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.     

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.     

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.     

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.     

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.     

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.     

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.     

Sequential facility location with distance dependent demand

Systems providing identical service to many population centers frequently face the issue of where to locate the next retail outlet, branch, store, etc. In such systems the demand for the facilities' service depends mainly on the distance between facilities and customers. It is assumed that there are already m facilities located on a network to respond to the demand at the nodes. The paper addresses the problems of finding a location on the network for the (m +1 )st facility corresponding to a given total expected demand and of determining which demand points will be served by which facility. Also the range of the total expected demand values that can be realized along each link in the m +1 facility system is determined. Examples and a discussion of the results are provided.     

A unified approach to nonparametric trend tests for dependent and independent samples

We consider testing nonparametric hypotheses against ordered alternatives and propose a new unified approach for dependent and independent samples and factorial designs. The new approach allows for arbitrary underlying distributions, including quantitative and discrete ordinal (ordered categorical), or even binary data. It is compared to procedures available in the literature and applied to different data examples. The new method is not only invariant under monotone transformations of the response, but also under monotone transformations of the weights describing the alternative pattern.     

The effect of lead-time variability: The case of independent demand

We show in this study, through analysis and examples, the impact on stockouts and stockout risk if the variability of lead time in independent demand systems is ignored. In calculating safety stocks, we recommend that the compound distribution of demand during lead time, or a good approximation to it, be used. We motivate the article by a case study on lead-time variability at the U.S. Air Force and show the impact of lead-time variability by means of numerical examples and by marginal analysis. Having established that it is essential to consider lead-time variability, we take advantage of theoretical developments and show how to calculate reorder points and safety stocks in some common situations.It is important to use the proper form for the compound distribution of demand during lead time. A normal approximation to it will often yield significant errors. This is because the true distribution is usually very much skewed to the right.     

Estimation of some limited dependent variable models with application to housing demand

A model which extends the switching regression models and combines several different limited dependent variable models into a general framework is introduced. Methods to get consistent estimates and asymptotic efficient estimates are derived. Our estimation procedures are then used to study a housing expenditure model which takes into account the simultaneous determination of whether or not to own, and how much to spend.     

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.     

Demography and the demand for housing A reinterpretation of the Mankiw-Weil demand variable

This paper argues that the Mankiw-Weil forecast of a 47% decline in house prices over the period to 2007 is based on a serious misinterpretation of their demand variable. In a time-series context this variable, which comes from a cross-section regression of house values against the age of occupants, is a measure of the adult population, not the demand for housing services or the stock of houses. Econometric work suggests that in addition to adult population, real income, relative prices and real interest rates are important factors determining the aggregate demand for housing. To be credible, forecasts of house prices need to integrate information on demand with information on cost factors and the supply of new houses.     

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 $\frac{1}{N}\sum\limits_{i = 1}^N {\xi _i } = z$ .     

The demand for and supply of assurance

Consumers want products and services that are safe and of good quality. Corresponding to such demand is the demand for assurance , before the fact, that the quality and safety will be as promised. his demand for assurance creates opportunities for entrepreneurs to profit by providing assurance - and they do so in a wide and largely unappreciated variety of ways. The essential dialectic of the free enterprise system does apply to assurance. Governments'quality and safety restrictions on the freedom of contract, known to be so costly, are, therefore, unredeemed and should be repealed.     

Consumers' surplus and the demand for cigarettes

This paper examines the demand for cigarettes in South Africa over a 20-year period from 1970 to 1989. Consumption per capita was found to be significantly determined by price and disposable income per capita; but not by advertising. Price and income elasticities and consumers' surplus were computed from the demand model. The question was raised as to whether or not consumers' surplus should be regarded as having been inferred from a health-hazard-discounted demand schedule. The answer depends on the degree to which smoking decisions are taken with full information or, conversely, are influenced by habit. Given the latter assumption, the consumers' surplus measured for cigarette consumption is nevertheless substantially higher than the estimated health costs of smoking as computed by the Medical Research Council.     

Long‐run neutrality of demand shocks: Revisiting Blanchard and Quah (1989) with independent structural shocks

With reference to a stylized theoretical macromodel, Blanchard and Quah (American Economic Review, 1989, 79, 655–673) identify empirical aggregate supply (e.g., productivity) and demand shocks by assuming that the latter are neutral for economic activity in the long run. Taking advantage of recent contributions to the structural VAR literature and data‐based identification, we find that effects of unique independent non‐Gaussian structural shocks support this assumption. Moreover, unlike the results in Blanchard and Quah, statistically identified supply shocks exhibit (insignificantly) opposite impacts on gross domestic product and unemployment in the short run. In comparison with benchmark results obtained under assumed long‐run neutrality, statistical identification points to a stronger role of aggregate supply shocks for shaping temporary profiles of US unemployment during the recessionary period 1973:Q3–1975:Q1.     

The industrial demand for energy

This paper uses a constant elasticity of substitution production function to examine the extent of factor substitutability in the production of industrial goods. Subsequently, the degree of interfuel substitution is estimated and it is demonstrated that all energy sources are substitutable. Finally, the stability of the demand for various energy sources is empirically tested for and it is concluded that over the period of investigation the demand has in fact remained unaltered.