates effectiveness of the proposed policy against cyclic policies is given.     

Step failures semantics and a complete proof system

Summary The (linear) failures semantics is a well-known model for the theoretical version of Hoare's CSP. We generalize this semantics by taking steps (i.e. multisets of simultaneously occurring actions) instead of single actions as the basic execution unit. Hence opposed to the linear semantics — where parallelism is modelled as arbitrary interleaving in order to avoid technical complication — the step failures semantics models parallelism explicitly and is equally easy to manage. In particular a sound and complete proof system is given. Opposed to the linear model divergence is treated uniformly here. The relation to the linear semantics can be established using our newly introduced deparallelize operator.The first author is supported by an Ernst von Siemens scholarship. A preliminary version of this paper appeared in [37]     

The benefit of VMI strategies in a stochastic multi-product serial two echelon system

We consider a multi-product serial two echelon inventory system with stochastic demand. Inventories at the downstream location are replenished periodically using an automatic ordering system. Under vendor managed inventory strategies the upstream stage is allowed to adapt these orders in order to benefit from economies of scale. We propose three different VMI strategies, aiming to reduce the order picking cost at the upstream location and the transportation costs resulting in reduced total supply chain costs. In a detailed numerical study the VMI strategies are compared with a retailer managed inventory strategy for two different demand models suitable for slow moving products. It is shown that if inventory holding costs are low, compared to handling and transportation costs, efficiencies at the warehouse are improved and total supply chain costs are reduced.     

A production-inventory model for decaying raw materials and a decaying single finished product system

In this paper, an attempt has been made to generalize Park's (1983) results on an inventory model for decaying raw materials. This paper extends the results to finished products which are also subject to decay or deterioration. The decay of raw materials and the finished product is assumed to be a constant fraction of the on-hand inventory. The finished product is produced in batches and the raw materials are obtained from outside vendors. The objective is to minimize the exact average total cost function and to obtain the inventory characteristics of the system. When there is no decay in the finished product, the model corresponds to the non-decaying finished product model by Park. An example is given to illustrate the derived results.     

Availability of a distributed computer system with failures

Summary A model for distributed systems with failing components is presented. Each node may fail and during its recovery the load is distributed to other nodes that are up. The model assumes periodic checkpointing for error recovery and testing of the status of other nodes for the distribution of load. We consider the availability of a node, which is the proportion of time a node is available for processing, as the performance measure. A methodology for optimizing the availability of a node with respect to the checkpointing and testing intervals is given. A decomposition approach that uses the steady-state flow balance condition to estimate the load at a node is proposed. Numerical examples are presented to demonstrate the usefulness of the technique. For the case in which all nodes are identical, closed form solutions are obtained.This research was performed while David Finkel and Satish Tripathi were visiting ISEM. Satish Tripathi's research was supported in part by grants from NSF (grant no. DCR-84-05235) and NASA (grant no. NAG5-235), and by Université de Paris-Sud     

Effect of product mix on multi-product pull control

Product mix influences the performance of pull production control strategy in multi-product manufacturing systems. The complexity of product mix on the performance of a manufacturing system is primarily based on the characteristics of the demand and production control strategies. Demands are mainly characterised by volume and product-type while production control strategy is characterised by material release time, part flow, inventory control and throughput times. In multi-product systems, pull production control strategy operates dedicated or shared Kanban allocation policy. This paper examines the performance of the Generalised Kanban Control Strategy (GKCS), Extended Kanban Control Strategy (EKCS) and Basestock Kanban-CONWIP (BK-CONWIP) control strategy operating Shared Kanban Allocation Policies (S-KAP) or Dedicated Kanban Allocation Policies (D-KAP) for a healthcare parallel/serial assembly line with setup times. A simulation based multi-objective optimisation technique was adopted to examine the effect of different product mixes on the strategies and policies. A ranking and selection technique for multiple systems was used to screen the performance of the strategies. It was shown that product mix variability in a system influence the inventory levels of the pull control strategies examined. However, the performances of the strategies vary with strategies operating S-KAP having better inventory control than strategies operating D-KAP. Similarly, BK-CONWIP outperformed its alternatives.     

Planning costs and revenues in a multi-product environment

Each year companies commit to development budgets which include funds for new and ongoing projects. Since the initial funding of a project implies future costs for continuing work and revenues (or other benefits) from the product, it is clear that new project funding for the coming year will continue to affect profit and loss into the future.If the distributions over time of the costs and the resulting revenues can be estimated, a planning model can be built which will facilitate decision-making under criteria such as steady growth in annual costs or specified revenue-to-cost ratio for particular years. The tedious manual application of this model can be greatly assisted by means of an interactive computer program. A long-range development budget can then be quickly prepared.This paper shows in non-mathematical terms how such a model can be developed and applied. The appendix contains the mathematical derivation of the model.     

Lot sizing and unequal-sized shipment policy for an integrated production-inventory system

This article develops a single-manufacturer single-retailer production-inventory model in which the manufacturer delivers the retailer’s ordered quantity in unequal shipments. The manufacturer’s production process is imperfect and it may produce some defective items during a production run. The retailer performs a screening process immediately after receiving the order from the manufacturer. The expected average total cost of the integrated production-inventory system is derived using renewal theory and a solution procedure is suggested to determine the optimal production and shipment policy. An extensive numerical study based on different sets of parameter values is conducted and the optimal results so obtained are analysed to examine the relative performance of the models under equal and unequal shipment policies.     

考虑缓冲区故障的多产品生产系统的性能分析

对带有生产准备时间和缓冲区故障且生产时间服从任意分布的多产品生产系统进行分析,通过构建系统状态向量,建立其离散时间马尔可夫链模型.根据多产品生产系统的工作过程对系统状态向量分4种情况进行讨论,计算出系统的状态转移矩阵;在计算系统稳态向量的基础上获得系统生产率的计算流程.根据所建立的模型,对参数对称且可生产两种产品的多产品生产系统进行详细求解,给出其系统生产率的计算过程,通过Matlab进行数学实验,分析总结出缓冲区的无故障率、产品到达率、生产准备时间、服务率及其变异系数对系统生产率的影响.     

Perceptions of system development failures

According to the expectation failure theory, information system failures can occur during development or during system use and may be viewed differently by various stakeholder groups. This premise is examined via a survey of system developers and system users about their perception of frequency of system development problems. The data indicates that users and developers of information systems perceive certain problems at different levels of occurrence.     

Optimal production planning for a multi-product closed loop system with uncertain demand and return

We study the production planning problem for a multi-product closed loop system, in which the manufacturer has two channels for supplying products: producing brand-new products and remanufacturing returns into as-new ones. In the remanufacturing process, used products are bought back and remanufactured into as-new products which are sold together with the brand-new ones. The demands for all the products are uncertain, and their returns are uncertain and price-sensitive. The problem is to maximize the manufacturer's expected profit by jointly determining the production quantities of brand-new products, the quantities of remanufactured products and the acquisition prices of the used products, subject to a capacity constraint. A mathematical model is presented to formulate the problem and a Lagrangian relaxation based approach is developed to solve the problem. Numerical examples are presented to illustrate the model and test the solution approach. Computational results show that the proposed approach is highly promising for solving the problems. The sensitivity analysis is also conducted to generate managerial insights.     

多阶灰色支持向量机集成预测模型研究

对灰色预测模型GM(1,1)和支持向量机SVM预测模型进行分析,提出了多阶灰色支持向量机集成预测模型Dm_GM(1,1)-SVM。通过多阶缓冲算子改进灰色预测模型的预测精度,对最终预测值的各个相关指标进行预测;同时,采用粒子群优化算法对支持向量机模型进行径向基核参数和惩罚参数寻优,得到最佳参数对(c,g),从而确定支持向量机的最佳回归模型;最后将各指标预测值作为支持向量机模型的输入,依据预测模型和预测模型的输入值求得预测结果。实验实例表明,多阶灰色支持向量机集成模型和传统的预测模型相比,在本例中预测精度更高,说明多阶灰色预测模型和支持向量机模型相结合在解决实际预测问题中具有实用价值。     

Modal control theory and industrial dynamics — a dual approach to the design of policy decisions in a multistage production-inventory system

This paper deals with the problem of designing realistic policy decisions in a Multistage Production-Inventory System (MPIS). First Modal Control Theory has been utilised for the synthesis of control policies in a two-stage production-inventory system. The structure of the resultant control policies, though somewhat idealised, has an underlying implication of central control. Two types of realistic policy decisions are made and tested in Forresters's ID simulation study of the MPIS. It is shown that both the policies result in more attenuated system behaviour than that obtained by Forrester.     

Performance monitoring of a multi-product semi-batch process

Traditionally principal components analysis (PCA) has been viewed as a single-population method. In particular in multivariate statistical process control, PCA has been used to monitor single product production. An extension to principal components analysis is presented which enables the simultaneous monitoring of a number of product grades or recipes. The method is based upon the existence of a common eigenvector subspace for the sample variance–covariance matrices of the individual products. The pooled sample variance–covariance matrix of the individual products is then used to estimate the principal component loadings of the multi-group model. The methodology is applied to a semi-discrete industrial batch process manufacturing a number of recipes. The industrial application illustrates that the detection and diagnostic capabilities of the multi-group model are comparable to those achieved by developing a separate statistical representation for the individual products.