Conditional Monte Carlo Gradient Estimation in Economic Design of Control Limits

The economic approach to determining the optimal control limits of control charts requires estimating the gradient of the expected cost function. Simulation is a very general methodology for estimating the expected costs, but for estimating the gradient, straightforward finite difference estimators can be inefficient. We demonstrate an alternative approach based on smoothed perturbation analysis (SPA), also known as conditional Monte Carlo. Numerical results and consequent design insights are obtained in determining the optimal control limits for exponentially weighted moving average and Bayes charts. The results indicate that the SPA gradient estimators can be significantly more efficient than finite difference estimators, and that a simulation approach using these estimators provides a viable alternative to other numerical solution techniques for the economic design problem.     

An optimal design for process quality improvement: modelling and application

Existing research works on process quality improvement focus largely on the linkages between quality improvement cost and production economics such as set-up cost and defect rate reduction. This paper deals with the optimal design problem for process improvement by balancing the sunk investment cost and revenue increments due to the process improvement. We develop an optimal model based on Taguchi cost functions. The model is validated through a real case study in automotive industry where the 6-sigma DMAIC methodology has been applied. According to this research, the management can adjust the investment on prevention and appraisal costs on quality improvement that enhances process capability, reduces product defect rate and, as a result, generates remarkable financial return.     

A COMPARISON OF DIRECT COST SAVINGS BETWEEN FLEXIBLE AUTOMATION AND LABOR WITH LEARNING

This paper compares flexible automation with labor‐intensive manufacturing processes in a batch production environment and considers learning, forgetting, inventory carrying costs, setup costs, production demand volume, previous production experience, and the proportion of material to labor cost. While flexible automation typically can reduce setup times, and therefore inventory carrying costs through smaller optimal batch sizes, the results of this research show that the effect of forgetting on relative cost savings is difficult to predict in some situations. When using optimal lot sizes in both the automated and labor environments, cost savings from flexible automation may be smaller than expected or may occur in different ways than anticipated.     

EFFECTS OF RANDOM SHIFTS OF TESTING EQUIPMENT ON PROCESS CONTROL SYSTEM DESIGN AND SELECTION OF PROCESS CONTROL POLICIES*

This paper studies issues associated with designing process control systems when the testing equipment is subjected to random shifts. We consider a production process with two states: in control and out of control. The process may shift randomly to the out‐of‐control state over time. The process is monitored by periodically sampling finished items from the process. The equipment used to test sampled items also is assumed to have two states and may shift randomly during the testing process. We formulate a cost model for finding the optimal process control policy that minimizes the expected unit time cost. Numerical results show that shifts of the testing equipment may significantly affect the performance of a process control policy. We also studied the effects of the testing equipment's shifts on the selection of process control policies.     

Equilibrium Joining Strategies and Optimal Control of a Make‐to‐Stock Queue

We consider a make‐to‐stock, finite‐capacity production system with setup cost and delay‐sensitive customers. To balance the setup and inventory related costs, the production manager adopts a two‐critical‐number control policy, where the production starts when the number of waiting customers reaches a certain level and shuts down when a certain quantity of inventory has accumulated. Once the production is set up, the unit production time follows an exponential distribution. Potential customers arrive according to a Poisson process. Customers are strategic, i.e., they make decisions on whether to stay for the product or to leave without purchase based on their utility values, which depend on the production manager's control decisions. We formulate the problem as a Stackelberg game between the production manager and the customers, where the former is the game leader. We first derive the equilibrium customer purchasing strategy and system performance. We then formulate the expected cost rate function for the production system and present a search algorithm for obtaining the optimal values of the two control variables. We further analyze the characteristics of the optimal solution numerically and compare them with the situation where the customers are non‐strategic.     

DYNAMIC INTERACTION OF PRICE AND DESIGN QUALITY FOR PRODUCTS WITH CONVEX PRODUCTION COSTS

Price and design quality define value for customers and are often used by firms to position products in the marketplace. Setting price and quality level on a new product for the first time and making appropriate changes over time to these variables to reflect changing conditions in the market requires careful coordination of design, manufacturing, and marketing variables. We present a control theoretic model to study the complex interaction among price, quality, and cost during the life cycle of a product. Our model considers the major design-manufacturing-marketing tradeoffs and helps determine optimal pricing, design quality, and production strategies in a dynamic environment with convex production costs.     

The Influence of Quality Inspections on the Optimal Safety Stock Level

Due to yields of less than 50% during the production of curved glass for the displays on their new cell phone series, Samsung has to deal with higher than expected production costs of several million dollars. Where there is random yield, production costs as well as holding costs can be reduced by introducing quality inspections, in which defective items are discarded before further production. To achieve the greatest cost savings, it is important to determine the optimal number and positions of these inspections across the production process which, due to several influencing parameters, is not simple. We show how the positions of inspection within a production process influence the safety stock level that is required to buffer against uncertainties due to demand and yield randomness. Our approach is the first one, combining decisions about the number and positions of inspections with inventory control strategies in a warehouse. We achieve a maximum safety stock reduction of more than 30% in our examples, which can be even larger depending on the parameter setting. For a company like Intel, reporting inventories for finished goods of nearly 1.5 billion dollars in the 2014 annual report, this allows for significant savings.     

A simple integrated production policy of an imperfect item for vendor and buyer

This article develops a simple approach for determining an optimal integrated vendor–buyer inventory policy for an item with imperfect quality. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. This model is assumed to produce a certain number of defective items during the production process. Items of poor quality detected in the screening process of a lot are sold at a discounted price. The expected annual integrated total cost function is derived and a solution procedure is proposed to determine the optimal policy. Finally, a numerical example is also given to illustrate the solution procedure presented in this article.     

Describing the influence of set-up optimised sequencing on output lateness of workstations

Productivity and schedule reliability are two key objectives when designing, planning and controlling an enterprise’s internal supply chain. Productivity can be increased by implementing set-up optimised order sequencing, which reduces the time and costs required for set-ups. However, since planned end-of-order-processing dates are ignored with set-up optimised sequencing, it tends to cause increased lateness and thus poorer schedule reliability. Accordingly, enterprises must weigh the highest possible productivity against a high schedule reliability. In this paper, we develop a logistic model that can be used by enterprises to facilitate describing the impact of set-up optimised sequencing on a workstation’s lateness behaviour. This logistic model depicts the extent of the output lateness’ standard deviation as a function of the mean WIP, mean workstation output and the input lateness’ standard deviation when applying set-up optimised sequencing. It is thus possible to quantitatively describe the effects of set-up optimised sequencing on the logistic objective ‘schedule reliability’ and compare possible productivity gains.     

Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions

The paper considers the classical single-period inventory model, also known as the Newsboy Problem, with the demand normally distributed and fully observed in successive inventory cycles. The extent of applicability of such a model to inventory management depends upon demand estimation. Appropriate estimators for the optimal order quantity and the maximum expected profit are developed. The statistical properties of the two estimators are explored for both small and large samples, analytically and through Monte-Carlo simulations. For small samples, both estimators are biased. The form of distribution of the optimal order quantity estimator depends upon the critical fractile, while the distribution of the maximum expected profit estimator is always left-skewed. Small samples properties of the estimators indicate that, when the critical fractile is set over a half, the optimal order quantity is underestimated and the maximum expected profit is overestimated with probability over 50%, whereas the probability of overestimating both quantities exceeds again 50% when the critical fractile is below a half. For large samples, based on the asymptotic properties of the two estimators, confidence intervals are derived for the corresponding true population values. The validity of confidence intervals using small samples is tested by developing appropriate Monte-Carlo simulations. In small samples, these intervals attain acceptable confidence levels, but with high unit shortage cost, for the case of maximum expected profit, significant reductions in their precision and stability are observed.     

Time‐Staged Overtime Staffing for Services with Updated Forecasts and Availabilities

This article develops a framework for staffing in a service environment when multiple opportunities exist for prescheduling overtime prior to the start of a shift. Demand forecasts improve as the shift approaches, while the availability of workers to be scheduled for overtime decreases. First, a single‐shift model is developed and used in computational studies to evaluate the benefits of time‐staged overtime staffing, which include slightly lower costs and significant reductions in unscheduled overtime and outside agents. A multishift model is then developed to consider constraints on consecutive hours worked and minimum rest intervals between shifts. A multishift computational study shows how the benefits of time‐staged overtime staffing depend on problem characteristics when interactions between shifts are considered. The article discusses how single‐shift and multishift models relate to each other and alternative ways the models may be used in practice, including decentralized open shift management and centralized overtime scheduling.     

风险质检行为下的模糊生产-库存决策

本文研究在风险质检行为下需求与生产率具有模糊属性的由一个制造商与一个零售商构成的生产-库存问题。在假设制造商生产的产品存在质量缺陷,零售商在质检过程中存在质检风险的基础上,分别建立了需求模糊下的生产-库存总成本模型,需求与生产率模糊下的总成本模型,运用符号距离法进行了逆模糊化处理,将模糊化的生产-库存总成本转化为确定性成本。证明了两类情形下的总成本均是关于最优订购量与最优缺货量的联合凸函数。数值分析结果表明：随着期望缺陷率的增加,最优订购量增加,最优缺货量减少,最优成本增加,且最优成本增加的速度越来越快。一类质检风险增大引起总成本增加,二类质检风险增大引起总成本减少。最优订购策略对质检一类风险敏感,对质检二类风险不敏感。     

The Effect of Misclassification Costs on Neural Network Classifiers

The potential of neural networks for classification problems has been established by numerous successful applications reported in the literature. One of the major assumptions used in almost all studies is the equal cost consequence of misclassification. With this assumption, minimizing the total number of misclassification errors is the sole objective in developing a neural network classifier. Often this is done simply to ease model development and the selection of classification decision points. However, it is not appropriate for many real situations such as quality assurance, direct marketing, bankruptcy prediction, and medical diagnosis where misclassification costs have unequal consequences for different categories. In this paper, we investigate the issue of unequal misclassification costs in neural network classifiers. Through an application in thyroid disease diagnosis, we find that different cost considerations have significant effects on the classification performance and that appropriate use of cost information can aid in optimal decision making. A cross-validation technique is employed to alleviate the problem of bias in the training set and to examine the robustness of neural network classifiers with regard to sampling variations and cost differences.     

考虑库存成本的企业集团转移定价决策分析

目前关于转移定价决策方法的研究文献中,大都忽略了中间产品流转过程中的库存管理成本问题.本文针对这种不足,在充分考虑中间产品流转过程中产生的库存持有成本、订货成本、订单处理成本和启动成本的基础上,研究了企业集团的转移定价决策问题.论文主要讨论了存在竞争性下游子公司的企业集团的转移定价决策问题,得出企业集团提供给一家子公司的最优转移价格为该子公司的边际成本与另一家子公司的最终产品利润加成.加成比例取决于最终产品市场的竞争程度.     

基于厂商理论的区域产业边界和最优要素配置结构

区域经济发展核心是产业结构优化升级和资源的优化配置。在全球经济结构亟待优化升级和要素资源呈现不同层次紧缺的大背景下,如何合理配置和引导区域资源配置,优化产业发展方向,确定包括新兴产业在内的产业发展战略,是每一个地区新形势下面临的重要问题。一方面,在经济全球化和零边际成本趋势驱动下,区域产业发展不再局限于区域内部资源禀赋,资源流动性加强,区域产业发展的选择更加广泛和灵活;另一方面,资源日益短缺和经济快速发展推动了劳动力成本和资本成本上升,产业的生产要素配置也随之变化。基于厂商理论,将区域作为市场经济中的生产主体,在考虑区域交易成本和生产要素成本的基础上,构建区域产业边界模型和产业的最佳要素配置结构模型,开创了资源和商品全球化趋势下的产业升级战略的研究范式,探索了成本约束下的产业生产要素优化配置模式,为经济新常态下的区域产业升级战略和资源配置研究提供理论指引,为区域制定个性化的产业发展战略提供实践依据,同时对零边际成本社会趋势下的产业格局进行了初步的探索。研究得出：产业边界能够在一定程度下反映区域产业长期演化趋势,在完全市场经济下产业边界是产业发展的最优规模;区域产业的要素配置格局取决于产业的资源占用和资源贡献情况,最优配置结构受各要素的相对贡献率和相对成本影响;产业边界与成本的关系取决于规模经济与否,在规模经济状态下与生产成本成正相关关系,与交易成本成负相关关系;大部分地区的农业有较大提升空间,最佳资源配置方案是加大机械动能投入。     

Demand and Production Management with Uniform Guaranteed Lead Time

Recently, innovation‐oriented firms have been competing along dimensions other than price, lead time being one such dimension. Increasingly, customers are favoring lead time guarantees as a means to hedge supply chain risks. For a make‐to‐order environment, we explicitly model the impact of a lead time guarantee on customer demands and production planning. We study how a firm can integrate demand and production decisions to optimize expected profits by quoting a uniform guaranteed maximum lead time to all customers. Our analysis highlights the increasing importance of lead time for customers, as well as the tradeoffs in achieving a proper balance between revenue and cost drivers associated with lead‐time guarantees. We show that the optimal lead time has a closed‐form solution with a newsvendor‐like structure. We prove comparative statics results for the change in optimal lead time with changes in capacity and cost parameters and illustrate the insights using numerical experimentation.     

An adaptation of the EOQ formula for JIT quasi-pull system production

This research demonstrates for the first time that in a just-in-time (JIT) quasi-pull production environment, a model adapted from the Economic Order Quantity and made up of two specific formulas can be employed for calculating an optimised lot size. The assumptions of our model are: a low level of defects, and insignificant shortage backordering and failure of the equipment. JIT quasi-pull production is the state typically reached by many manufacturing companies because it is almost impossible to achieve zero set-ups and zero work-in-process (WIPs) even in the best Lean Production implementations. In this model, finished products are shipped at once in a JIT way. The two developed formulas are specialised: one for balanced stations/processes and the other for unbalanced stations; the formulas allow calculation of an optimised lot size. Several applications of the formulas have been tested and discussed through a case study. Findings demonstrated that the optimised quantity of a lot size has to be smaller than the customer’s daily demand for the product. Moreover, in case of unbalanced stations with long cycle times, the formula forces the company to reduce its set-up times and the cycle times. The new model will be of interest to practitioners who are seeking a way to balance the costs of set-ups and the cost of holding some WIPs and offers interesting avenues for new research.     

THE BIAS OF COST CONTROL CHARTS TOWARD TYPE II ERRORS

Application of control charts has significantly improved process control by explicitly recognizing uncontrollable variation in the process. A dangerous misapplication of the technique involves the use of control charts with data produced by accounting systems. This paper points out the weaknesses inherent in using aggregated accounting data for inferences about cost control.     

ON-LINE QUALITY MANAGEMENT: INTEGRATION OF PRODUCT INSPECTION AND PROCESS CONTROL

A growing recognition that quality management is an important factor in defining a firm's competitive position has led to renewed attention to this function and has resulted in implementation of elaborate systems for on-line quality control comprising product inspection and process control. Traditionally, these functions have been treated independently, with very little interaction. In this paper we examine, in detail, a scheme that integrates the two functions, and we demonstrate that such an approach can result in significant cost savings. The motivation for this work comes from our experience in a wafer fabrication facility that suggested that exchange of quality information between different stages of production could result in significant performance improvements. To illustrate this approach, we consider a specific environment characterized by a single-stage continuous production process whose status is monitored by an X̄ control chart. We assume that quality-related costs may be described as a function of the process output. This is analogous to Taguchi's quality loss function and may be interpreted as a generalization of conventional classification of process output as either acceptable or defective units. The integrative scheme essentially relies on utilization of the process status information (based on process control) in making product inspection decisions. For this system we derive a cost model and develop a solution procedure to determine optimal decision parameters. Limited computational results indicate that the scheme has significant potential for reducing quality-related costs.     

Optimal Inspection of Imports to Prevent Invasive Pest Introduction

The United States imports more than 1 billion live plants annually—an important and growing pathway for introduction of damaging nonnative invertebrates and pathogens. Inspection of imports is one safeguard for reducing pest introductions, but capacity constraints limit inspection effort. We develop an optimal sampling strategy to minimize the costs of pest introductions from trade by posing inspection as an acceptance sampling problem that incorporates key features of the decision context, including (i) simultaneous inspection of many heterogeneous lots, (ii) a lot‐specific sampling effort, (iii) a budget constraint that limits total inspection effort, (iv) inspection error, and (v) an objective of minimizing cost from accepted defective units. We derive a formula for expected number of accepted infested units (expected slippage) given lot size, sample size, infestation rate, and detection rate, and we formulate and analyze the inspector's optimization problem of allocating a sampling budget among incoming lots to minimize the cost of slippage. We conduct an empirical analysis of live plant inspection, including estimation of plant infestation rates from historical data, and find that inspections optimally target the largest lots with the highest plant infestation rates, leaving some lots unsampled. We also consider that USDA‐APHIS, which administers inspections, may want to continue inspecting all lots at a baseline level; we find that allocating any additional capacity, beyond a comprehensive baseline inspection, to the largest lots with the highest infestation rates allows inspectors to meet the dual goals of minimizing the costs of slippage and maintaining baseline sampling without substantial compromise.