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.     

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.     

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.     

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.     

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.     

Full fixed cost recovery lot sizing with quantity discounts

Purchasers must often make lot sizing decisions when facing price schedules of price-quantity discounts. It is important to determine the supplier's pricing philosophy when establishing a solution procedure.One approach is to evaluate total costs at all of the appropriate break points. This offers limited information: a lot size and a set of total costs. This is especially true in the case of full fixed cost recovery pricing. In actual practice price schedules can be extremely lengthy: indeed, it may be in the supplier's best interests to offer comprehensive discount schedules. This situation complicates the purchaser's decision making process.An efficient alternative, which solves the price-quantity discount problem when the supplier insists on a full fixed cost recovery schedule, is presented. Computations are reduced to a few simple steps; the result is a least total cost lot size for a simple linear package price model given parameters obtained by an appropriate analysis of the supplier's price-quantity discount schedule. A starting point is determined and the choice of the lot size is made using a simple criterion. Rapid convergence is assured, given a reasonably well-behaved schedule.     

The impact of a rolling schedule in a multi-level MRP system

This paper presents a cost performance comparison of different lot-sizing algorithms under multi-level rolling schedule conditions. Most multi-level studies have focused on fixed horizon problems, omitting an important characteristic of an operating MRP system. The results indicate that, under certain conditions, the computationally simple Silver-Meal heuristic provides lower lot-sizing costs than the Wagner-Whitin algorithm. In addition, cost modifications are introduced which greatly enhance the multi-level performance of these single-level lot-sizing heuristics.     

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.     

Optimization for hierarchical multi-level planning systems using interaction prediction principle

This paper is concerned with the optimization of large-scale dynamic systems composed of interconnected subsystems. The decomposition and hierarchical multi-level approach with coordination is described for linear quadratic problem which has been available for socio-economic and production planning. In particular, we present a general solution algorithm for the two-level optimization using interaction prediction principle. A sample example for which the approach is applicable is illustrated.     

Analytic models of resource allocation in hierarchical multi-level systems

Most analytic models of resource allocation do not consider the structure of the organization as a factor in the decision process, i.e. they assume a monolithic decision making entity. This paper surveys in a critical fashion those economic and management science models that explicitly reflect organization structure in the model structure. The theoretical and practical advantages and limitations of each model type are indicated, and developmental trends are noted and related to research requirements in the area of resource allocation in hierarchical multi-level systems.     

Toward a better understanding of lead times in MRP systems

Lead times in MRP systems represent the planned amount of time allowed for orders to flow through the manufacturing system. Setting lead times is a major issue in the operation of MRP systems. There exists, however, very little documentation on just how lead times should be set.This study examines the effects lead times have on MRP-based manufacturing logistics systems. In particular, it examines the effects that lead times have on backlogs, order tardiness, and finished component inventories.A major finding is that changes to the level of planned lead times have both transient and steady state effects that may not necessarily operate in the same direction. A simple methodology is presented for setting the level of planned lead times when the criterion is finished component inventory.     

The cost of inflated planned lead times in MRP systems

Much of the current literature in the field of production and inventory control systems stresses the need to revise traditional forms of thinking regarding production processes, the role of inventories for work in process, and the need for reduced lead times or flow times. Group technology, manufacturing cells, and other means of incorporating repetitive manufacturing techniques into traditional job-shop settings constitute the leading edge in system development.Still, there is resistance to these dramatic changes, and traditional “business as usual” methods still predominate. This study attempts to illustrate graphically the cost justification associated with reduction in lead times which generally results from these new concepts. In most job shops today, lead times are much longer than they need to be due to inflation of lead time estimates. Actual lead times for the manufacture of fabricated and assembled products have been shown to be a direct consequence of the planning lead times used in the MRP planning process—a form of self-fulfilling prophesy.The research employs a simulation model of a factory using MRP as a planning tool in a multiproduct, multilevel production environment. Manufacturing costs constitute the dependent variable in the experiments, defined as the sum of material costs (including expedite premiums), direct labor costs (including overtime premiums), inventory carrying costs, and overhead costs. The independent variable being manipulated is the planned lead time offset used in the MRP planning process. Twenty values of planned lead time are evaluated ranging from a value that includes no slack time at all (pure assembly line) up to a value that allows 95% slack (queue) time which, unfortunately, is not uncommon in many job shops today. Stochastic variables in the model include customer demand and actual processing times—the sum of set-up and run times.The result of the study is a cost curve formed over the range of independent lead time variables that is constructed using nonlinear regression techniques. The conclusions from the resultant graph clearly indicate the cost consequences of long lead times, with exponential cost increases beyond the 80–90% queue time level. Total costs are 41% higher at the maximum lead time allowance compared to the minimum. Clearly, this study demonstrates the need for lead time reduction, either through downward adjustment of MRP planned lead times or by introducing new manufacturing concepts.     

Ethical issues in human resources systems

Currently, the topic of ethics is enjoying a surge in popularity among the media and corporate America. It is unclear if the reason for all the attention is “just for show” or if companies truly believe in the substantive benefits, which can be gained by facilitating an ethical context. However, by examining the negative consequences of unethical corporate cultures, as well as the benefits of ethical ones, we demonstrate that perhaps, in this case, the action is what is important, not the motivation. Human resource systems may be a means to promulgating an ethical culture in that ethics pervade selection and staffing, performance appraisal, compensation, and retention decisions. Thus, human resource systems and ethical corporate cultures should be considered partners in the process of creating competitive advantage for organizations.     

Irregular workloads with MRP systems: Some causes and consequences

Material Requirements Planning (MRP) systems have been widely applied in industry to better manage multiproduct, multistage production environments. Although many applications have been quite successful, much is still left to the planner's intuition as to how to assure that master schedules, component lot sizes, and priorities realistically conform to the capacity limits at individual work centers. Capacity issues may indeed be the soft spot in MRP logic.This paper explores some possible causes of irregular workload patterns when using an MRP system. Better insight on which factors cause temporary bottlenecks could help managers better assess the vulnerability of their plants to this problem. It might also suggest ways of dampening peaks and valleys. The problem setting is a multistage environment; several products are made from various subassemblies and parts. Each shop order is routed through one or more capacitated work centers. An order is delayed either by temporary capacity shortages or the unavailability of components. Of course, the second delay can be caused by capacity problems previously encountered by the shop orders of its components.Seven experimental factors are tested with a large-scale simulator, and five performance measures are analyzed. The factors are the number of levels in the bill of material, the average load on the shop, the average lot size, the choice of priority rule, demand variability, the use of a gateway department, and the degree of equipment specialization. We have one measure of customer service, two for inventory, and two for workload. The workload measures are unconventional, since our interest is when workload variability occurs and how it affects inventory and customer service.The simulator has been developed over the course of eight years, and since this study has been further enhanced to handle many more factors. The simulator was validated recently with real data at two manufacturing plants. It is quite general, in that the bills of material, shop configuration, routings, worker efficiencies, and operating rules can be changed as desired.An initial screening experiment was performed, whereupon the average load and priority rules were not statistically significant at even the .05 level. A full factorial analysis with two replications was then conducted on the five remaining factors. Multivariate analysis of variance (MANOVA) and analysis of variance (ANOVA) statistical tests have been performed.The results confirm that workload variability can have a detrimental impact on customer service and inventory. The following structural changes to the manufacturing system can be beneficial, but tend to be more difficult to achieve. More BOM levels improve customer service, but increase inventory and capacity bottlenecks. Resource flexibility is a powerful tool to reduce workload variability. Capacity slack averaging much over 10% is wasteful, having no benefits for inventory and customer service. In general, revising the routing patterns only, such as creating more dominant paths, will not give big payoffs. The following procedural changes are easier to implement. Master schedules which smooth aggregate resources are an excellent device to reduce workload variability. Even with a smooth MPS, debilitating workload variability can still occur due to the design of the BOM, lot size, and leadtime offset parameters. Selecting a priority rule does not seem to be of overriding importance compared to master scheduling and component lot sizing. These findings must be considered within the context of the range of plant environments encompassed by this study.     

MRP系统下的物流管理

研究了ＭＲＰ系统中常的流管理策略,长期前期的物料采购模型,主生产计划的稳定性,主动性库存控制策略问题。     

Typical lots for detached houses in residential blocks and lot shape analysis

The notion of shape distance between lots is the basis for further development of the economics of dealing with lot shapes in real estate. The distance between two lots is defined as the relative area of the set difference of two lots. Using this notion, a method for identifying typical lots in a residential block based on the shape distance matrix among all the lots in the block is proposed. The method is applied to 20 blocks in the Setagaya ward in Tokyo. Typical lots tend to be rectangular-type lots even in irregularly shaped blocks. This suggests that consumers prefer rectangular shapes when choosing residential lots. Moreover, rectangular blocks tend to contain typical rectangular lots that have a depth about half as long as the shorter edge of the block and two variations of width. This suggests that some lots were previously subdivided in half.     

基于MATLAB的物料需求计划优化模型研究

根据企业对物料的需求预测和企业自身的资源约束条件,基于某种目标建立物料需求计划的线性优化模型,利用MATLAB软件求得满足该目标的最优物料需求计划。结合某汽车配件产品的实例分析,获得物料需求计划的可行且最优的方案,避免了传统物料需求计划制定后再通过细能力计划检验物料需求计划是否可行的过程,提高了物料需求计划制定的效率。     

Tests of significance for the mean of a finite lot

Let ξ₁, ξ₂, ξ₃, ... be independent identically distributed random variables each with normal distribution with mean μ and variance σ². Tests for the process mean μ are well-known elements of statistical analysis: the Gauß test under known process variance σ², Student’st-test under unknown process variance σ². Let the process be partitioned in lots (ξ₁, ..., ξ _N ), (ξ _N+1, ..., ξ_2N ), ... of sizeN. Consider (ξ₁, ..., ξ _N ) as a stochastic representative of this lot sequence and let the lot be characterized by the lot mean $\frac{1}{N}\sum\limits_{i = 1}^N {\xi _i } $ . The lot mean can be considered as a parameter of the joint conditional distribution function of the lot variables under $\frac{1}{N}\sum\limits_{i = 1}^N {\xi _i } = z$ . The present paper investigates the analogies of the Gauß test and Student’st-test for the lot situation, i.e. tests of significance for the lot meanz under known and unknown process variance σ². This approach is of special interest for the statistical control of product quality in situations where the quality of a lot of items 1, 2, ...,N with quality characteristics ξ₁, ξ₂, ..., ξ _N is identified with the lot average $\frac{1}{N}\sum\limits_{i = 1}^N {\xi _i } = z$ .     

MRP库存管理在冷藏箱调运中的应用

文中对MRP(Material Resources Planning)的原理进行了说明,结合某班轮公司的实际冷藏箱设备调运的流程,阐述MRP在调运冷藏箱中的运用,尽可能的降低库存,提高冷藏箱设备的周转率。