Simulating alternative production policies with sequence-dependent costs

This article studies various sequencing and inventory rules in a manufacturing environment with nonlinear technological coefficients and stochastic demand. Multiple products require setup on a single machine and setup time and setup cost decrease with repeated setups. Furthermore, setup operations for different products have common components and an item can benefit from the setup operation of another item. The single-level, multi-item lot size model is used to model the production environment. The learning curve is used to represent this decrease in setup time with repeated setups. The learning transmission between items affects the scheduling of the products and the resulting model considers simultaneous decisions about lot sizing and sequencing in a nonlinear formulation. The problem is formulated and various production policies are simulated. Two sequencing rules and four inventory rules are examined. A simulation experiment of 6400 runs is used to compare the schedules produced by simple policies and those produced by more involved ones. A statistical analysis of the simulation results indicates that the simple rules perform equally well and in some cases better than the computationally harder rules.     

A learning curve model for an equivalent number of units

Conventional learning curve models are able to deal only with past data that includes an integer number of cycles and time per cycle. However, in real-life situations, the data collected are of a different nature: periodical information, which includes total work time, in-process inventory and completed units, for example. In such circumstances it would be wrong to consider just the completed units, disregarding the in-process inventory. The concept of Equivalent Number of Units (ENU) has been introduced to permit one to sum up all the work performed, and express it in a manner that allows one to use the learning curve model for such cases. Also, time per unit may not be given for single units and the ENU produced per reported period may not be an integer. In order to solve the above problems, a simple procedure was developed for periodical non-integer data. The end result of the procedure is the product learning curve parameters.     

An integrated production-inventory model with reprocessing and inspection

Competitive pressures continually force management to examine cost and quality levels of production systems. In this paper these issues are addressed via a model that synthesizes several potential features of production systems: production processes, quality control procedures, in-process inventory and reprocessing. For any specified inspection configuration the model can be used, for serial production systems, to obtain closed-form expressions for two important decision variables: optimal lot size and reprocessing batch size, which minimize the total system costs. A numerical example highlights the interdependencies and the role of various system features in determining the values of the decision variables and hence in reducing the total costs. The paper also discusses the managerial implications of the model.     

The Acquisition of Automation Subject to Diminishing Returns

In this paper, it is assumed that the purchase of automation has the effect of reducing the per unit production and in-process inventory costs. The optimal dynamic mix of automation and manual output is derived to minimize the cost incurred over the planning horizon due to (1) deviating from the future goal levels of output, (2) production, (3) inventory, (4) changing the level of manual output, and (5) acquiring automation. The cost of purchasing automation and the effectiveness of automation on reducing the per unit. production and in-process inventory costs are expressed as functions of time to include the impact of learning or anticipated technological advancement. Furthermore, the effectiveness of automation on reducing the per unit production and in-process inventory costs is assumed to decrease as the level of automation held by the organization increases due to diminishing returns. We show that it is rarely optimal to increase automation without simultaneously modifying the level of manual output. In addition, a numerical solution algorithm is presented to compute the optimal times and levels of changes in automation and manual output.     

A Hierarchical structure of key performance indicators for operation management and continuous improvement in production systems

Key performance indicators (KPIs) are critical for manufacturing operation management and continuous improvement (CI). In modern manufacturing systems, KPIs are defined as a set of metrics to reflect operation performance, such as efficiency, throughput, availability, from productivity, quality and maintenance perspectives. Through continuous monitoring and measurement of KPIs, meaningful quantification and identification of different aspects of operation activities can be obtained, which enable and direct CI efforts. A set of 34 KPIs has been introduced in ISO 22400. However, the KPIs in a manufacturing system are not independent, and they may have intrinsic mutual relationships. The goal of this paper is to introduce a multi-level structure for identification and analysis of KPIs and their intrinsic relationships in production systems. Specifically, through such a hierarchical structure, we define and layer KPIs into levels of basic KPIs, comprehensive KPIs and their supporting metrics, and use it to investigate the relationships and dependencies between KPIs. Such a study can provide a useful tool for manufacturing engineers and managers to measure and utilize KPIs for CI.     

Selection of a pull production control system in multi-stage production processes

In this paper, we conduct an analytical comparison of three pull production control systems: Kanban, CONWIP and Base-stock in multi-stage production processes. First, we compare the three control systems in a multi-stage serial production process. Then, we compare them in multi-stage assembly production processes, and present guidelines that allow us to select the best system. As a result, we show which structural parameters decide the superiority of one control scheme to the others, and how they are related. A key for superiority is a configuration of parameters, such as processing times and number of cards employed in the system. We show that there is no general superiority amongst the analysed concepts. Finally, we verify the effect of variability on the system performance, and generalise the analytical results of deterministic cases by conducting numerical experiments.     

Multi-cyclic flow shop scheduling: An application in multi-stage,multiproduct production processes

This paper focuses primarily on multi-cyclic flow shop scheduling. Multi-cyclic scheduling is a generalization of common cycle scheduling in which the cycle time for each product is required to be an integer multiple of the base cycle time. After reviewing the literature, this paper presents an efficient heuristic procedure which generates near-optimal multi-cyclic schedules for a flow shop production environment under deterministic and stationary conditions. This heuristic accounts for all inventory costs including in-process inventory and idle time. The proposed heuristic is then implemented and tested at CONMAT Inc. CONMAT Inc. is a construction materials company based in Pennsylvania, USA. The solution procedure compared to the performance of the current production process at CONMAT proved to be very cost and time efficient.     

Selecting key performance indicators for production with a linear programming approach

Modern production systems are prone to disruptions due to shorter product life cycles, growing variant diversity and progressively distributed production. At the same time, reduced time and capacity buffers diminish mitigation opportunities, requiring better tools for production control. Performance measurement with key performance indicators (KPIs) is a widely used instrument to detect changes in production system performance in order to coordinate appropriate countermeasures. The main challenge in planning KPI systems consists in determining relevant KPIs. On the one hand, enough KPIs must be selected for a sufficiently high information content. On the other hand, the cognitive abilities of users are not to be overstrained by selecting too many KPIs. This tradeoff is addressed in a proposed selection process using an integer linear programme for objective KPI selection. In order to achieve this goal, crucial facets of the information content requirement are formalised mathematically. The developed method is validated using a practical application example, showing the influence of model parameter selection on optimisation results. The formalisation of the information content is shown to be a novel and promising approach.     

Simulating operator learning during production ramp-up in parallel vs. serial flow production

The aim of this research is to demonstrate how human learning models can be integrated into discrete event simulation to examine ramp-up time differences between serial and parallel flow production strategies. The experimental model examined three levels of learning rate and minimum cycle times. Results show that while the parallel flow system had longer ramp-up times than serial flow systems, they also had higher maximum throughput capacity. As a result, the parallel flow system frequently outperformed lines within the first weeks of operation. There is a critical lack of empirical evidence or methods that would allow designers to accurately determine what the critical learning paramters might be in their specific operations, and further research is needed to create predictive tools in this important area.     

An inventory model with emergency orders under explicit energy cost considerations

The inventory model in this paper is targeted to production systems with constant production rates but underlying possibilities for undesirable circumstances to threaten the production schedule. The inventory policy proposed explicitly considers energy cost when determining optimal size for order quantity, safety stock and inventory cycle length such that the total expected cost per unit time is minimised. The results are compared to a traditional inventory policy that does not consider the direct impact of energy cost. An analysis of the model reveals three production environment characteristics in which inventory policies are most significantly affected by changes in energy cost: heavy product weight, high regular product demand or high emergency product demand. If any one of the three key factors increases, then changes of the inventory decisions or related logistics costs become more significant. The cost effectiveness of implementing the proposed inventory policy also becomes more significant as any one of the three key factors increase with respect to energy cost.     

Incomplete convolutions in production and inventory models

In this paper, we study incomplete convolutions of continuous distribution functions, as they appear in the analysis of (multi-stage) production and inventory systems. Three example systems are discussed where these incomplete convolutions naturally arise. We derive explicit, nonrecursive formulae for these convolutions, for the relevant case in which the underlying distributions are (mixtures of) Erlang distributions with the same scale parameter. Numerical results for one example system, the multi-stage serial inventory system, are presented to show the effectiveness of these formulae.     

Dynamic programming algorithms for multi-stage safety stock optimization

The task of multi-stage safety stock optimization is very complex. Therefore, simplifying models with specific assumptions are considered. In this paper, the inventory system is controlled by a base-stock policy where each stockpoint of the inventory system follows a periodically reviewed order-up-to policy. End item demands are assumed to be normally distributed. To reduce the occurrences or size and duration of internal and external stockouts, appropriate service level constraints are specified for all items. Applying such a control policy within systems of serial, convergent or divergent structure, solution properties hold which reduce the solution set to a limited number of cut-levels. Dynamic programming allows to evaluate the relevant alternatives with little computational effort. For the serial system, both a forward and a backward recursion with different types of service levels are presented and extended to a backward algorithm for divergent and a forward algorithm for convergent systems. Bounds for the complexity of the algorithms are discussed and numerical examples are presented to demonstrate differences in size and allocation of safety stocks according to the prespecified type of service level.     

填料生产线精益生产的整合方案研究

以某化工填料生产线为研究对象,通过对填料生产系统工艺流程现状的物流分析,提出了生产设备成组布局的整合方案,从设备布置方式和生产系统优化两个方面找到影响物流顺畅运行与在制品库存最小化的改进措施,设计了满足不同生产批量与不同生产周期的精益物流过程,通过对生产流程改进的前后对比与过程仿真,验证了改进后的生产设备与物流的重组模式是实现填料生产线精益生产的一个切实可行的解决途径。     

Product quality inspection in Bernoulli lines: analysis,bottlenecks, and design

This paper is devoted to serial production lines consisting of producing and inspection machines that obey the Bernoulli reliability and Bernoulli quality models. Such production lines are encountered in automotive assembly and painting operations where the downtime is relatively short and the defects are due to uncorrelated random events. For these systems, this paper develops analytical methods for performance analysis, bottleneck identification, and design. In addition, insights into the nature of bottlenecks in such systems are provided, and an empirical rule for placing an inspection machine that maximises the production rate of non-defectives is formulated.     

Mixed model assembly system with multiple secondary feeder lines: layout design and balancing procedure for ATO environment

The constant research for efficiency and flexibility has forced assembly systems to change from simple/single assembly lines to mixed model assembly lines, while the necessity to reduce inventory has led the transition from single to multi-line systems, where some components are assembled in secondary lines, called feeder lines, connected to the main one by a ‘pull philosophy’. A possible approach to configure such an assembly system is to balance the main line first and use the retrieved cycle time to balance each feeder line separately, which is a questionable solution, especially if operators can perform tasks on both the feeder and the main line. Moreover for its complexity the mixed model balancing problem is usually solved transforming it into a single model by creating a single ‘virtual average model’, representative of the whole production mix. The use of a virtual average model assumes that the processing times of some models are higher or lower than the cycle time, which creates overload/idle time at the stations. This approach, especially in complex multi line production systems, largely reduces the assembly line productivity and increases the buffers dimensions. This paper faces the mixed model assembly line balancing problem in the presence of multiple feeder lines, introducing an innovative integrated main-feeder lines balancing procedure in case of unpaced assembly systems. The proposed approach is compared with the classical one and validated through simulation and industrial applications.     

Feedback method of production ordering system in multi-stage production and inventory systems

This paper deals with the problem of developing a production ordering system which maintains high reliability and productivity of multi-stage production and inventory systems with capacity-constraint and machine breakdown. In this paper, two ‘push type’ production ordering systems (Matsuura and Soshiroda 1981) are proposed according to information feedback methods. The influence of forecasting error, the difference between forecasted demands, down-time, and the backlog caused by the restriction of production capacity, upon the production and inventory levels is analysed by each production ordering system. The results indicate that, in designing an effective production ordering system, a feedback method must be chosen according to the conditions of the average loading ratio, the down-time, and the autocorrelation coefficient of demand.     

Optimising replenishment policy for an integrated production inventory deteriorating model considering green component-value design and remanufacturing

This paper develops an integrated deteriorating production inventory model with green component design, remanufacturing and JIT deliveries. We provide a rigorous analysis to derive the number of deliveries, the optimal cycle time of deliveries, and the delivery sise for the integrated buyer-supplier inventory deteriorating model. Distinct from the former concept of average inventory level, our paper proposes a significantly different approach to deal with the first production batch and uses a revised method to approximate the relationship between the supplier's production and storage time. A manufacturing case example of Taiwan computer power-supply component producers is presented to illustrate the theory. It is shown that the parameters of component-value design and unit holding cost are the critical factors affecting the deteriorating inventory planning.     

Economic packaging frequency of two items jointly manufactured in a multi-stage system

The objective of this paper is to show that the models suggested in the literature for optimizing the packaging frequency of jointly replenished items are invalid when the material to be packaged is processed in a multi-stage production/inventory system. Two basic models are presented for the case in which the internally manufactured material is packaged into two items of different size on the same packaging facility. Deterministic and constant demand and production rates, as well as fixed (set-up) costs and linear inventory unit holding costs, are assumed over an infinite time horizon. The ratio of the packaging frequency of the two items is restricted to be an integer and no back-logging of packaged items is allowed. A quite simple solution method and a computational example are given for each model.     

Effect of production cost on shelf life

We consider a manufacturing system which produces a family of items and the production policy of the system is to produce all items in every production cycle. Some items can be stored in the inventory only for a certain shelf-life period which may be shorter than the production cycle time. If such problem arises, then the cycle-time period for which an item is stored in the inventory has to be reduced to less than or equal to the shelf life of that item to accommodate the feasible schedule. This storage time can be reduced by frequent replenishment of the items and consequently reducing the inventory held up in the store. This objective may be achieved by reducing either the total cycle time or the production rate, or by using a mix of reduced cycle time and production rate. This paper focuses on deciding the best of the first two known options: to reduce the production rate or to reduce the cycle time; the third option is not addressed here because of its complexity. An optimum quantity and its corresponding production cycle time, for each item are found using the standard economic order quantity model under constant and known demand rates. Although the computational results indicates that reducing the cycle time is better than reducing the production rate, the choice depends actually on the shelf life, machine-setup time, product-setup time, the production time (uptime) and unit costs.     

Incorporating engineering process improvement activities into production planning formulations using a large-scale wafer fab model

In most semiconductor wafer fabrication facilities (wafer fabs), both production and engineering lots share the same expensive equipment. Production lots will be shipped to customers whereas engineering lots are used to support production and process development efforts. While production activities might lead to large revenue, engineering activities result in increased future output. In the present paper, we propose three different production planning formulations. The first formulation assumes a reduced available capacity for production due to engineering activities. Costs for production products are minimised. The second formulation is based on the idea that aggregated demand is available for engineering activities for the entire planning window. Costs for production and engineering products are minimised. Learning effects are incorporated to model the capacity increase due to engineering activities. The third model assumes that demand information for engineering activities is available only for the first period. In addition to learning effects, forgetting effects are modelled to provide an incentive to plan releases of engineering lots in later periods. Costs for production and engineering products and forgetting effects are minimised. The performance of the production planning models is assessed using a simulation model of a large-scale wafer fab including specific dispatching strategies to deal with production and engineering lots. The simulation results demonstrate that the second model slightly outperforms the third one when a rolling horizon approach is taken, while the second model provides significantly higher profit than the first one.