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.     

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.     

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.     

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.     

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     

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.     

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.     

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.     

The queueing equivalence to a manufacturing system with failures

The authors consider optimal production rate control in a failure prone manufacturing system. It is well known that the hedging point policy is the optimum controller for such a system. They show that under the hedging point policy the system can be treated as an M/M/1 queue. Therefore, existing results in queuing theory can be readily applied to obtaining the steady-state probability density function of the production surplus, based on which the optimal hedging point policy can be computed. To a large extent, the approach is based on sample path analysis. It not only provides an alternative way to solve the problem but also reveals some interesting insights     

Artificial bee colony algorithm for CONWIP production control system in a multi-product multi-machine manufacturing environment

In this paper, a multi-product multi-machine serial production line operated under a constant-work-in-process protocol is considered. A mathematical model for the system is first presented, and then an artificial bee colony optimization algorithm is applied to simultaneously find the optimal work-in-process inventory level as well as job sequence order in order to minimize the overall makespan time. Unlike many existing approaches, which are based on deterministic search algorithms such as nonlinear programming and mixed integer programming, the proposed method does not use a linearized or simplified model of the system. A production line simulator implemented on MATLAB is, instead, employed to model the highly nonlinear dynamics of the production line and is used to evaluate the candidate solutions. The efficiency of the proposed approach, even for systems of large sizes, is validated via numerical simulations.     

A new algorithm for optimally determining lot-sizing policies for a deteriorating item in an integrated production-inventory system

In this study, we focus on optimally determining lot-sizing policies for a deteriorating item among all the partners in a supply chain system with a single-vendor and multiple-buyers so as to minimize the average total costs. We revise Yang and Wee's [1] model using the Fourier series to precisely estimate the vendor's inventory holding costs. Also, we transform our revised model into a more concise version by applying anapproximation to the exponential terms in the objective function. In order to solve this problem, we analyze the optimality structure of our revised model and derive several interesting properties. By utilizing our theoretical results, we propose a search algorithm that can efficiently solve the optimal solution. Based on our numerical experiments, we show that the proposed algorithm outperforms the existing solution approach in the literature, especially when the number of buyers is larger in the supply chain system.     

Detecting system failures from durations and binary cues

Durations are often used to judge the status of an invisible process. However, the apparent duration of an interval depends on the actual duration and on other variables, such as the workload during the interval and the person's expectations. An experiment dealt with the use of durations as an information source on the state of an invisible process and the effects of expectations and workload on decisions regarding the process. Eighty-nine participants observed a computerized simulation of a process which could be either intact or faulty, with intact processes ending on average sooner than faulty ones, and they had to indicate whether or not the process is intact and to estimate its duration. A binary cue with either intermediate or no validity indicated whether the process was supposedly intact or not, generating expectations about the duration of the process. Perceived durations and the decisions about the intactness of a process depended on the actual process duration, as well as on the expectations generated by the binary cue. In addition, task workload affected time estimates, but it had no effect on participants' tendency to adhere to cue recommendations or their ability to distinguish between intact and faulty processes. Results show that users' duration-based decisions about the status of a computerized process are affected by internal and external cues. While users can use durations as an information source, they should, whenever possible, be accompanied by additional indicators, lowering the inherent uncertainty in the duration estimation process.     

低轨卫星系统数字上变频器的多级内插设计

在研究了低轨卫星DS-CDMA系统数字上变频器的内插技术之后,提出了以成型滤波器、半带滤波器和CIC滤波器等多级内插级联的结构来实现抽样率的变换。在具体实现上采用了基于多相结构实现的成型滤波器、高效的半带滤波器和改进的多级CIC滤波器,节省了系统的硬件资源,提高了系统的性能。     

Design of multi-product manufacturing lines with the consideration of product change dependent inter-task times,reduced changeover and machine flexibility

Traditional research work in manufacturing line design assumes that the times between manufacturing tasks performed on a workstation are independent of the task sequence on that station. Furthermore, such studies paid little attention to the sequence dependent inter-task times in multi-model production. Since the inter-task times related to product model changeover have significant impact on manufacturing line performance, it is necessary to take into account the inter-task times explicitly in multi-model manufacturing line design. The need for this consideration is growing as product variety increases. This paper presents mathematical models of manufacturing line design with the consideration of product change related inter-task times in evaluating station times for multi-model production. An optimization model is developed using mixed integer programming to minimize manufacturing line cost. The model takes into account the recurrence of manufacturing tasks in a station to determine the machine type in a station. This paper also presents a heuristic solution procedure developed for efficient calculation. This paper also investigates how product model build sequences and inter-task times affect manufacturing line performance. The developed models will help enhance task-station assignment in multi- and mixed-model production by increasing line cost effectiveness and reducing line changeover impact as well as shortening long re-balancing processes.