A cost/benefit model for investments in inventory and preventive maintenance in an imperfect production system

In this research, a cost/benefit model is developed for supporting investment strategies about inventory and preventive maintenance in an imperfect production system. The effect of such investments on the return is expressed as a function of measurable variables. Using this model, the decision maker can decide whether investments in inventory and preventive maintenance are necessary and how much to invest. This investment model is developed for an imperfect production system with imperfect product quality and supplied quantity. Investments in inventory and preventive maintenance increase service level for the customer and reduce the proportion of defective products, and hence affect stockout and backlog of supplied products and the delivery time to the customer. This model includes in its scope investment in inventory and preventive maintenance, manufacturing cost, inventory cost, backlog cost, stockout cost, and delay cost. This model can be used to evaluate the effects of investments on the financial cost/benefit and other relevant critical performance measures. This model can be solved by an iterative process using the Sequential Quadratic Programming Method. The optimal investment in inventory with respect to the service level and the optimal investment in preventive maintenance with respect to the proportion of defective items can be obtained first, and then other relevant costs can also be obtained.     

Optimal production run length and capital investment in quality improvement with an imperfect production process

The paper studies the effects of an imperfect production process on the optimal production run length when capital investment in process quality improvement is adopted. The mathematical model is derived to determine the optimal production run length and capital investment under the assumption of logarithmic investment function such that the total annual cost is minimized. In addition, an efficient algorithm is provided to find both the optimal production run length and the optimal process quality. Therefore, the optimal lot sizing and capital investment are appropriately determined. A numerical example is provided to illustrate the results and to assess the cost savings realized by adopting capital investment. Furthermore, some managerial implications are also included.     

Fuzzy opportunity cost for EOQ model with quality improvement investment

The cost of capital (i.e. opportunity cost) is one of the key factors that will influence the inventory and investment decisions. Previously, the classical EOQ model has been extended to include an imperfect production process and quality improvement investment, where the opportunity cost rate (interest rate or discounted rate) for evaluating the cost of capital investment is known with certainty. However, in some practical situations, the opportunity cost rate probably incurs disturbance due to the unstable environments. To capture this reality, this paper attempts to combine the statistical technique and fuzzy sets concept to deal with the unstable opportunity cost rate, so as to modify the aforementioned inventory/investment model. We derive the optimal lot size and the optimal process quality level in the fuzzy sense utilizing the logarithmic investment cost function. A numerical example is provided, and the results are compared with those obtained from a crisp opportunity cost rate model.     

An integrated vendor–buyer inventory model with backorder price discount and effective investment to reduce ordering cost

The single-vendor single-buyer integrated production inventory system has been an object of study for a long time, but little is known about the effect of investing in reducing ordering cost on the integrated inventory models with backorder price discount and variable lead time. The purpose of this article is to investigate in the continuous review model with backorder price discount and variable lead time to effectively increase investment and to reduce the joint expected annual total cost. The integrated strategy discussed here is one in which the buyer orders a quantity, then the vendor produces n times order quantity in each production cycle, in order to reduce setup cost. In addition, the buyer offers backorder price discounts to the customers that may motivate the customers’ desire for backorders, and buyer ordering cost can be reduced through effective investment. An integrated inventory model is established to find the optimal solutions of order quantity, ordering cost, backorder price discount, lead time, and the number of shipments from the vendor to the buyer in one production run, so that the joint expected annual total cost incurred has the minimum value. Furthermore, numerical examples are used to demonstrate the benefits of the model.     

Multiple lot-sizing decisions with an interrupted geometric yield and variable production time

This study examines a multiple lot-sizing problem for a single-stage production system with an interrupted geometric distribution, which is distinguished in involving variable production lead-time. In a finite number of setups, this study determined the optimal lot-size for each period that minimizes total expected cost. The following cost items are considered in optimum lot-sizing decisions: setup cost, variable production cost, inventory holding cost, and shortage cost. A dynamic programming model is formulated in which the duration between current time and due date is a stage variable, and remaining demand and work-in-process status are state variables. This study then presents an algorithm for solving the dynamic programming problem. Additionally, this study examines how total expected costs of optimal lot-sizing decisions vary when parameters are changed. Numerical results show that the optimum lot-size as a function of demand is not always monotonic.     

Capacity and flexibility planning of an economical manufacturing system

This paper presents a simple dynamic model for determining the capacity and the flexibility of a manufacturing system over a finite planning horizon. We consider a problem that arises from the development phase of an investment plan for an economical manufacturing system. The objective is to minimize the total cost associated with the capacity expansion, flexibility expansion and operation. This problem is formulated as an integer program. A Lagrangian heuristic is developed for determining a near optimal solution to this integer program. Finally, we show how to incorporate aggregate production planning into the model.Based on a presentation given at the ORSA/TIMS Miami meeting in 1986.     

An integrated approach for the optimization of tolerance design and quality cost

Different normality-based optimization strategy (NBOS) methods have been developed and used to perform quality improvement in the past few decays. Improving the quality of a production process using a NBOS method possibly incurs misleading results if the quality measurements follow a skewed distribution. An integrated model, with components of a tolerance cost model for the determinations of optimal tolerance limits and a quality investment model for the identification of optimal investment level, is applied to establish a new optimization strategy method for the skew normal distribution (SND), named SNDOS method. The SND generalizes the normal distribution to include skewed distributions as members, and hence the SNDOS method is applicable for quality improvement either the distribution of quality measurements follow a symmetric or skewed distribution. Two examples about car seat production process are used to illustrate the application of the SNDOS method. The sensitivity of the SNDOS method to the loss coefficient of the integrated model is evaluated for different inputs of the skewness parameter of the SND through a numerical study.     

A joint design of production run length,maintenance policy and control chart with multiple assignable causes

Although economic production quantity, statistical process monitoring and maintenance are three major concepts in process optimization of industrial environments, they have been often investigated separately in literature. Furthermore, in studies that consider these three concepts simultaneously, it is assumed that there is only one assignable cause in the production process. This simplified assumption is unlikely to occur in real production processes due to the usual complexity of manufacturing systems, which may lead to a poor performance in both economic and statistical criteria if the assignable cause originating the shift is different from the one anticipated at the design of the chart. To overcome these drawbacks, this paper develops an integrated model ofeconomic production quantity, statistical process monitoring and maintenance in the presence ofmultiple assignable causes. The particle swarm optimization algorithm is used to minimize the expected total cost per production cycle, subject to statistical quality constraints. Also, a comparative study is performed to illustrate the effect of considering multiple assignable causes on model’s costs. Finally, a sensitivity analysis is conducted on the expected total cost per production cycle and process variable values to extend insights into the matter.     

An integrated production–distribution inventory system involving probabilistic defective and errors in quality inspection under variable setup cost

This paper presents a probabilistic defective vendor–buyer integrated inventory model with the consideration of quality inspection errors at the buyer's end and setup cost as function of capital investment. An integrated inventory model is established to find the optimal solutions of lot size, setup cost, and the total number of shipments from the vendor to the buyer in one production run, so that the joint expected total cost incurred has the minimum value. We consider three types of continuous probabilistic defective function to find the associated cost of the system. The expected total cost function is derived for each of these three distributions, its convexity is proved via differential calculus. An efficient iterative algorithm is designed to obtain the optimal solution of the model. The computational effort and time are small for the proposed algorithm and it is simple to implement. Numerical examples and sensitivity analysis are used to demonstrate the application and the performance of the proposed methodology. The computational results indicate that if we make decisions with the capital investment in reducing setup cost, it will help to lower the system cost, and we obtain a significant amount of savings to increase the competitive edge in business.     

A strategic investment model for phased implementation of flexible manufacturing systems

This paper describes a set of strategic, tactical, and operational models that can be used to analyze the phased implementation of flexible technology in a manufacturing system. The strategic model represents capital investment decisions, the tactical model represents aggregate production decisions, and the operational model represents the functional form of the production costs. Learning effects and other nonlinearities (such as setup costs, economies of scale, and congestion effects) can be quantified in the models. An efficient solution procedure (using dynamic programming and minimum cost network flow optimization) is described. The efficiency of the solution method permits a host of 'what-if' scenarios to be examined by the decision maker.     

Design of attribute control charts for multistage production systems-based on cost criteria

This paper develops a method to design attribute control charts, p-charts and c-charts, for multistage production systems based on quality cost criteria. The production systems are structured and formulated as a dynamic programming model. Each productions station and its inspection station is viewed as a combined station and is treated as the stage in the dynamic programming model. The model has quality distribution as the state variable and the stage transformation of this model is also developed. the stage return of this dynamic programming model is the quality cost of implementing an attribute control chart to that stage and the decision variables are the control chart parameters, n-sample size and control limits. Methods to combine quality distributions for finding type I and type II errors are then developed. As the dynamic programming model has quality distribution as state variable, conventional methods of solving dynamic programming problems are not applicable. A method, for solving this model, is thus developed based on branch and bound approach. The method itself may be applied to other dynamic programming problems where conventional methods are inefficient or not applicable. An example of the foundry process of cylinder liners is included to illustrate the developed method.     

基于缺陷度量的软件质量成本分析模型

针对软件项目的质量成本效益无法直接度量的这一难题,提出了建立组织级质量成本度量基线的解决方案。设计了基于缺陷度量的软件质量成本分析模型,实现了对软件质量成本及其效益的定量度量与分析,为评价软件质量保证活动绩效、指导质量投资决策提供了试用方法。     

PS转炉造渣过程的动态优化控制

建立了Pierce-Smith(PS)转炉造渣过程的非线性状态空问模型,并提出了基于生产质量指标反馈校正的铜锍造渣过程的动态优化控制方案.该方案首先基于最优模型求得最优控制律.为消除吹炼过程中的扰动以及其他不确定因素所带来的影响,再引入基于生产质量指标的反馈调整机制.其中反馈信息由软测量模犁根据进出转炉的物料计算得到,智能控制单元根据反馈的质量信息和期望的质量目标间的偏差对最优控制律进行补偿修正.并在该动态优化控制方案基础上,设计并开发了铜锍吹炼过程的优化控制指导决策系统.实际运行结果表明该系统优化了产品的质量,同时也实现了铜锍生产过程的节能.     

Optimal lot-sizing in multi-item production inventories

A model for multi-item production inventories with known constant demand and finite shortage cost is developed. The model is deterministic, and includes items competing for limited storage space and capital investment. Price breaks either in the production cost or in the holding cost are further considered. A three-level computational algorithm is developed to solve the constrained optimization problem in each case. Finally, the model is tested for a simulated assembly of six different gear boxes in a machine tool company implementing group family technology in its production and storage system. The obtained results have demonstrated the potential of our approach.     

Complexity of discrete investment competition model based on heterogeneous participants

A discrete nonlinear dynamics model has been established based on investment competition for heterogeneous financial institutions in this paper. The cost functions of financial institutions are different in the competitive investment. Theoretical analysis and numerical simulations of the system are investigated in detail. The results show that the dynamic system can undergo chaotic orbits. The stability control is realized by the method combining the feedback control with the parameter variation. The numerical simulation results show that the control method is effective. In practice, by utilizing the sensitivity to disturbance of the model, we can put a tiny perturbation on the chaotic system and induce large influence on investments in order to realize a desirable behaviour.     

Multi-agent approach and stochastic optimization: random events in manufacturing systems

We propose a method to solve industrial problems and to take into account random events. It is called the triple coupling. It is based on stochastic algorithms, a simulation model and the multi-agents model of artificial intelligence. The method we propose is easy to use and allows us to take into account most of the constraints found in manufacturing systems. Experts look for solutions to increasing the capacity of production. But the production can be disturbed by random events experienced by the system. Industrial experts need schedules which prevent the consequences of random events. Minimizing such consequences is very important to increasing system delivery. Capital investment is often very high in factories and the cost of the investment goes on regardless of whether the resources are running or not. The multi-agent approach is used to determine schedules for which the consequences of random events are low, and a stochastic algorithm is proposed which permits us to optimize a random variable. We prove that this algorithm finds, with probability one, the schedule of the production for which the consequences of random events are the lowest. We propose to measure the consequences of random events using an influence ratio. Our approach has been used to study the consequences of random events in Peugeot sand foundries of Sept-Fons (France). A benchmark test is presented to prove the efficiency of our solution. For the Peugeot sand foundry of Sept-Fond, random events increase the production time by about 20% compared with the production time without any random events occurring. We have determined schedules of production for which the consequences of random events are about 0.5%.     

Dynamic optimisation of price,warranty length and production rate

This study investigates a marketing and production problem that uses price, warranty length and production rate as simultaneous dynamic decision variables. Furthermore, this study was conducted under a policy of free replacement of defective items; and under conditions where demand was dynamic and dependent on price, warranty and cumulative sales. A continuous profit maximisation model was formulated, which first considers the expected warranty cost per item. Then, it considers the steps for dynamic optimisation, which eventually derive the optimal price, warranty length and production rate. Discretisation was then applied to the profit maximisation model and a digital computer was used to identify the optimal control paths, obtaining a finite solution that is a set of real numbers for practical application. A model-driven Decision Support System is finally established, which provides a graphical user interface for overcoming the complexity of the analytical process. Subsequently, the proposed system was tested and the analytical solution was verified using several demand functions for additive lifetime distributions, thereby demonstrating the system's effectiveness.     

基于排队论的生产物流系统的仿真优化

研究生产过程中物流运输资源配置的问题。为了有效提高企业生产过程中物流效率并控制投资,依据排队理论,建立等待费用和配置资源费用的综合比较模型,从而选择最佳资源配置方案。通过对仓储物流系统的详细调研和数据采集,建立生产系统物流模型,运用Arena 7.0仿真软件进行仿真,从而设计和选择一个较好的策略。     

An imperfect production process for time varying demand with inflation and time value of money – An EMQ model

The paper deals with an economic manufacturing quantity (EMQ) model for time-dependent (quadratic) demand pattern. Every manufacturing sector wants to produce perfect quality items. But in long run process, there may arise different types of difficulties like labor problem, machinery capabilities problems, etc., due to that the machinery systems shift from in-control state to out-of-control state as a result the manufacturing systems produce imperfect quality items. The imperfect items are reworked at a cost to become the perfect one. The rework cost may be reduced by improvements in product reliability i.e., the production process depend on time and also the reliability parameter. We want to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process using Euler–Lagrange theory to build up the necessary and sufficient conditions for optimality of the dynamic variables. Finally, a numerical example is discussed to test the model which is illustrated graphically also.     

New integration of preventive maintenance and production planning with cell formation and group scheduling for dynamic cellular manufacturing systems

This paper proposes a new integration method for cell formation, group scheduling, production, and preventive maintenance (PM) planning problems in a dynamic cellular manufacturing system (CMS). The cell formation sub-problem aims to form part families and machine groups, which minimizes the inter-cell material handling, under-utilization, and relocation costs. The production planning aspect is a multi-item capacitated lot-sizing problem accompanied by sub-contracting decisions, while the group scheduling problem deals with the decisions on the sequential order of the parts and their corresponding completion times. The purpose of the maintenance sub-problem is to determine the availability of the system and the time when the noncyclical perfect PM must be implemented to reduce the number of corrective actions. Numerical examples are generated and solved by Bender’s decomposition pack in GAMS to evaluate the interactions of the proposed model. Statistical analysis, based on a nonparametric method, is also used to study the behavior of the model’s cost components in two different situations. It is shown that by adding the PM planning decisions to the tactical decisions of the dynamic CMS, the optimal configuration and production plans of the system are heavily affected. The results indicate that omitting the PM actions increases the number of sudden failures, which leads to a higher total cost. Finally, it is concluded that the boost in the total availability of the dynamic CMS is one of the main advantages of the proposed integrated method.