Effects of Product Structure Complexity on Multi-level Lot Sizing*

As an input to the materials requirement planning (MRP) process, the product structure interacts with the lot-sizing rules to affect inventories, materials flow, and production costs. Despite engineering constraints, considerable latitude is still available to construct alternate product structures for the same product. An important concern of MRP managers and designers is the impact of product structure complexity on the cost performance of the lot-sizing rules. To date, there exists no detailed research that provides managers with guidelines that relate the lot-sizing rules to individual product structure parameters. We report on an extensive experiment to test the effects of individual product structure parameters on the relative cost performance of 11 lot-sizing rules. Three parameters—the number of items, number of levels, and commonality index—are proposed to characterise product structure complexity and used as factors in an experiment involving a large variety of product structures. The results indicate that all three parameters affect the relative cost differences but not the ranking of the rules. The overall best lot-sizing rule is Bookbinder and Koch's [11] rule.     

An Experimental Analysis of Capacity-Sensitive Setup Parameters for MRP Lot Sizing

Most material requirements planning (MRP) systems apply standard costing (absorption costing) approaches to define setup costs that are used as fixed (time invariant) setup parameters in single-level lot-sizing methods. This paper presents a computationally simple approach for estimating more appropriate setup parameters based on estimates of work-center shadow prices. These setup parameters then are used in traditional single-level MRP lot-sizing procedures. The shadow price of capacity at each work center is calculated as the increase in the overall inventory carrying cost for each additional hour of capacity lost to setups. The opportunity cost of a setup for an order subsequently is determined based on the routing information for each order and is used by traditional MRP lot-sizing procedures to calculate lot sizes. A simulation experiment compares the performance period order quantity lot sizing with capacity-sensitive setup parameters with the fixed accounting-based setup parameters. The simulation replicates the planning and control functions of a typical MRP system. The results of the experiment show that capacity-sensitive setup parameters can make significant reductions in both carrying cost and lateness and can achieve many of the benefits of optimized production technology in the context of an MRP system.     

A Comparative Analysis of the Relative Effectiveness of Four Dynamic Lot-Sizing Techniques on Return on Investment

The relative performance of dynamic lot-sizing techniques has been of considerable interest to researchers in recent years. While research has addressed performance in terms of cost-effectiveness, researchers have not determined the impact of dynamic lot-sizing techniques on return on investment (ROI) as it applies to finished goods' schedules. The purpose of this research is to explore the relative performance of four dynamic lot-sizing techniques with regard to ROI, namely the Wagner-Whitin, Incremental Part Period, Silver-Meal, and Groff techniques. Computer graphics are employed to analyze the relative ROI effectiveness.     

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.     

Master Scheduling in Assemble-To-Order Environments: A Capacitated Multiobjective Lot-Sizing Model

Basic characteristics of an assemble-to-order environment make effective master scheduling extremely difficult. Limited resource capacities and dynamic customer end-item demand contribute to the complexity of the master production scheduling problem. To gain flexibility and responsiveness within this system, the master production schedule (MPS) focuses at the component level. This research proposes a master scheduling technique for manufactured components which combines a multiobjective capacitated multi-item/multi-stage lot-sizing model with an interactive multiple objective optimization solution procedure. To evaluate the model's performance as a realistic and practical master scheduling tool, this study focuses on the National Cash Register (NCR) electronics manufacturing facility in Columbia, South Carolina.     

Integrative Cycle Scheduling Approach for a Capacitated Flexible Assembly System*

This study revisits the traditional single stage, multi-item, capacitated lot-sizing problem (CLSP) with a new integrative focus on problem structuring. Unlike past research, we develop integrative cycle scheduling approaches which simultaneously address lot-sizing, capacity, and sequencing issues. Our purposes are to (1) explore the effect of sequencing on inventory levels, (2) examine the problem of infeasibility in the economic lot scheduling problem (ELSP), and (3) provide a simple methodology of generating low-cost cycle schedules in an environment with discrete shipping, dynamic demands, limited capacity, zero setup cost, and sequence-independent setup times. Our procedures are compared to benchmark cycle scheduling approaches in terms of both inventory cost and computation time under different demand scenarios, using the operating data from a flexible assembly system (FAS) at the Ford Motor Company's Sandusky, Ohio plant.     

REPETITIVE LOTS: FLOW-TIME REDUCTIONS THROUGH SEQUENCING AND DYNAMIC BATCH SIZING

This paper presents a new integrative concept for job sequencing, dispatching, and lot sizing. The interrelation between these procedures and their impact on flow-time performance is examined in a capacitated production environment. Generally, lot-sizing decisions are made without regard to shop conditions and do not consider their impact on job sequencing procedures. The repetitive lots (RL) concept (developed and tested in this paper) attempts to integrate these decision processes. RL uses a number of features which have not been considered jointly in either the lot-sizing or job-dispatching/sequencing literature. These include operation batch sizes which vary by operation, transfer of work within the shop in quantities less than operation batch size, and the use of overlapped operations. A simulation model is used to analyze flow-time characteristics in a hypothetical production system. Traditional measures of flow-time performance are compared to a set of nontraditional measures which capture the interaction between lot sizing and the sequencing procedure used.     

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.     

Combined demand and lead time uncertainty with back-ordering in a multi-level product structure environment

The performance of two lot-sizing algorithms incorporating back-orders is evaluated and compared with several traditional lot-sizing rules. This comparison is undertaken for a multi-level product structure environment operating under a rolling horizon in the presence of both demand and lead time uncertainties. By means of simulation and statistical analysis of the simulation output, the impact on system performance of a variety of demand and lead time scenarios, product structures, cost parameters and lot-sizing, is evaluated. The conclusions drawn emphasize important differences in the influence of the factors on system performance given the presence or absence of uncertainty.     

Access to Long‐Term Care: The True Cause of Hospital Congestion?

Much attention has been paid to lengthy wait times in emergency departments (EDs) and much research has sought to improve ED performance. However, ED congestion is often caused by the inability to move patients into the wards while the wards in turn are often congested primarily due to patients waiting for a bed in a long‐term care (LTC) facility. The scheduling of clients to LTC is a complex problem that is compounded by the variety of LTC beds (different facilities and room accommodations), the presence of client choice and the competing demands of the hospital and community populations. We present a Markov decision process (MDP) model that determines the required access in order for the census of patients waiting for LTC in the hospitals to remain below a given threshold. We further present a simulation model that incorporates both hospital and community demand for LTC in order to predict the impact of implementing the policy derived from the MDP on the community client wait times and to aid in capacity planning for the future. We test the MDP policy vs. current practice as well as against a number of other proposed policy changes.     

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.     

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.     

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.     

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.     

Freezing the master production schedule in multilevel material requirements planning systems under deterministic demand

This paper extends the studies by Sridharan, Berry, and Udayabhanu from single-level MPS systems to multilevel material requirements planning (MRP) systems, and examines the impact of product structure, lot-sizing rules and cost parameters upon the selection of MPS freezing parameters under deterministic demand. A model is built to simulate the master production scheduling and material requirements planning operations in a make-to-order environment. The results show that all the MPS freezing parameters studied have a significant impact upon total inventory costs and schedule instability in multilevel MRP systems. First, the order-based freezing method is preferable to the period-based method. Secondly, the study finds that increasing the freezing proportion reduces both total inventory costs and schedule instability. This finding contradicts the finding by Sridharan et al. in single-level systems. Thirdly, the study finds that a higher replanning periodicity results in both lower total inventory cost and lower schedule instability. The study also indicates that the product structure and lot-sizing rules do not significantly influence the selection of MPS freezing parameters in a practical sense under most situations. However, the cost parameter seems to significantly influence the selection of replanning periodicity.     

Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms

Due to their importance in industry and mathematical complexity, dynamic demand lot-sizing problems are frequently studied. In this article, we consider coordinated lot-size problems, their variants and exact and heuristic solutions approaches. The problem class provides a comprehensive approach for representing single and multiple items, coordinated and uncoordinated setup cost structures, and capacitated and uncapacitated problem characteristics. While efficient solution approaches have eluded researchers, recent advances in problem formulation and algorithms are enabling large-scale problems to be effectively solved. This paper updates a 1988 review of the coordinated lot-sizing problem and complements recent reviews on the single-item lot-sizing problem and the capacitated lot-sizing problem. It provides a state-of-the-art review of the research and future research projections. It is a starting point for anyone conducting research in the deterministic dynamic demand lot-sizing field.     

An Efficient Zero-One Formulation of the Multilevel Lot-Sizing Problem

This paper presents a zero-one linear formulation of the multilevel lot-sizing problem for materials requirement planning systems without capacity constraints. The model is an efficient statement of the problem and has a structure that is particularly convenient for research work. In addition, it is demonstrated that the relaxed linear programming solution to this formulation will always be integer. The results of a rather large computational history are reported along with a variable reduction methodology that allows for the solution of reasonably sized research problems.     

Longitudinal Analysis of Inhibitors of Manufacturer Delivery Performance

This article examines demand, manufacturing, and supply factors proposed to inhibit manufacturer delivery execution. Extant research proposes many factors expected to harm delivery performance. Prior cross‐sectional empirical research examines such factors at the plant level, generally finding factors arising from dynamic complexity to be significant, but factors arising from detail complexity to be insignificant. Little empirical research examines the factors using product‐level operating data, which arguably makes more sense for analyzing how supply chain complexity factors inhibit delivery. For purposes of research triangulation, we use longitudinal product‐level data from MRP systems to examine whether the factors inhibit internal manufacturing on time job rates and three customer‐oriented measures of delivery performance: product line item fill rates, average delivery lead times, and average tardiness. Our econometric models pool product line item data across division plants and within distinct product families, using a proprietary monthly dataset on over 100 product line items from the environmental controls manufacturing division of a Fortune 100 conglomerate. The data summarize customer ordering events of over 900 customers and supply chain activities of over 80 suppliers. The study contributes academically by finding significant detail complexity inhibitors of delivery that prior studies found insignificant. The findings demonstrate the need for empirical research using data disaggregated below the plant‐level unit of analysis, as they illustrate how some factors previously found insignificant indeed are significant when considered at the product‐level unit of analysis. Managers can use the findings to understand better which drivers and inhibitors of delivery performance are important.     

The moderating effect of product complexity on new product development and supply chain management integration

The purpose of this study is to investigate whether product complexity moderates the impact of integration programs in both new product development (NPD) and supply chain (SC) management on operational performance. Results are based on statistical analyses of data collected from an international sample of manufacturing firms through the fifth edition of the International Manufacturing Strategy Survey (IMSS 5). The main findings are that NPD and SC integration do have an impact on performance, while product complexity alone has not. When considering the moderating effect, complexity has no impact on NPD integration, while there is a negative moderating impact on SC integration. This study bridges together different streams of research, showing how both NPD and SC integration allow managing product complexity while improving performance.     

On the Joint Lot-Sizing Problem with Zero Setup Costs

In a recent paper, Pinto and Mabert [5] presented a lot-sizing rule and an improvement procedure for the joint lot-sizing problem with zero setup costs. We show that this procedure often yields infeasible schedules. We also present and discuss two interesting properties of the joint lot-sizing problem with zero setup costs. A numerical example to illustrate the second property is provided.