Production lot sizing for deterministic rolling schedules

In this article, we study production planning for a rolling horizon in which demands are known with certainty for a given number of periods in the future (the forecast window M). The rolling horizon approach implements only the earliest production decision before the model is rerun. The next production plan will again be based on M periods of future demand information, and its first lot-sizing decision will be implemented.Six separate lot-sizing methods were evaluated for use in a rolling schedule. These include the Wagner-Whitin algorithm, the Silver-Meal heuristic, Maximum Part-Period Gain of Karni, Heuristics 1 and 2 of Bookbinder and Tan, and Modification 1 to the Silver-Meal heuristic by Silver and Miltenburg.The performance of each lot-sizing rule was studied for demands simulated from the following distributions: normal, uniform (each with four different standard deviations); bimodal uniform (two types); and trend seasonal (both increasing and decreasing trends). We considered four values of the setup cost (leading to natural ordering cycles in an EOQ model of three, four, five, and six periods) and forecast windows in the range 2 M 20.Eight 300-period replications were performed for each combination of demand pattern, setup cost, and lot-sizing method. The analysis thus required consideration of 2304 300-period replications (6 lot-sizing methods × 12 demand patterns × 4 values of setup cost × 8 realizations), each of which was solved for nineteen different values of the forecast window M. The performance of the lot-sizing methods was evaluated on the basis of their average cost increase over the optimal solution to each 300-period problem, as though all these demands were known initially.For smaller forecast windows, say 4 M 8, the most effective lot-sizing rules were Heuristic 2 of Bookbinder and Tan and the modified Silver-Meal heuristic. Rolling schedules from each were generally 1% to 5% in total cost above that of the optimal 300-period solution. For larger forecast windows, M 10 or so, the most effective lot-sizing method was the Wagner-Whitin algorithm. In agreement with other research on this problem, we found that the value of M at which the Wagner-Whitin algorithm first becomes the most effective lot-sizing rule is a decreasing function of the standard deviation of the demand distribution.     

Dynamic lot sizing techniques: Survey and comparison

Numerous heuristics have been proposed in the past two decades for the dynamic lot sizing problem, many of them in APICS journals. Their relative performance is explored in extensive numerical tests measuring expected costs, risks of higher than expected costs and computer time consumed. The results indicate that users of pertinent standard software systems could benefit substantially from an incorporation of more recently proposed methods, specifically Groff's (1979) stop rule and a fathoming algorithm expanding it to a look-ahead heuristic.     

Research issues for multi-level lot sizing in MRP systems

What lot size model(s) to use in a Material Requirements Planning (MRP) system is an unresolved and often debated issue. The concept of dependent demand, the complex network defined by the product structure, the dynamics of an operating MRP-based system, and the subsequent use of the planned order release schedule by other company subsystems represent a totally new environment for making and managing lot size decisions.The purpose of this paper is to identify and briefly examine ten research issues related to lot sizing in a dependent demand product structure. These ten issues expand the solution space for lot sizing in an MRP-based system compared to a reorder point based system. Areas for further research are suggested.     

A generalized lot sizing model for the process cycling problem

Most scheduling/lot sizing models for the single-machine problem assume that aggregate demand equals aggregate production; and that backorders are to be avoided. Where working inventories are low, the scheduler may wish to avoid short production runs and willingly incur some backorder penalties so as to increase the length of production runs and reduce setup costs per unit of time. The model proposed here identifies optimal lot sizes with respect to the backorder/setup cost relationships. Use of the model will result in an optimally balanced inventory even when aggregate inventory levels are changing.     

Learning curves and lot sizing for independent and dependent demand

This paper explores the effect of learning curve cost behavior, as opposed to linear, on lot sizing. The first portion of the paper develops optimizing models for the independent demand situation. The second portion examines lot sizing for dependent demand, developing a lot sizing rule similar to Part Period Balancing.After examining the shortcomings of previous attempts at the independent demand lot sizing problem, two models are derived. Excluding material costs (for an assembly operation, the cost of all components), the optimal lot size is seen to vary linearly with demand and inversely with the carrying cost rate.When material costs are included a smaller optimal lot size is derived. The difference between the two, expressed as a fraction of the smaller lot size, equals the material/labor ratio of the last unit produced in the smaller lot size. For dependent demand, the incremental model developed by Freeland and Colley as an improvement on Part Period Balancing is used as a beginning concept. An analogous model, called Assembly Period Balancing, is developed for learning curve cost behavior. The decision rule for combining lots is expressed as a comparison of the material/labor ratio of the lot considered for combining with another expression involving the carrying cost rate, relative lot size and the learning curve exponent.Finally, cost data from an electronics manufacturer are used to examine the cost penalties of failing to recognize learning curve cost behavior. It is shown that optimal lot sizes for learning curve costs can be much larger than those obtained assuming linear costs. It is also shown that much larger lots can be economically combined in the dependent demand case when costs follow a learning curve.     

A comparison of MRP lot sizing methods considering capacity change costs

Capacity management is the planning and leveling of resources required (load) against the resources available (capacity). In this study, the lot size models used by Material Requirements Planning (MRP) had a major effect on the work center load profiles generated by Capacity Requirements Planning (CRP). Therefore, the selection of lot size models for MRP systems is an important decision for capacity management as well as materials management.The results of this study highlight the operating characteristics of specific lot size models considering setup, inventory carrying, and capacity associated costs. For example, the Economic Order Quantity model and the Lot-For-Lot model in certain situations can help level load. The Periodic Order Quantity and Least Total Cost models especially for high cost structure ratios tend to result in erratic and lumpy work center load profiles. The reasons for such operating behavior are examined. Other concepts and relationships important to capacity management are discussed.     

Integer goal programming for multistage lot sizing: Experimentation and implementation

This article considers the issues involved in implementing a large-scale multistage lot sizing model in a pharmaceutical manufacturing environment, and reports on a series of sensitivity experiments that subsequently examined the critical impacts of system capacity and inventory policy on the specification of a multistage schedule. The model was initially developed as an aggregate scheduling aid for a class of tablet pharmaceuticals. The manufacture of tablet products is a serial-type process characterized by batch flow. The model placed multiple resource capacity restrictions on various stages of the multistage system to ensure the feasibility of the resultant schedules. Difficulties in estimating penalty costs for shortages were circumvented by employing a multi-objective formulation of the lot-sizing problem.Various obstacles encountered during the implementation process are discussed. Model implementation encompassed the development of an approximation algorithm for efficiently solving the large-scale problem. The performance of the algorithm was evaluated by examining the closeness to optimality of the solutions obtained using the procedure. Performance statistics are presented for the sensitivity experiments discussed herein. Another essential aspect of implementation involved the timely revision of model input parameters. This facet of implementation proved to be at least as important to management as the efficient provision of a “good” solution.Model experimentation centered on variations in the capacities of bottleneck resources and changes in target inventory parameters whose values are predetermined by company policy. The first set of experiments was designed to demonstrate the importance of system capacity to the lot-sizing process and to illustrate that the location of a system bottleneck can vary over time as a function of both internal and external factors. The results indicated that lot-sizing procedures that fail to incorporate capacity information or that focus on a single bottleneck production stage in order to schedule production are severely limited with respect to practical and/or long-term applicability.The final set of inventory-related experiments indicated that the specification of target ending inventory levels was a crucial factor in the lot-sizing process. The determination of appropriate target levels must reflect the inherent trade-off between the objective of minimizing shortages and the desire to avoid excessive inventory accumulations. The generation of usable model information was found to be contingent upon the realistic definition of target level parameters.     

A lot sizing and sequencing algorithm for dynamic demands upon a single facility

A heuristic algorithm is developed and applied to determine lot sizes and production sequence on a single facility. The various product demands are treated as deterministic and time varying (dynamic) over a finite planning horizon, such as that generated from a material requirements planning (MRP) system.In contrast to other approaches available, the algorithm considers the sequencing decision in each period by realistically assuming inventory holding cost occurrence in the period of production, and in addition, it is capable of considering set-up times where such set-up times consume available productive capacity. The ability to handle numerous products, and the capability of being able to specify maintenance time and holidays is an integral aspect of the algorithm.The results of an application of the algorithm in a medium size bearing company have shown very significant reduction in the controllable inventory holding cost while eliminating late deliveries. In an effort to cope with potential realistic schedule alterations, different solutions were developed for managerial evaluation providing greater flexibility but at a higher cost.     

完全信息下供应链数量折扣设计

文章讨论了供应链数量折扣存在的可能性和必要性,并表明:供应链各方的独立决策不是最优决策,联合决策可以提高系统的利润、降低交易成本,数量折扣是能够实现联合决策的一种有效供应链契约。     

Estimating banking cost efficiency with the consideration of cost management

This study re-investigates the bank cost efficiency by a combination of two strands of literature. The first strand is related to bank cost efficiency; the other is related to earnings management. Employing the findings reported in bank earnings management literature, this study argues that bank observed total cost (“accounting cost”) may be the biased estimator of the true total cost. Using the biased total cost may thus yield incorrect inferences from estimating bank cost efficiency. We propose a method to modify accounting cost, which is referred to as “economic cost”, to be consistent with the economic theory; that is, one that is free of cost management. Both accounting and economic costs are then adopted to analyze the efficiency of 29 commercial banks in Taiwan banking industry. Our results show that estimated efficiency, with the application of economic cost, offers results that are more reasonable results than those of the accounting cost.     

Interval censored regression with fixed effects

This paper considers identification and estimation of a fixed-effects model with an interval-censored dependent variable. In each time period, the researcher observes the interval (with known endpoints) in which the dependent variable lies but not the value of the dependent variable itself. Two versions of the model are considered: a parametric model with logistic errors and a semiparametric model with errors having an unspecified distribution. In both cases, the error disturbances can be heteroskedastic over cross-sectional units as long as they are stationary within a cross-sectional unit; the semiparametric model also allows for serial correlation of the error disturbances. A conditional-logit-type composite likelihood estimator is proposed for the logistic fixed-effects model, and a composite maximum-score-type estimator is proposed for the semiparametric model. In general, the scale of the coefficient parameters is identified by these estimators, meaning that the causal effects of interest are estimated directly in cases where the latent dependent variable is of primary interest (e.g., pure data-coding situations). Monte Carlo simulations and an empirical application to birthweight outcomes illustrate the performance of the parametric estimator.     

A fixed point algorithm with economic applications

A new fixed point algorithm applicable to large scale economic problems is developed. Motivated by successive approximation the algorithm iterates on a convex combination of the traditional price to price map and the identity map. The actual combination used is determined from the convergence error of the previous iteration. The specified convex combination is guaranteed to be a contraction if the original map is Lipschitz continuous and antitonal. These sufficient conditions are shown to be weaker than the contraction requirement. A simple supply-demand example is presented to show the advantages of this algorithm over successive approximation.     

让学生的口袋盛满成长的快乐——石景山区教委搭"管理"台唱"创新"戏

教育是一门艺术,因为人是最神秘最复杂的生物。面对一群有思想有感情的学生,如何赢得他们的信任与尊重,如何对他们实施德育教育呢？石景山区教委主任王兰芳认为,教育理想的境界是每一所学校都能得到优质均衡发展,每一名学生都能实现全面健康发展。她说：“一枝独秀不是春,只有满园花开才是春。”教育公平与均衡的思想就蕴涵在这形象的语言中。[编者按]     

Less is sometimes more: The role of information quantity and specific assets in the propensity to engage in cost data exchange processes

The mutual disclosure of cost information among companies can lead to significant cost reductions. This experimental study examines how the quantity of cost information disclosed (high vs. low) and the offering of a joint specific investment (yes vs. no) influence the willingness of a buyer and supplier to engage in open book cost data exchange. The results show that when a large quantity of cost information is offered initially, participants reciprocate and reveal more cost information themselves, consistent with a tit-for-tat strategy. We also show that information quantity and the offering of a joint specific investment exhibit substitutive effects rather than additive effects on the willingness to engage in open book cost data exchange. For example, when a small amount of cost information is disclosed, the offering of a joint specific investment increases the willingness of the partner to engage in cost data exchange. However, consistent with the theory of reactance, a large quantity of cost information coupled with the offer of a joint specific investment does not result in a greater willingness than when a large quantity of information is offered alone.     

如何进行项目成本管理

究竟如何进行项目成本管理呢?简单地说,就是通过开源和节流并举来实现。     

Weighted rank statistics in factorial designs with fixed effects

Nonparametric methods for the analysis of factorial designs with two fixed factors are considered. The sample sizes may be unequal and the distribution functions are not assumed to be continuous. Nonparametric hypotheses for the main effects and for the interaction are tested by ranking procedures where the statistics are weighted according to the different sample sizes within the levels of one factor. Simulations show that the approximations by the limiting normal distribution and by the t - and F -distributions are quite accurate if the samples sizes within the cells are at least 7 for all treatment combinations. Moreover, it turns out that the power for the weighted statistics is much higher than for the unweighted statistics. The application of the suggested procedures is demonstrated by the analysis of a data set from a clinical trial with ordered categorical data.     

Quantile regression for dynamic panel data with fixed effects

This paper studies a quantile regression dynamic panel model with fixed effects. Panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors. To reduce the dynamic bias, we suggest the use of the instrumental variables quantile regression method of Chernozhukov and Hansen (2006) along with lagged regressors as instruments. In addition, we describe how to employ the estimated models for prediction. Monte Carlo simulations show evidence that the instrumental variables approach sharply reduces the dynamic bias, and the empirical levels for prediction intervals are very close to nominal levels. Finally, we illustrate the procedures with an application to forecasting output growth rates for 18 OECD countries.     

Transportation cost changes with statewide school district consolidation

This article studies the relationship between school district size and bus transportation costs, and estimates the change in such costs when a statewide policy of consolidation is pursued. To explore this relationship, we develop a multiple-objective model and solution procedure that combines a geographic aggregation and bus routing heuristic to generate consolidation scenarios. The heuristic was developed to explicitly consider efficiency, effectiveness, and equity objectives, and can be applied in both urban and rural states. The scenarios will generate average statewide bus transportation costs. As applied to the State of Iowa, within the legislature's proposed range of consolidation of 500-1000 students, it was found that transportation operational and capital cost increases range from 0.6 to 10.6 percent and 0.7 to 7.7 percent, respectively.     

A note on output hedging with cost uncertainty

Using a general framework and a multiple‐input technology, we thoroughly investigate the hedging and production decisions under cost uncertainty. In doing so, we show the impact of the cost risk on the optimal output, hedge and hedge ratio. Copyright © 2006 John Wiley & Sons, Ltd.