COMMENTS ON “COST INCREASES DUE TO DEMAND UNCERTAINTY IN MRP LOT SIZING”: A VERIFICATION OF ORDERING PROBABILITIES

In a recent article in this journal, De Bodt and Van Wassenhove [1] presented analytic derivations related to lot-sizing behavior under uncertainty. Although their models appear to have been verified in the aggregate by simulation experiments, detailed justifications for several of the derivations are missing. The present paper looks at De Bodt and Van Wassenhove's analysis and provides verifications of (and corrections to) the ordering probabilities and order cycles used by the authors to estimate the cost effects of forecast errors in the particular operating environment studied. The probabilities simulated in this study also generate additional insight into the “system nervousness” caused by lot-sizing and forecast errors.     

A NOTE ON DYNAMIC LOT SIZING IN A ROLLING-HORIZON ENVIRONMENT

This paper presents a modification of the dynamic lot-size algorithm of Wagner and Whitin for rolling horizon environments. The computational results show that the modified algorithm gives better cost performance than the Wagner-Whitin algorithm and the Silver-Meal heuristic. The improvements over the Wagner-Whitin algorithm require very few additional computations.     

Location of Inventories in an MRP Environment

Previous research on MRP systems has rarely considered at what level in a modular sub-assembly product structure to hold inventories. Based on a simulation study of an MRP environment, we show that the correct decision concerning where to hold inventory depends on the variance in end-item demand, the amount of inventory investment, and concomitantly, the desired level of customer service. In particular, for small investment in inventories and moderate end-item demand variance, it is equally effective to hold inventories at the subassembly level or the end-item level. But when end-item demand variance is high, subassembly level inventories are better. As inventory investment grows, however, it is best to use a diversified approach of holding both subassembly and end-item inventories, irrespective of end-item demand variance. The robustness of these conclusions is validated by simulating a hypothetical firm that also uses safety time to hedge against uncertainties.     

The Performance of MRP Purchase Lot-Size Procedures Under Actual Multiple Purchase Discount Conditions

Several heuristic procedures for purchase lot sizing in material requirements planning (MRP) systems were tested with actual data from manufacturing companies. Information provided by the companies for each purchased item included the estimated requirements and costs, the price discount structure from the vendor, and the actual company ordering policy. Simulation tests for each purchased item involved comparisons of several purchase lot-size procedures from the research literature along with the actual procedure used by the company providing the data. Results indicate that one of the heuristic lot-size procedures from the literature consistently outperformed the company policies as well as all other models tested. Another noteworthy result is that, in some cases, the actual company order policy was more cost-effective than some of the models from the research literature.     

THE PERFORMANCE OF A SIMPLE INCREMENTAL LOT-SIZING RULE IN A MULTILEVEL INVENTORY ENVIRONMENT

A simple incremental cost approach to lot sizing was tested in a multilevel inventory environment. The incremental approach has not previously been tested in a large-scale study involving multiple product-structure levels. Using the Wagner-Whitin (WW) algorithm as a benchmark, the simple incremental rule (IPPA) was compared to three heuristic procedures (LFL, EOQ, and POQ) frequently used in material requirements planning (MRP) lot-sizing research. The incremental rule consistently generated lower total order/setup and carrying costs than the three heuristics across the 3,200 multilevel test situations examined. In many of the test situations, the incremental rule also outperformed the WW benchmark.     

Efficient Heuristics for MRP Lot Sizing with Variable Production/Purchasing Costs*

Two heuristics based on branch and bound (B&B) are developed to solve closed-loop material requirements planning (MRP) lot-sizing problems that have general product structures and variable costs. A “look ahead method'’(LAM) heuristic allows for variable production/purchasing costs and uses a single-level B&B procedure to rapidly improve lower bound values; thus, LAM efficiently uses computer-storage capacity and allows solution of larger problems. The “total average modification'’(TAM) heuristic uses B&B, applied level by level, and modified setup and carrying costs to solve the variable production/purchasing costs MRP lot-sizing problem. LAM and TAM are tested on problems and compared to heuristics in the literature. TAM may be used to solve large MRP lot-sizing problems encountered in practice.     

PRODUCT STRUCTURE COMPLEXITY AND MULTILEVEL LOT SIZING USING ALTERNATIVE COSTING POLICIES*

This research evaluates the effect of product structure complexity on the performance of several lot-sizing procedures in a multilevel manufacturing environment. The experiment compares two different costing policies, full value added (FVA) and marginal value added (MVA), for calculating inventory holding cost. The major finding of the research is that product structure complexity has very little effect on the performance of various lot-sizing procedures. A second finding is that when product structures with varying components per parent and stocking points for a particular end item are present, the MVA costing policy emerges as the policy of choice because it favors slightly the Silver-Meal (SM)/least-total-cost (LTC) procedures over the Wagner-Whitin (WW)/LTC procedures.     

HEURISTIC LOT-SIZING PERFORMANCE IN A ROLLING-SCHEDULE ENVIRONMENT*

This paper examines the impact of a rolling-schedule implementation on the performance of three of the better known lot-sizing methods for single-level assembly systems——Part-Period-Cost-Balancing, Silver-Meal, and Wagner-Whitin algorithms—and a modified version of the Silver-Meal procedure. The main finding is that under certain conditions the computationally simpler Silver-Meal heuristic can provide cost performance superior to that of the Wagner-Whitin algorithm.     

TOTAL SETUP LOT SIZING WITH QUANTITY DISCOUNTS*

Often, order quantity decisions are made by purchasers facing a price schedule of quantity discounts. Traditional solution procedures have consisted of the evaluation of total cost at numerous price-break points in search of the lowest total cost. This approach is tedious and not particularly informative, especially when one is faced with lengthy schedules. This paper presents a total setup lot-sizing model that reduces the computations required to find the least-total-cost quantity, given parameters from a supplier's price schedule. The parameters are first obtained by simple regression (graphical or computer) and in themselves can provide valuable insight for the purchaser's decision making. A total setup lot-sizing model is next developed to define a “critical interval” that contains the solution. The model and algorithm are tested under a variety of conditions. Their application offers the decision maker a convenient alternative to determine the best quantity to order from a tendered price schedule.     

An Integrative,Experiential Approach to Production Management Education

This paper addresses the important relationship between production and operations management (POM) and information technology. An approach to POM education is presented in which information technology is used to create an experiential learning environment that integrates the topics taught in POM courses. Results of an implementation of the proposed approach are presented and implications are discussed for POM education.     

A Comparative Analysis of Master Production Scheduling Techniques for Assemble-To-Order Products

This paper studies the master production scheduling (MPS) activity of manufacturing firms that produce assemble-to-order (ATO) products. It describes four techniques for master scheduling ATO products: end-product bills, modular bills, super bills, and percentage bills. These procedures are compared in terms of the percentage of customer orders delivered late, the mean tardiness of customer order deliveries, and the total cost of inventory using simulation analysis. The results indicate that the performance of an MPS technique is affected by the level of uncertainty of the end products' demands and the degree of component commonality in the product structure. In particular, modular bills produce the highest customer service level and super bills produce the lowest total inventory cost under most operating conditions. The conclusions also suggest that the choice of a particular MPS technique is often a compromise between the benefits of improved MPS performance and the costs of implementing and executing the MPS system.     

SOME COMMENTS ON “A SYSTEMS PERSPECTIVE ON MATERIALS REQUIREMENTS PLANNING”*

We believe there are some serious deficiencies in the Morecroft article on MRP problems which appeared in a recent issue of this journal. The article, at the most, shows that MRP, inappropriately imposed on an existing production system, can result in undesirable system performance. This does not represent a new or startling conclusion. Four problem areas in the article are discussed, and suggested alternative approaches are offered.     

UNCERTAINTY AND THE LOT-SIZE REORDER-POINT MODEL

Noori and Keller [1] recently proposed a lot-size reorder-point model in which the quantity received is a random variable. The authors failed, however, to explore the full implications of their initial definitions. This oversight leads to some misleading inferences that we try to correct in this note.     

DYNAMIC LOT SIZING FOR A SINGLE-FACILITY MULTIPRODUCT PROBLEM IN A ROLLING-HORIZON ENVIRONMENT

This paper considers a production planning model for a single-facility multiproduct problem where backlogging is not allowed. A planning-horizon theorem is derived. From that theorem, a forward algorithm for finding an optimal solution over a finite horizon and a procedure for selecting the first-period production in a rolling-horizon environment are developed. Computational results from a set of simulation experiments designed to investigate the cost effectiveness of the procedure demonstrate its effectiveness.     

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.     

Order Promising and the Master Production Schedule*

Previous research on material requirements planning (MRP) systems has rarely considered the impact of the master production scheduling method used to promise customer orders and to allocate production capacity. Based on a simulation study of an MRP environment, we show that the correct selection of a master production schedule (MPS) method depends on the variance of end-item demand. In addition, we find evidence that the effectiveness of a particular MPS method can be enhanced by holding buffer inventory at the same level in the product structure as in the MPS.     

A ONE-PERIOD STOCHASTIC INVENTORY PROBLEM WITH A LUMP-SUM PENALTY COST

This paper presents an inventory problem related to the one-period stochastic inventory (or “newsboy”) problem. In this problem, the firm has to decide how much product to order to meet a random one-period demand. The version of the problem presented is novel in two respects. First, demand is explicitly permitted to be negative, and second, the penalty (or shortage) cost is assumed to be independent of the magnitude of the shortage. This situation is shown to change the form of the cost function and to complicate the determination of optimal policies. The form of the optimal policy is developed, and two example problems are presented in some detail.