Establishing safety stocks for master production schedules

The basic master production scheduling problem assumes that periodic demands are known with certainty. Uncertainty in the forecasts arc typically accommodated afterwards by adding safety stocks to a schedule. Two popular methods for establishing safety stocks are: (1) the constant cycle service level method; and (2) the constant safety stock method. This paper outlines these methods and then develops a third method which results in optimal safety stocks. The paper includes an experimental investigation aimed at comparing performances of the three safety stock methods. The constant safety stock method is shown to perform within one or two per cent of optimal, while the constant cycle service level method performs worse under most conditions. Shorter lead times, variable order interval lengths, and time-dependent forecast errors all adversely affect the performances of the non-optimal methods. An operations manager could use these results to evaluate the appropriateness of the methods for his master production scheduling environment.     

Evaluation of safety stock methods in multilevel material requirements planning (MRP) systems

This paper evaluates alternative methods of establishing the safety stock level taking into consideration of historical measures of forecasting accuracy and the needs for master production scheduling and material requirement planning under a rolling time horizon. A computer model is used to simulate the forecasting, master production scheduling and material planning activities in a company that produces to stock and the production activities are managed by multilevel MRP systems. The simulation output is analysed to evaluate the impact of safety stock methods on MRP system performance. The result of the study shows that using safety stock can help to reduce total cost, schedule instability and improve service level in the MRP systems. Guidelines are developed to help managers select methods to determine safety stock in MRP system operations.     

基于通货膨胀和风险偏好视角的资产配置研究

不确定条件下的资产配置问题无论对于学术研究还是投资行为都具有重大的理论和实际意义。本文选取广义范围上的现金、股票、债券作为投资者进行资产配置的产品,在CRRA(Constant Relative Risk Aversion)和HARA(Hyperbolic Absolute Risk Aversion)两种偏好假设下,分别求出了投资者效用最大化时的最优财富以及最优资产组合中各资产的权重,并比较分析了两种偏好假设下通货膨胀、风险偏好、投资期限三种因素对资产配置的影响。研究结论表明:通货膨胀会影响股票和债券的风险溢价,进而影响最优资产组合中各资产的权重;股票的权重不会受投资期限的影响,在通货膨胀率和风险偏好不变时,其值始终为一常数,但债券和现金的权重则由投资期限、通货膨胀和风险偏好共同决定;此外,在CRRA和HARA偏好假设下,以上三种因素对资产配置的影响存在较大差异,特别是在HARA框架下存在买空行为。     

Safety Stock,Excess Capacity or Diversification: Trade‐Offs under Supply and Demand Uncertainty

Firms mitigate uncertainty in demand and supply by carrying safety stock, planning for excess capacity and diversifying supply sources. In this study, we provide a framework to jointly optimize these three levers in a periodic review infinite horizon setting, and in particular we examine how one can reduce inventory and capacity investments through proper diversification strategies. Observing that a modified base‐stock inventory policy is optimal, we find that the capacity‐diversification problem is well behaved and characterize the optimal mix of safety stock, excess capacity and extra number of supply sources. We find that higher supply uncertainty results in higher safety stock, more excess capacity, and higher diversification. But safety stock and diversification are non‐monotonic in demand uncertainty. Our results can be extended to situations in which suppliers are heterogeneous, and can be used to develop effective heuristics.     

THE EFFECTIVENESS OF EXTENDING THE HORIZON IN ROLLING PRODUCTION SCHEDULING

In recent work, Baker [1] has investigated the use of rolling schedules for multiperiod production scheduling problems. One of his results is that the longest possible forecast horizon is not necessarily the best. He also found that the rolling schedules' effectiveness fluctuates widely depending upon the length of the forecast horizon. To smooth these fluctuations we have investigated use of forecasting to extend the problem horizon. Some of our results confirm the previous conclusions, but other results support the position that “the more information the better.”     

A Model for Master Production Scheduling in Uncertain Environments

In uncertain environments, the master production schedule (MPS) is usually developed using a rolling schedule. When utilizing a rolling schedule, the MPS is replanned periodically and a portion of the MPS is frozen in each planning cycle. The cost performance of a rolling schedule depends on three decisions: the choice of the replanning interval (R), which determines how often the MPS should be replanned; the choice of the frozen interval (F), which determines how many periods the MPS should be frozen in each planning cycle; and the choice of the forecast window (T), which is the time interval over which the MPS is determined using newly updated forecast data. This paper uses an analytical approach to study the master production scheduling process in uncertain environments without capacity constraints, where the MPS is developed using a rolling schedule. It focuses on the choices of F, R, and T for the MPS. A conceptual framework that includes all important MPS time intervals is described. The effects of F, R, and T on system costs, which include the forecast error, MPS change, setup, and inventory holding costs, are also explored. Finally, a mathematical model for the MPS is presented. This model approximates the average system cost as a function of F, R, T, and several environmental factors. It can be used to estimate the associated system costs for any combination of F, R, and T.     

Interfacing aggregate plans and master production schedules via a rolling horizon feedback procedure

Aggregate planning and master scheduling are two important levels of a hierarchical production planning process. They serve as the front end of production and operations planning and control systems. It is imperative to have the front end well planned and coordinated. In this study, we demonstrate that a rolling horizon feedback procedure can be an effective coordination mechanism for interfacing aggregate planning and master scheduling. Each time the schedule is rolled ahead, the feedback of performance results from master scheduling provides the aggregate planning subsystem useful information for improving its planning activities. Our experiments show that there are at least three factors that make a rolling horizon procedure attractive: (i) the use of a horizon with a fractional portion of a seasonal cycle, (ii) high smoothing costs, and (iii) high setup costs. Using rolling horizons reduces the total aggregate costs in these situations relative to not using rolling horizons. The potential impacts of the rolling-horizon strategy are greater under some circumstances than others.     

On‐Call Overtime for Service Workforce Scheduling when Demand Is Uncertain

This article builds on prior research to develop shift scheduling models that include on‐call overtime for service environments where demand is uncertain. The research is motivated by recent developments in nurse scheduling, such as laws prohibiting mandatory overtime and the popularity of self‐scheduling systems. For single‐period scenarios, models are developed, solution methods are described, and results are explored for a variety of environments. Results show that the use of on‐call overtime can reduce costs slightly, with the amount of savings dependent on characteristics of the scheduling environment. The factor that most significantly affects cost savings is the cost of outside agency workers relative to overtime workers. In addition to lowering costs, on‐call overtime greatly reduces reliance on outside agency workers, which can have important practical implications in terms of quality of service and workforce morale. Results based on single‐period models motivate multiperiod formulations for single‐ and multidepartment scenarios, and solution methods are outlined for those cases. The possibility of using multiperiod models within a rolling horizon framework with forecast updating is discussed. This goes along with an extension of the traditional workforce management hierarchy that separates overtime and regular‐time scheduling, as seen in practice with self‐scheduling and shift‐bidding systems.     

A LOWER BOUND FOR THE SINGLE-LEVEL DYNAMIC HORIZON LOT-SIZING PROBLEM

Conventional production planning methods assume the existence of a medium- or longrange demand horizon. However, demand usually is known over a much shorter range; scheduling decisions must be made within this “decision window,” which rolls forward in time. This paper presents a new lower bound for lot-sizing heuristics in a rolling-horizon framework and compares it to the well-known Wagner-Whitin bound. The new bound indicates heuristic schedules that have costs close to the optimum. Rolling-horizon schedule costs are compared to corresponding static-horizon schedule costs (assuming the whole horizon is known in advance), using the ratio of decision-window size to the natural order cycle as a parameter. For values below unity, the rolling-horizon policy is significantly more costly. For values above one, the two policies have similar costs and actually converge as the parameter value increases.     

Optimal market timing strategies under transaction costs

In this paper, we consider optimal market timing strategies under transaction costs. We assume that the asset's return follows an auto-regressive model and use long-term investment growth as the objective of a market timing strategy which entails the shifting of funds between a risky asset and a riskless asset. We give the optimal trading strategy for a finite investment horizon, and analyze its limiting behavior. For a finite horizon, the optimal decision in each step depends on two threshold values. If the return today is between the two values, nothing needs to be done, otherwise funds will be shifted from one asset to another, depending on which threshold value is being exceeded. When investment horizon tends to infinity, the optimal strategy converges to a stationary policy, which is shown to be closely related to a well-known technical trading rule, called Momentum Index trading rule. An integral equation of the two threshold values is given. Numerical results for the limiting stationary strategy are presented. The results confirm the obvious guess that the no-transaction region increases as the transaction cost increase. Finally, the limiting stationary strategy is applied to data in the Hang Seng Index Futures market in Hong Kong. The out-of-sample performance of the limiting stationary strategy is found to be better than the simple strategy used in literature, which is based on an 1-step ahead forecast of return.     

EXISTENCE AND DERIVATION OF FORECAST HORIZONS IN A DYNAMIC LOT SIZE MODEL WITH NONDECREASING HOLDING COSTS

We are concerned with a discrete-time undiscounted dynamic lot size model in which demand and the production setup cost are constant for an initial few periods and the holding cost of inventory is an arbitrary nondecreasing function assumed to be stationary (i.e., explicitly independent of time) in the same initial few periods. We show that there exists a finite forecast horizon in our model and obtain an explicit formula for it. In addition, we obtain fairly general conditions under which the existence of a solution horizon in the model implies the existence of a forecast horizon. We also derive an explicit formula for the minimal solution horizon. These results extend the earlier ones obtained for the dynamic lot size model with linearly increasing holding costs.     

A COMPARISON OF PRODUCTION SCHEDULING POLICIES ON COSTS,SERVICE LEVEL,AND SCHEDULE CHANGES

We consider a single product, single level, stochastic master production scheduling (Mps ) model where decisions are made under rolling planning horizons. Outcomes of interest are cost, service level, and schedule stability. The subject of this research is the Mps control system: the method used in determining the amount of stock planned for production in each time period. Typically, Mps control systems utilize a single buffer stock. Here, two Mps dual-buffer stock systems are developed and tested by simulation. We extend the data envelopment analysis (dea ) methodology to aid in the evaluation of the simulation results, where Dea serves to increase the scope of the experimental design. Results indicate that the dual-buffer control systems outperform existing policies.     

COST INCREASES DUE TO DEMAND UNCERTAINTY IN MRP LOT SIZING

This paper analyzes the cost increases due to demand uncertainty in single-level MRP lot sizing on a rolling horizon. It is shown that forecast errors have a tremendous effect on the cost effectiveness of lot-sizing techniques even when these forecast errors are small. Moreover, the cost differences between different techniques become rather insignificant in the presence of forecast errors. Since most industrial firms face demand uncertainty to some extent, our findings may have important managerial implications. Various simulation experiments give insight into both the nature and the magnitude of the cost increases for different heuristics. Analytical results are developed for the constant-demand case with random noise and forecasting by exponential smoothing. It is also shown how optimal buffers can be obtained by use of a simple model. Although the analysis in this paper is restricted to simplified cases, the results merit further consideration and study. This paper is one of the first to inject forecast errors into MRP lot-sizing research. As such it attempts to deal with one of the major objections against the practical relevance of previous research in this area.     

Freezing the Master Production Schedule Under Demand Uncertainty

Managing the trade-off between achieving a stable master production schedule (MPS) and being responsive to changes in customer requirements is a difficult problem in many firms where providing a high level of customer service is viewed as an important competitive factor. One alternative for managing this trade-off is to freeze an agreed portion of the MPS. This paper investigates the impact of adjustments in the design parameters of MPS freezing methods on two performance measures (MPS lot-sizing cost and stability) under stochastic demand conditions in a rolling planning horizon environment given a service level target. Simulation experiments are reported which indicate that many of the conclusions regarding the design of MPS freezing methods obtained under deterministic demand conditions hold under stochastic demand.     

Designing Distribution Systems to Support Vendor Strategies in Supply Chain Management*

The interactions among a firm's distribution strategy, market share, and distribution costs are an important consideration in the design of supply chain networks. However, these interactions are largely ignored by existing distribution system design methodologies, which assume demand is constant regardless of the firm's distribution strategy. This paper describes a multidisciplinary framework that considers these interactions in the design of “profit maximizing” distribution networks. The framework employs two major decision support methodologies: (1) binary logit models for estimating market share considering various demand-influencing parameters such as product price and distribution service, and (2) a mixed-integer programming (MIP) model for finding optimal distribution network designs. We applied the framework to an actual design problem facing a national distributor of industrial chemical products. The test results verify the framework's large-scale capability and the potential benefit of the integrated solution methodology.     

INVESTMENT IN SETUP COST,LEAD TIME,AND DEMAND PREDICTABILITY IMPROVEMENT IN THE EOQ MODEL

We study an economic order quantity/reorder point (EOQ/ROP) model with stochastic demand and backorders where options of investing in reducing setup cost, lead time, and variance of demand forecast errors are available. The model is quite comprehensive relative to previous models since it simultaneously addresses the strategic decisions associated with these three investment opportunities as well as the tactical decisions of determining both the lot size and the safety stock. We develop a simple search procedure to obtain the optimal values of setup cost, lead time, variance of demand forecast errors, order quantity, and safety stock multiplier. Computational studies are performed to determine the sensitivity of the optimal solution of the model to changes in the model's parameters.     

The Value of Production Schedule Integration in Supply Chains

This study explores the value of integrated production schedules for reducing the negative effects of schedule revisions in supply chains involving buyer and supplier firms. A stochastic cost model is developed to evaluate the total supply chain cost with integrated purchasing and scheduling policies. The model minimizes the costs associated with assembly rate adjustment, safety stock, and schedule changes for all supply chain members. Through experimentation, the paper examines the impact of several environmental factors on the value of schedule integration. This study finds that schedule integration can lead to overall cost savings in a supply chain, but some firms may have to absorb costs in excess of those they would incur with independent scheduling. Environments with high inventory holding costs and long supplier lead times may not find it beneficial to adopt an integrated schedule. Forecast effectiveness plays a critical role in realizing the benefits of schedule integration. The paper concludes with suggestions for future research.     

中国股市泡沫破裂临界时点动态置信区间研究

本文在对数周期幂率(LPPL)模型基础上,分别构建了“滚动窗口”以及“固定起点并移动终点”两种泡沫临界点动态置信区间构建方法,并以中国股市沪深300指数在2007年和2015年发生的两次大牛市股市崩盘为研究对象,采用两种新的方法进行样本外预测,计算出泡沫破裂的临界时点以及动态置信区间。研究结果表明,随着时间的不断推移,泡沫破裂临界时点的置信区间基本上能稳定覆盖实际发生泡沫破裂的时点。相比单纯利用LPPL模型预测临界时点方法,置信区间法能更好地克服预测临界时点随机性的情况,并能很好显示股市泡沫临界区间的变化轨迹,为投资者风险管理提供参考。     

基于前景理论的跨市场状态转移多阶段资产配置研究

在行为金融前景理论框架下研究跨市场间的状态转移资产配置问题,构建隐Markov——混合正态分布模型描述股票、债券和商品混合市场间的状态特征,用Baum-Welch算法估计模型参数,并利用状态转移思想进行情景生成建立多阶段随机优化模型。进一步,以我国股票、债券和商品混合市场的实际数据为背景,利用滚动窗口方法实证分析基于状态转移的多阶段随机模型的表现,并与忽略状态转移特征的基准模型、等权重组合、沪深300指数的结果进行对比。结果表明,与其他组合相比,基于状态转移的投资组合有助于规避风险,且混合市场间的状态转移信息能够对前景理论投资者的最优投资决策产生影响。     

Integrated project operations and personnel scheduling with multiple labour classes

The main theme of this paper is improving project schedules by integrating the scheduling of project jobs and labour resources. An ILP model is presented of the integrated project operations and personnel scheduling problem with multiple labour categories. Traditionally, this problem is solved in two steps: first, operations are scheduled by solving the resource-constrained project scheduling problem; then, labour categories are scheduled by solving the personnel days-off scheduling problem. The proposed model combines the two stages into an integrated problem, which is solved in one step. Using 48 test problems, the two methods were compared in terms of total cost, labour cost and scheduling efficiency. The results clearly indicate that the integrated model outperforms the traditional two-step method.